Difference between revisions of "Linear Traction Law"

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(Created page with "__TOC__ == The Traction Law == This traction law applies a linearly increasing stress and it never fails. == Failure == This traction does not fail; as CO...")
 
 
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This [[Traction Laws|traction law]] applies a linearly increasing stress and it never fails.
This [[Traction Laws|traction law]] applies a linearly increasing stress and it never fails.
[[File:Linear.jpg|center]]


== Failure ==
== Failure ==


This traction does not fail; as COD increases, the traction increases. If you want to model failure, use a [[Triangular Traction Law||trangular traction law]] instead.
This traction does not fail or release energy; as COD increases, the traction keeps increasing. If you want to model failure, use a [[Triangular Traction Law|trangular traction law]] instead. For example, to model a linear law that suddenly drops to zero stress at some critical COD, use a [[Triangular Traction Law|trangular traction law]] with the same elastic slope, enter the critical COD (&delta;<sub>c</sub>), and set its [[Triangular Traction Law#Traction Law Properties|delpkI and/or delpkII parameters]] to 1. The toughness of this law would be
 
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<math>J_c = {1\over 2} k \delta_c^2</math>


== Traction Law Properties ==
== Traction Law Properties ==
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! Property !! Description !! Units !! Default
! Property !! Description !! Units !! Default
|-
|-
| stress || Enter constant normal stress. Use negative stress for a pressure loaded crack.|| MPa || none
| kIe || The elastic slope, k, in mode I || [[ConsistentUnits Command#Legacy and Consistent Units|pressure/length units]] || 0
|-
|-
| function || Alternatively, the stress can be entered as a [[User Defined Functions|user-defined function]] of time. || MPM || none
| kIIe || The elastic slope, k, in mode II || [[ConsistentUnits Command#Legacy and Consistent Units|pressure/length units]] || 0
|}
|}


If a function is used, any entered stress property is ignored.
== Traction History Variables ==
 
This material tracks no history variables.

Latest revision as of 22:07, 2 January 2021

The Traction Law

This traction law applies a linearly increasing stress and it never fails.

Linear.jpg

Failure

This traction does not fail or release energy; as COD increases, the traction keeps increasing. If you want to model failure, use a trangular traction law instead. For example, to model a linear law that suddenly drops to zero stress at some critical COD, use a trangular traction law with the same elastic slope, enter the critical COD (δc), and set its delpkI and/or delpkII parameters to 1. The toughness of this law would be

      [math]\displaystyle{ J_c = {1\over 2} k \delta_c^2 }[/math]

Traction Law Properties

The following properties are used to create a linear traction law:

Property Description Units Default
kIe The elastic slope, k, in mode I pressure/length units 0
kIIe The elastic slope, k, in mode II pressure/length units 0

Traction History Variables

This material tracks no history variables.

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