Difference between revisions of "Isotropic Plastic Softening Material"

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== Constitutive Law ==
== Constitutive Law ==


This [[Material Models|MPM Material]] is an isotropic, elastic-plastic material that can also develop aniostropic damage. The material is available only in [[OSParticulas]].
This [[Material Models#Softening Materials|MPM softening material]] is an isotropic, elastic-plastic material that can also develop anisotropic damage.


In the absense of damage, this material is identical to an [[Isotropic, Elastic-Plastic Material]]. In the absence of plasticity, this material is identical to an [[Isotropic Softening Material]]. If conditions allow, the material can develop both plasticity and damage with softening. Note that if plastic yield properties are below damage initiation stress, the material may have never reach stress to cause damage. But, if the plastic properties had hardening, the material can yield first and then start damage after hardening allows stresses to reach stress for initiation of damage.
In the absence of damage, this material is identical to an [[Isotropic, Elastic-Plastic Material]]. In the absence of plasticity, this material is identical to an [[Isotropic Softening Material]]. If conditions allow, the material can develop both plasticity and damage with softening. Note that if plastic yield properties are below damage initiation stress, the material may never reach stress to cause damage. But, if the plastic properties allow hardening, the material can yield first and then start damage after hardening allows stresses to reach stress for initiation of damage.


== Material Properties ==
== Material Properties ==


For material properties, combine all options available to an [[Isotropic, Elastic-Plastic Material]] and to an [[Isotropic Softening Material]]. This material must, however, use large rotation mode (as is also required for an [[Isotropic Softening Material]]).
For material properties, combine all options available for an [[Isotropic, Elastic-Plastic Material]] and for an [[Isotropic Softening Material]]. This material must, however, use large rotation mode (as is also required for an [[Isotropic Softening Material]]).


{| class="wikitable"
{| class="wikitable"
Line 15: Line 15:
| ([[Isotropic Material#Material Properties|Isotropic Properties]]) || Enter all properties needed to define the underlying isotropic material response || varies || varies
| ([[Isotropic Material#Material Properties|Isotropic Properties]]) || Enter all properties needed to define the underlying isotropic material response || varies || varies
|-
|-
| ([[Isotropic, Elastic-Plastic Material#Material Properties|Isotropic, Elastic-Plastic Properties]]) || Enter yield properties and a hardening law || varies || varies
| ([[Isotropic, Elastic-Plastic Material#Material Properties|Isotropic, Plastic Properties]]) || Enter yield properties and a [[Hardening Laws|hardening law]], but cannot use a [[Hardening Laws|hardening law]] that changes shear modulus ([[Steinberg-Cochran-Guinan Hardening]] or [[Steinberg-Lund Hardening]]) || varies || varies
|-
|-
| ([[Isotropic Softening Material#Material Properties|Isotropic Softening Material]]) || Enter damage properties for initiation and for softening laws  || varies || varies
| ([[Isotropic Softening Material#Material Properties|Isotropic Softening Properties]]) || Enter properties for initiation of damage and for two softening laws  || varies || varies
|-
|-
| ([[Common Material Properties|other]]) || Properties common to all materials || varies || varies
| ([[Common Material Properties|other]]) || Properties common to all materials and must use the large rotation option || varies || varies
|}
|}


== History Variables ==
== History Variables ==


The first history variables apply to the [[Isotropic, Elastic-Plastic Material]]
The chosen [[Hardening Laws|hardening law]] will have at least one history variable and will start with history variable number 1. After the  [[Hardening Laws|hardening law]] history variables, the remaining variables will be the same as for the [[Isotropic Softening Material]] material, but the history variable will be offset by the number of [[Hardening Laws|hardening law]] history variables. Because plastic strain is used for plasticity, three additional history variables (compared to an [[Isotropic Softening Material]]) track the three components of cracking strains in the crack axis system corresponding to normal and shear crack opening displacements.


This material stores several history variables that track the extent of the damage and orientation of the damage plane:
Let P and S be number of history variables for the plastic law in use and for damage needed by an [[Isotropic Softening Material]], respectively. The history variables for this material are then:


# 0, 0.9, 1.1, 1.9, or 2.1 to indicate undamaged (0), damage propagation (0.9 or 1.1), or post failure (decohesion) state of the particle (1.9 or 2.1). 0.9 and 1.9 indicate the failure initiated by tensile strength while 1.1 and 2.1 indicate failure initiated by shear strength.
* 1 to P: Plastic law history variables
# δ<sub>n</sub> or the maximum normal cracking strain.
* P+1 to P+S: [[Isotropic Softening Material]] history variable <tt>S</tt>
# δ<sub>xy</sub> or the maximum x-y shear cracking strain.
* P+S+1: ε<sub>c,xx</sub> or x direction cracking strain normal to crack in the crack axis system
# δ<sub>xz</sub> or the maximum x-z cracking strain (zero for 2D).
* P+S+2: γ<sub>c,xy</sub> or x-y direction shear cracking strain in the crack axis system
# d<sub>n</sub> or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.
* P+S+3: γ<sub>c,xz</sub> or x-z direction shear cracking strain in the crack axis system
# d<sub>xy</sub> or damage variable for x-y shear loading. It varies from 0 to 1 where 1 is complete damage or failure.
# d<sub>xz</sub> or damage variable for x-z shear loading. It varies from 0 to 1 where 1 is complete damage or failure (zero for 2D).
# For 2D it is cos(θ), but for 3D it is Euler angle α.
# For 2D it is sin(θ), but for 3D it is Euler angle β.
# For 2D it is not used, but for 3D it is Euler angle γ.
# ''A<sub>c</sub>''/''V<sub>p</sub>'' where ''A<sub>c</sub>'' is crack area within the particle and ''V<sub>p</sub>'' is particle volume.
# Relative strength derived at the start by <tt>strengthCoefVariation</tt> property.


Variables 8-10 define the normal to the damage crack plane. For 2D, θ is the counter clockwise angle from the x axis to the crack normal. For 3D, (α, β, γ) are the three Euler angles for the normal direction using a Z-Y-Z rotation scheme. You can use the [[MPM Archiving Options|<tt>damagenormal</tt> archiving option]] to save enough information for plotting the normal. Although damaged normal is a unit vector, it is archived with magnitude equal to ''A<sub>c</sub>''/''V<sub>p</sub>'' (which gets another history variable archived and the value is used for some visualization options).
For example when P=1 and S=13, this material defines 17 history variables.
This material also tracks plastic strain, which can be saved by using the [[MPM Archiving Options|<tt>plasticstrain</tt> archiving option]]. The total plastic strain is archived in the global axis system.


This material also tracks the cracking strain which can be saved by using the  [[MPM Archiving Options|<tt>plasticstrain</tt> archiving option]]. The strain is archived in the global axis system. If you also [[MPM Archiving Options|archive the <tt>damagenormal</tt>]], you will be able to plot a vector along the crack-opening displacement vector.
If you also [[MPM Archiving Options|archive the <tt>damagenormal</tt>]], you will be able to plot a vector along the crack-opening displacement vector.


== Examples ==
== Examples ==


  Material "isosoft","Isotropic Softening Material",50
  Material "isoplastsoft","Isotropic Plastic Softening Material",53
   E 1000
   E 1000
   nu .33
   nu .33
Line 60: Line 54:
   SofteningII Linear
   SofteningII Linear
   II-Gc 10000
   II-Gc 10000
  Hardening Linear
  yield 20
  Ep 200
  Done
  Done
== References ==
<references/>

Latest revision as of 09:48, 18 November 2023

Constitutive Law

This MPM softening material is an isotropic, elastic-plastic material that can also develop anisotropic damage.

In the absence of damage, this material is identical to an Isotropic, Elastic-Plastic Material. In the absence of plasticity, this material is identical to an Isotropic Softening Material. If conditions allow, the material can develop both plasticity and damage with softening. Note that if plastic yield properties are below damage initiation stress, the material may never reach stress to cause damage. But, if the plastic properties allow hardening, the material can yield first and then start damage after hardening allows stresses to reach stress for initiation of damage.

Material Properties

For material properties, combine all options available for an Isotropic, Elastic-Plastic Material and for an Isotropic Softening Material. This material must, however, use large rotation mode (as is also required for an Isotropic Softening Material).

Property Description Units Default
(Isotropic Properties) Enter all properties needed to define the underlying isotropic material response varies varies
(Isotropic, Plastic Properties) Enter yield properties and a hardening law, but cannot use a hardening law that changes shear modulus (Steinberg-Cochran-Guinan Hardening or Steinberg-Lund Hardening) varies varies
(Isotropic Softening Properties) Enter properties for initiation of damage and for two softening laws varies varies
(other) Properties common to all materials and must use the large rotation option varies varies

History Variables

The chosen hardening law will have at least one history variable and will start with history variable number 1. After the hardening law history variables, the remaining variables will be the same as for the Isotropic Softening Material material, but the history variable will be offset by the number of hardening law history variables. Because plastic strain is used for plasticity, three additional history variables (compared to an Isotropic Softening Material) track the three components of cracking strains in the crack axis system corresponding to normal and shear crack opening displacements.

Let P and S be number of history variables for the plastic law in use and for damage needed by an Isotropic Softening Material, respectively. The history variables for this material are then:

  • 1 to P: Plastic law history variables
  • P+1 to P+S: Isotropic Softening Material history variable S
  • P+S+1: εc,xx or x direction cracking strain normal to crack in the crack axis system
  • P+S+2: γc,xy or x-y direction shear cracking strain in the crack axis system
  • P+S+3: γc,xz or x-z direction shear cracking strain in the crack axis system

For example when P=1 and S=13, this material defines 17 history variables. This material also tracks plastic strain, which can be saved by using the plasticstrain archiving option. The total plastic strain is archived in the global axis system.

If you also archive the damagenormal, you will be able to plot a vector along the crack-opening displacement vector.

Examples

Material "isoplastsoft","Isotropic Plastic Softening Material",53
  E 1000
  nu .33
  a 60
  rho 1
  largeRotation 1
  Initiation MaxPrinciple
  sigmac 30
  tauc 20
  SofteningI Linear
  I-Gc 10000
  SofteningII Linear
  II-Gc 10000
  Hardening Linear
  yield 20
  Ep 200
Done
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