Surface Normals - Revision history

Nairnj: /* Explicit Crack Normal Vector */

2026-03-29T18:14:48Z

Explicit Crack Normal Vector

← Older revision		Revision as of 18:14, 29 March 2026
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	[[File:CrackNormals.jpg\|right]]		[[File:CrackNormals.jpg\|right]]

	Because [[Defining Cracks\|explicit cracks]] are defined by connections of massless particles, those connections can be used to find contact normals. For example, the figure on the right shows a 2D crack and each crack segment has a normal vector pointing from below to above the crack. When MPM with explicit cracks (''i.e''., CRAMP<ref name='CRAMP'/>) extrapolates particle information to the grid, it determines which crack velocity field to ~~used~~ by checking if a line from the particle to the node crosses a crack. If the line crosses a crack, the normal for the crossed segment is also extrapolated to the grid. When needed, all nodes near cracks will have multiple velocity fields and will have normal vectors for use in contact calculations.		Because [[Defining Cracks\|explicit cracks]] are defined by connections of massless particles, those connections can be used to find contact normals. For example, the figure on the right shows a 2D crack and each crack segment has a normal vector pointing from below to above the crack. When MPM with explicit cracks (''i.e''., CRAMP<ref name='CRAMP'/>) extrapolates particle information to the grid, it determines which crack velocity field to use by checking if a line from the particle to the node crosses a crack. If the line crosses a crack, the normal for the crossed segment is also extrapolated to the grid. When needed, all nodes near cracks will have multiple velocity fields and will have normal vectors for use in contact calculations.

	Because finding normals for explicit crack is easier than for multimaterial methods, none of the methods described [[#Multimaterial Normal Vector Options\|above]] for multimaterial mode contact are needed. Instead, cracks always use the normals extrapolated from the crack's geometrical definition.		Because finding normals for explicit crack is easier than for multimaterial methods, none of the methods described [[#Multimaterial Normal Vector Options\|above]] for multimaterial mode contact are needed. Instead, cracks always use the normals extrapolated from the crack's geometrical definition.

Nairnj: /* Maximum Gradient */

2026-03-29T18:12:28Z

Maximum Gradient

← Older revision		Revision as of 18:12, 29 March 2026
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	[[File:maxgrad.png\|right]]		[[File:maxgrad.png\|right]]

	This method looks at the volume ~~gradient's~~ for the two materials and choses the vector that has the largest magnitude (and then normalizes to get a unit vector). The logic is that volume gradient is zero within an object and only non-zero around the edge. Thus the material that is closer the edge might have more accurate information about the normal and it will have the larger volume gradient. Perhaps this material's normal should be used in preference to the other material's normal. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the maximum gradient is found by comparing the one material to the remaining materials lumped into a virtual material.		This method looks at the volume gradients for the two materials and choses the vector that has the largest magnitude (and then normalizes to get a unit vector). The logic is that volume gradient is zero within an object and only non-zero around the edge. Thus the material that is closer the edge might have more accurate information about the normal and it will have the larger volume gradient. Perhaps this material's normal should be used in preference to the other material's normal. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the maximum gradient is found by comparing the one material to the remaining materials lumped into a virtual material.

	A maximum gradient calculation resolves some edge node issues. The figure on the left shows two materials in contact near an edge notch in an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Now the gradient from the red material is correct for the surface normal while the gradient for the black material is not. An average would be better, but still inaccurate. For this situation, the material with the maximum gradient will be the red material (because it has more particles). Therefore this method will get the correct normal. A maximum gradient resolves this one edge node issue, but not all. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.		A maximum gradient calculation resolves some edge node issues. The figure on the left shows two materials in contact near an edge notch in an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Now the gradient from the red material is correct for the surface normal while the gradient for the black material is not. An average would be better, but still inaccurate. For this situation, the material with the maximum gradient will be the red material (because it has more particles). Therefore this method will get the correct normal. A maximum gradient resolves this one edge node issue, but not all. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.

Nairnj: /* Average Gradient */

2026-03-29T18:11:33Z

Average Gradient

← Older revision		Revision as of 18:11, 29 March 2026
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	described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between materials with different densities.		described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between materials with different densities.

	An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all ~~(see the [[#Volume Screening\|volume screen method]] and example)~~. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.		An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all issues. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.

	This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).		This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).

Nairnj: /* Average Gradient */

2026-03-29T18:09:57Z

Average Gradient

← Older revision		Revision as of 18:09, 29 March 2026
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	Prior to regression methods, this method was the best option; it is		Prior to regression methods, this method was the best option; it is
	described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between ~~two~~ materials with different densities.		described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between materials with different densities.

	An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all (see the [[#Volume Screening\|volume screen method]] and example). The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.		An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all (see the [[#Volume Screening\|volume screen method]] and example). The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.

Nairnj: /* Average Gradient */

2026-03-29T18:09:03Z

Average Gradient

← Older revision		Revision as of 18:09, 29 March 2026
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	[[File:avggrad.png\|right]]		[[File:avggrad.png\|right]]

	Prior to regression methods, this method ~~(and other improvements below)~~ was the best option; it is		Prior to regression methods, this method was the best option; it is
	described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between two materials with different densities.		described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between two materials with different densities.

Nairnj: /* Specified Normal */

2026-03-29T18:08:39Z

Specified Normal

← Older revision		Revision as of 18:08, 29 March 2026
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	The ultimate accuracy of normals is to specifying the normal in the input file using known values.<ref name="Nairn"/> This approach, however, only works if the normals can be determined prior to the analysis and if those normals remain the same throughout the analysis. In other words, this option works for problems with a single contact plane such as a straight rigid plane contacting an object.		The ultimate accuracy of normals is to specifying the normal in the input file using known values.<ref name="Nairn"/> This approach, however, only works if the normals can be determined prior to the analysis and if those normals remain the same throughout the analysis. In other words, this option works for problems with a single contact plane such as a straight rigid plane contacting an object.

	You can use a specified normal vector by [[Multimaterial MPM#Multimaterial Mode Input Commands\|<tt>(normals)</tt> setting]] of <tt>specify</tt> (or numerically to 4) and then ~~providing~~ the azimuth and polar angles for the normal vector.		You can use a specified normal vector by [[Multimaterial MPM#Multimaterial Mode Input Commands\|<tt>(normals)</tt> setting]] of <tt>specify</tt> (or numerically to 4) and then provide the azimuth and polar angles for the normal vector.

	=== Average Gradient ===		=== Average Gradient ===

Nairnj: /* Multimaterial Normal Vector Options */

2026-03-29T18:07:47Z

Multimaterial Normal Vector Options

← Older revision		Revision as of 18:07, 29 March 2026
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	Regression methods are selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>logreg</tt> (or numerically to 6) or <tt>linreg</tt> (or numerically to 5). The <tt>logreg</tt> option is preferred. The only drawback of <tt>logreg</tt> is that it requires solution to a numerical problem to find the normal at each contact node. In many problems, the number of contact nodes will be much less then number of nodes in the grid and thus the extra calculations are not a burden. A possible option for faster simulations with lots of contact is to switch to <tt>linreg</tt>. Although the theory is different than <tt>logreg</tt>, mathematically it is equivalent to using <tt>logreg</tt> but stopping the numerical solution after one interation. It retains advantages of regressions methods,<ref name="logreg"/> but has reduced accuracy in normal calculations.		Regression methods are selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>logreg</tt> (or numerically to 6) or <tt>linreg</tt> (or numerically to 5). The <tt>logreg</tt> option is preferred. The only drawback of <tt>logreg</tt> is that it requires solution to a numerical problem to find the normal at each contact node. In many problems, the number of contact nodes will be much less then number of nodes in the grid and thus the extra calculations are not a burden. A possible option for faster simulations with lots of contact is to switch to <tt>linreg</tt>. Although the theory is different than <tt>logreg</tt>, mathematically it is equivalent to using <tt>logreg</tt> but stopping the numerical solution after one interation. It retains advantages of regressions methods,<ref name="logreg"/> but has reduced accuracy in normal calculations.

			=== Specified Normal ===

			The ultimate accuracy of normals is to specifying the normal in the input file using known values.<ref name="Nairn"/> This approach, however, only works if the normals can be determined prior to the analysis and if those normals remain the same throughout the analysis. In other words, this option works for problems with a single contact plane such as a straight rigid plane contacting an object.

			You can use a specified normal vector by [[Multimaterial MPM#Multimaterial Mode Input Commands\|<tt>(normals)</tt> setting]] of <tt>specify</tt> (or numerically to 4) and then providing the azimuth and polar angles for the normal vector.

	=== Average Gradient ===		=== Average Gradient ===
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	This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>maxvol</tt> (or numerically to 1). Experience shows this method is less helpful than the average or maximum gradient methods and therefore not recommended.		This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>maxvol</tt> (or numerically to 1). Experience shows this method is less helpful than the average or maximum gradient methods and therefore not recommended.

	~~=== Specified Normal ===~~

	The ultimate accuracy of normals is to specifying the normal in the input file using known values.<ref name="Nairn"/> This approach, however, only works if the normals can be determined prior to the analysis and if those normals remain the same throughout the analysis. In other words, this option works for problems with a single contact plane such as a straight rigid plane contacting an object.

	You can use a specified normal vector by [[Multimaterial MPM#Multimaterial Mode Input Commands\|<tt>(normals)</tt> setting]] of <tt>specify</tt> (or numerically to 4) and then providing the azimuth and polar angles for the normal vector.

	=== Rigid Material Bias Option ===		=== Rigid Material Bias Option ===

Nairnj: /* Multimaterial Normal Vector Options */

2026-03-29T18:07:17Z

Multimaterial Normal Vector Options

← Older revision		Revision as of 18:07, 29 March 2026
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	Regression methods are selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>logreg</tt> (or numerically to 6) or <tt>linreg</tt> (or numerically to 5). The <tt>logreg</tt> option is preferred. The only drawback of <tt>logreg</tt> is that it requires solution to a numerical problem to find the normal at each contact node. In many problems, the number of contact nodes will be much less then number of nodes in the grid and thus the extra calculations are not a burden. A possible option for faster simulations with lots of contact is to switch to <tt>linreg</tt>. Although the theory is different than <tt>logreg</tt>, mathematically it is equivalent to using <tt>logreg</tt> but stopping the numerical solution after one interation. It retains advantages of regressions methods,<ref name="logreg"/> but has reduced accuracy in normal calculations.		Regression methods are selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>logreg</tt> (or numerically to 6) or <tt>linreg</tt> (or numerically to 5). The <tt>logreg</tt> option is preferred. The only drawback of <tt>logreg</tt> is that it requires solution to a numerical problem to find the normal at each contact node. In many problems, the number of contact nodes will be much less then number of nodes in the grid and thus the extra calculations are not a burden. A possible option for faster simulations with lots of contact is to switch to <tt>linreg</tt>. Although the theory is different than <tt>logreg</tt>, mathematically it is equivalent to using <tt>logreg</tt> but stopping the numerical solution after one interation. It retains advantages of regressions methods,<ref name="logreg"/> but has reduced accuracy in normal calculations.

	~~=== Each Material's Gradient ===~~

	When multimaterial mode MPM was initially developed, contact was handled separately for each material's velocity field and the normal vector was found from that material's mass gradient.<ref name="bard"/> The alorithm is straightforward and is extended to more than two materials in contact simply for iterating for each material. Experience shows it suffers in accuracy. For one thing, the normals for the two materials will generally not be in equal and opposite directions. When that occurs, the contact algorithm does not conserve momentum.

	This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>owngrad</tt> (or numerically to 3). This option is available in [[NairnMPM]] for comparison to improved methods and not recommended for general use.

	=== Average Gradient ===		=== Average Gradient ===
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	This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).		This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).

			=== Each Material's Gradient ===

			When multimaterial mode MPM was initially developed, contact was handled separately for each material's velocity field and the normal vector was found from that material's mass gradient.<ref name="bard"/> The alorithm is straightforward and is extended to more than two materials in contact simply for iterating for each material. Experience shows it suffers in accuracy. For one thing, the normals for the two materials will generally not be in equal and opposite directions. When that occurs, the contact algorithm does not conserve momentum.

			This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>owngrad</tt> (or numerically to 3). This option is available in [[NairnMPM]] for comparison to improved methods and not recommended for general use.

	=== Maximum Gradient ===		=== Maximum Gradient ===

Nairnj: /* References */

2026-03-29T18:05:13Z

References

← Older revision		Revision as of 18:05, 29 March 2026
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	<ref name="bard">S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," <i>Computer Modeling in Engineering & Sciences</i>, <b>2</b>, 509-522 (2001).</ref>		<ref name="bard">S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," <i>Computer Modeling in Engineering & Sciences</i>, <b>2</b>, 509-522 (2001).</ref>

	<ref name="Nairn">J.A. Nairn, "Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods," ''Computer Modeling in Eng. & Sci.'', '''92''', 271-299 (2013).</ref>		<ref name="Nairn">J.A. Nairn, "Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods," ''Computer Modeling in Eng. & Sci.'', '''92''', 271-299 (2013). ([https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MMInterfaces.pdf See PDF])</ref>

	<ref name='CRAMP'>J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," <i>Computer Modeling in Engineering & Sciences</i>, <b>4</b>, 649-664 (2003). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMCracks.pdf See PDF])</ref>		<ref name='CRAMP'>J. A. Nairn, "Material Point Method Calculations with Explicit Cracks," <i>Computer Modeling in Engineering & Sciences</i>, <b>4</b>, 649-664 (2003). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMCracks.pdf See PDF])</ref>

	</references>		</references>

Nairnj: /* References */

2021-01-22T18:32:04Z

References

← Older revision		Revision as of 18:32, 22 January 2021
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	<references>		<references>
	<ref name="logreg">J. A. Nairn, C. C. Hammerquist, and G. Smith, "New ~~MPM~~ contact ~~methods~~ for improved accuracy, large-deformation problems, and proper null-space filtering," ''Computer Methods in Applied Mechanics and Engineering'', ~~in press~~ (2020).</ref>		<ref name="logreg">J. A. Nairn, C. C. Hammerquist, and G. Smith, "New material point method contact algorithms for improved accuracy, large-deformation problems, and proper null-space filtering," ''Computer Methods in Applied Mechanics and Engineering'', '''362''', 112859 (2020). ([http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/MPMContactRevisited.pdf See PDF])</ref>

	<ref name="bard">S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," <i>Computer Modeling in Engineering & Sciences</i>, <b>2</b>, 509-522 (2001).</ref>		<ref name="bard">S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," <i>Computer Modeling in Engineering & Sciences</i>, <b>2</b>, 509-522 (2001).</ref>

← Older revision		Revision as of 18:14, 29 March 2026
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	[[File:CrackNormals.jpg\|right]]		[[File:CrackNormals.jpg\|right]]

	Because [[Defining Cracks\|explicit cracks]] are defined by connections of massless particles, those connections can be used to find contact normals. For example, the figure on the right shows a 2D crack and each crack segment has a normal vector pointing from below to above the crack. When MPM with explicit cracks (''i.e''., CRAMP<ref name='CRAMP'/>) extrapolates particle information to the grid, it determines which crack velocity field to ~~used~~ by checking if a line from the particle to the node crosses a crack. If the line crosses a crack, the normal for the crossed segment is also extrapolated to the grid. When needed, all nodes near cracks will have multiple velocity fields and will have normal vectors for use in contact calculations.		Because [[Defining Cracks\|explicit cracks]] are defined by connections of massless particles, those connections can be used to find contact normals. For example, the figure on the right shows a 2D crack and each crack segment has a normal vector pointing from below to above the crack. When MPM with explicit cracks (''i.e''., CRAMP<ref name='CRAMP'/>) extrapolates particle information to the grid, it determines which crack velocity field to use by checking if a line from the particle to the node crosses a crack. If the line crosses a crack, the normal for the crossed segment is also extrapolated to the grid. When needed, all nodes near cracks will have multiple velocity fields and will have normal vectors for use in contact calculations.

	Because finding normals for explicit crack is easier than for multimaterial methods, none of the methods described [[#Multimaterial Normal Vector Options\|above]] for multimaterial mode contact are needed. Instead, cracks always use the normals extrapolated from the crack's geometrical definition.		Because finding normals for explicit crack is easier than for multimaterial methods, none of the methods described [[#Multimaterial Normal Vector Options\|above]] for multimaterial mode contact are needed. Instead, cracks always use the normals extrapolated from the crack's geometrical definition.

← Older revision		Revision as of 18:12, 29 March 2026
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	[[File:maxgrad.png\|right]]		[[File:maxgrad.png\|right]]

	This method looks at the volume ~~gradient's~~ for the two materials and choses the vector that has the largest magnitude (and then normalizes to get a unit vector). The logic is that volume gradient is zero within an object and only non-zero around the edge. Thus the material that is closer the edge might have more accurate information about the normal and it will have the larger volume gradient. Perhaps this material's normal should be used in preference to the other material's normal. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the maximum gradient is found by comparing the one material to the remaining materials lumped into a virtual material.		This method looks at the volume gradients for the two materials and choses the vector that has the largest magnitude (and then normalizes to get a unit vector). The logic is that volume gradient is zero within an object and only non-zero around the edge. Thus the material that is closer the edge might have more accurate information about the normal and it will have the larger volume gradient. Perhaps this material's normal should be used in preference to the other material's normal. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the maximum gradient is found by comparing the one material to the remaining materials lumped into a virtual material.

	A maximum gradient calculation resolves some edge node issues. The figure on the left shows two materials in contact near an edge notch in an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Now the gradient from the red material is correct for the surface normal while the gradient for the black material is not. An average would be better, but still inaccurate. For this situation, the material with the maximum gradient will be the red material (because it has more particles). Therefore this method will get the correct normal. A maximum gradient resolves this one edge node issue, but not all. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.		A maximum gradient calculation resolves some edge node issues. The figure on the left shows two materials in contact near an edge notch in an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Now the gradient from the red material is correct for the surface normal while the gradient for the black material is not. An average would be better, but still inaccurate. For this situation, the material with the maximum gradient will be the red material (because it has more particles). Therefore this method will get the correct normal. A maximum gradient resolves this one edge node issue, but not all. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.

← Older revision		Revision as of 18:11, 29 March 2026
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	described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between materials with different densities.		described in more detail in Nairn (2013).<ref name="Nairn"/>. The first obvious improvement to conserve momentum is to find the average volume gradient between the two materials and use that vector to define the normal for both sides of the surface. If the multimaterial mode has [[Multimaterial MPM#More than Two Materials\|more than two materials]], the average is found between one material and the remaining materials lumped into a virtual material. Note that whenever averaging or comparing gradients, it is important to use volume gradients instead of mass gradients. This minor change is needed to correctly model contact between materials with different densities.

	An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all ~~(see the [[#Volume Screening\|volume screen method]] and example)~~. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.		An average gradient calculation can also resolve some complications at edge nodes. The figure on the right shows two materials in contact at the edge of an object. The volume gradients for the red and black materials on the multimaterial node marked in blue are shown by the vectors. Both of these normals are inaccurate for the contacting surfaces, but averaging the normals (with correct signs), gives a normal vector in the horizontal direction that exactly matches the contact surface normal. An average gradient resolves this one edge node issue, but not all issues. The preferred [[#Regression Methods\|regression methods]] appear to handle all edge issues well, which is a motivation for using them.

	This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).		This method is selected by [[Multimaterial MPM#Multimaterial Mode Input Commands\|setting <tt>(normals)</tt>]] to <tt>avggrad</tt> (or numerically to 2).