<?xml version="1.0"?>
<feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en">
	<id>http://osupdocs.forestry.oregonstate.edu/index.php?action=history&amp;feed=atom&amp;title=Adhesive_Friction_Law</id>
	<title>Adhesive Friction Law - Revision history</title>
	<link rel="self" type="application/atom+xml" href="http://osupdocs.forestry.oregonstate.edu/index.php?action=history&amp;feed=atom&amp;title=Adhesive_Friction_Law"/>
	<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;action=history"/>
	<updated>2026-05-29T19:13:52Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.36.2</generator>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=26070&amp;oldid=prev</id>
		<title>Nairnj: /* Properties */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=26070&amp;oldid=prev"/>
		<updated>2026-03-26T18:23:05Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Properties&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:23, 26 March 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l40&quot;&gt;Line 40:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 40:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| vhalf || Velocity where transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; is half done || [[ConsistentUnits Command#Legacy and Consistent Units|(velocity units)]] || 0&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| vhalf || Velocity where transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; is half done || [[ConsistentUnits Command#Legacy and Consistent Units|(velocity units)]] || 0&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;displacementOnly || Set to: 0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;lt;0; 1 to detect contact whenever COD&amp;amp;lt;0 regardless of stress; &amp;amp;lt;0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;amp;lt;&amp;lt;tt&amp;gt;-&lt;/del&gt;displacementOnly&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/tt&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(in [[ConsistentUnits Command#Legacy and Consistent Units|pressure units]])|| none || 0&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| displacementOnly&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;Dc || &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;These properties implemented some alternative methods for detecting &lt;/ins&gt;contact&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. They are no longer implemented. If an old file enters values&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the output for that contact law will explain the feature is &amp;quot;no longer used&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;quot; &lt;/ins&gt;|| &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;none &lt;/ins&gt;|| none&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|-&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;| &lt;/del&gt;Dc || &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;0 to find separation assuming perfect interfaciall &lt;/del&gt;contact, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;ge;0 to use [[Linear Imperfect Interface|imperfect interface methods]] to find separation&lt;/del&gt;. || &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[ConsistentUnits Command#Legacy and Consistent Units|pressure/length units]] &lt;/del&gt;|| none&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;See [[Coulomb Friction Law#Comments on Parameters|some comments]] about the &amp;lt;tt&amp;gt;displacementOnly&amp;lt;/tt&amp;gt; and &amp;lt;/tt&amp;gt;Dc&amp;lt;/tt&amp;gt; parameters.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;See [[Coulomb Friction Law#Comments on Parameters|some comments]] about the &amp;lt;tt&amp;gt;displacementOnly&amp;lt;/tt&amp;gt; and &amp;lt;/tt&amp;gt;Dc&amp;lt;/tt&amp;gt; parameters.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25066&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25066&amp;oldid=prev"/>
		<updated>2025-11-11T20:20:23Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:20, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l18&quot;&gt;Line 18:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 18:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 implying zero adhesive strength. With zero adhesive strength, surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 implying zero adhesive strength. With zero adhesive strength, surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;slightly &lt;/del&gt;more efficient &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;)&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is more efficient.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Properties ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Properties ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25065&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25065&amp;oldid=prev"/>
		<updated>2025-11-11T20:18:55Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:18, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 implying zero adhesive strength. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Surfaces &lt;/del&gt;not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 implying zero adhesive strength. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;With zero adhesive strength, surfaces &lt;/ins&gt;not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25064&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25064&amp;oldid=prev"/>
		<updated>2025-11-11T20:18:02Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:18, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mean &lt;/del&gt;zero adhesive strength. Surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &amp;amp;gt; 1 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;implying &lt;/ins&gt;zero adhesive strength. Surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25063&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25063&amp;oldid=prev"/>
		<updated>2025-11-11T20:17:42Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:17, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;%&lt;/del&gt;gt; 1 mean zero adhesive strength. Surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the above check is always &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;&lt;/ins&gt;gt; 1 mean zero adhesive strength. Surfaces not in contact will always move freely. This approach extends the [[Coulomb Friction Law]] to allow smooth transition from static to dynamic coefficient of friction and to allow velocity-dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25062&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25062&amp;oldid=prev"/>
		<updated>2025-11-11T20:16:58Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:16, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, ''k'' allows friction coefficient to depend linearly on sliding velocity (Δv), and S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, ''k'' allows friction coefficient to depend linearly on sliding velocity (Δv), and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;''&lt;/ins&gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;'' &lt;/ins&gt;is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25061&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25061&amp;oldid=prev"/>
		<updated>2025-11-11T20:16:33Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:16, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;'&lt;/del&gt;''k&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;'&lt;/del&gt;'' allows friction coefficient to depend linearly on sliding velocity (Δv), and S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, ''k'' allows friction coefficient to depend linearly on sliding velocity (Δv), and S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25060&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25060&amp;oldid=prev"/>
		<updated>2025-11-11T20:16:18Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:16, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over  v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}&amp;gt; \mu_s N+S_a&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, k allows friction coefficient to depend linearly on sliding velocity (Δv), and S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; and µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; are the static and dynamic coefficients of friction, v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; allows a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;'''&lt;/ins&gt;k&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;''' &lt;/ins&gt;allows friction coefficient to depend linearly on sliding velocity (Δv), and S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The leading term in the above law achieves this goal by monotonically transitioning from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; when Δv = 0 to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; for high Δv. The law parameter v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; is the velocity at which that term is half way from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;. The default value of  v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; for a given problem may require experimentation.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the surfaces are not in contact, the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;surface &lt;/del&gt;continue to stick as long as:&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;If the surfaces are not in contact, the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;surfaces &lt;/ins&gt;continue to stick as long as:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;surfaces &lt;/del&gt;will &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;have no separation adhesion and therefore &lt;/del&gt;always move freely &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;when not in contact&lt;/del&gt;. This approach extends [[Coulomb Friction]] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;contact loaw &lt;/del&gt;to allow smooth transition from static to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dynamice &lt;/del&gt;coefficient of friction and to allow velocity dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;i&amp;gt;&lt;/ins&gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;gt;&amp;lt;/i&lt;/ins&gt;&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; or &amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; are zero, the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;above check is always %gt; 1 mean zero adhesive strength. Surfaces not in contact &lt;/ins&gt;will always move freely. This approach extends &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the &lt;/ins&gt;[[Coulomb Friction &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Law&lt;/ins&gt;]] to allow smooth transition from static to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dynamic &lt;/ins&gt;coefficient of friction and to allow velocity&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/ins&gt;dependent coefficient of friction.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25059&amp;oldid=prev</id>
		<title>Nairnj: /* Description */</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=25059&amp;oldid=prev"/>
		<updated>2025-11-11T20:12:45Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Description&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:12, 11 November 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l16&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;\left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 &amp;lt; 1&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Sa &lt;/del&gt;or &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Na &lt;/del&gt;are zero, the surfaces will have no separation adhesion and therefore always move freely when not in contact.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;i&amp;gt;S&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; &lt;/ins&gt;or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;i&amp;gt;N&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt; &lt;/ins&gt;are zero, the surfaces will have no separation adhesion and therefore always move freely when not in contact&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. This approach extends [[Coulomb Friction]] contact loaw to allow smooth transition from static to dynamice coefficient of friction and to allow velocity dependent coefficient of friction&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple [[Coulomb Friction Law|Coulomb friction]] contact law is a special case of this law for Sa = 0, k = 0, and v&amp;lt;sub&amp;gt;1/2&amp;lt;/sub&amp;gt; = 0. If all these properties are zero, the simpler law is slightly more efficient (although the  [[Coulomb Friction Law|simpler law]] cannot model a smooth transition  µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt;).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
	<entry>
		<id>http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=7146&amp;oldid=prev</id>
		<title>Nairnj at 19:58, 18 September 2020</title>
		<link rel="alternate" type="text/html" href="http://osupdocs.forestry.oregonstate.edu/index.php?title=Adhesive_Friction_Law&amp;diff=7146&amp;oldid=prev"/>
		<updated>2020-09-18T19:58:50Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:58, 18 September 2020&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l40&quot;&gt;Line 40:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 40:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| vhalf || Velocity where transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; is half done || [[ConsistentUnits Command#Legacy and Consistent Units|(velocity units)]] || 0&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| vhalf || Velocity where transition from µ&amp;lt;sub&amp;gt;s&amp;lt;/sub&amp;gt; to µ&amp;lt;sub&amp;gt;d&amp;lt;/sub&amp;gt; is half done || [[ConsistentUnits Command#Legacy and Consistent Units|(velocity units)]] || 0&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| displacementOnly || Set to: 0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;lt;0; 1 to detect contact whenever COD&amp;amp;lt;0 &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and &lt;/del&gt;stress &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is ignored&lt;/del&gt;; &amp;amp;lt;0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;amp;lt;&amp;lt;tt&amp;gt;-displacementOnly&amp;lt;/tt&amp;gt; (in [[ConsistentUnits Command#Legacy and Consistent Units|pressure units]])|| none || 0&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| displacementOnly || Set to: 0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;lt;0; 1 to detect contact whenever COD&amp;amp;lt;0 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;regardless of &lt;/ins&gt;stress; &amp;amp;lt;0 to detect contact when COD&amp;amp;lt;0 &amp;lt;i&amp;gt;and&amp;lt;/i&amp;gt; stress&amp;amp;lt;&amp;lt;tt&amp;gt;-displacementOnly&amp;lt;/tt&amp;gt; (in [[ConsistentUnits Command#Legacy and Consistent Units|pressure units]])|| none || 0&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Dc || &amp;amp;lt;0 to find separation assuming perfect interfaciall contact, &amp;amp;ge;0 to use [[Linear Imperfect Interface|imperfect interface methods]] to find separation. || [[ConsistentUnits Command#Legacy and Consistent Units|pressure/length units]] || none&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| Dc || &amp;amp;lt;0 to find separation assuming perfect interfaciall contact, &amp;amp;ge;0 to use [[Linear Imperfect Interface|imperfect interface methods]] to find separation. || [[ConsistentUnits Command#Legacy and Consistent Units|pressure/length units]] || none&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Nairnj</name></author>
	</entry>
</feed>