Difference between revisions of "Isotropic Plastic Softening Material"

Latest revision as of 10:48, 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: ε_c,xx or x direction cracking strain normal to crack in the crack axis system
P+S+2: γ_c,xy or x-y direction shear cracking strain in the crack axis system
P+S+3: γ_c,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

@@ Line 1: / Line 1: @@
 == 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 The constitutive law for this material is
+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.
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-<math>\mathbf{\sigma} = (\mathbf{I} - \mathbf{D}) \mathbf{C}( \mathbf{\varepsilon}- \mathbf{\varepsilon}_{res})</math>
-where '''C''' is stiffness tensor for the underlying isotropic material and '''D''' is an anisotropic 4<sup>th</sup> rank damage tensor appropriate for damage in isotropic materials, and <math>\mathbf{\varepsilon}_{res}</math> is any residual strain (such as thermal or solvent induced strains).
-An appropriate damage tensor was first proposed by Chaboche<ref>J. Chaboche (1979). Le concept de contrainte effective appliqu ́e a` l’ ́elasticit ́e et a` la viscoplasticit ́e en pr ́esence d’un endommagement anisotrope. In Boehler, J.-P., editor, Mechanical Behav- ior of Anisotropic Solids / Comportment M ́echanique des Solides Anisotropes, pages 737–760. Springer Netherlands.</ref>, and was implemented in this material for complete modeling of anisotropy caused by 3D damage evolution<ref name="dmref">J. A. Nairn, C. Hammerquist, and Y. E. Aimene (2016), Numerical Implementation of Anisotropic Damage Mechanics, in press.</ref>. This fourth rank tensor depends on three damage variables, which can be shown to relate to one tensile and two shear damage processes related to a crack plane. These three damage variables can be related to mode I and lumped mode II/III fracture mechanics failure modes.
-== Damage Initiation ==
-Damage initiation is controlled by attaching a [[Damage Initiation Laws|damage initiation law]] to the material. These laws define a failure envelop. Once the response reaches the envelop, the damage process is initiated and the normal to the envelop defines the normal to the crack plane modeled by this damage mechanics material. The normal is need to find the anisotropic '''D''' tensor (which involves rotating analysis into the crack axis system where the ''x'' axis is aligned with the crack normal.
-== Damage Evolution ==
-Damage evolution is determined by [[Softening Laws|softening laws]] laws to predict degradation of normal and shear tractions across the crack plane. You need to attach two [[Softening Laws|softening laws]] to this material. These two laws handle tensile and shear damage and the areas under the laws correspond to fracture toughnesses ''G<sub>Ic</sub>'' and lumped ''G<sub>IIc</sub>''/''G<sub>IIIc</sub>'' for the material.
-In brief, this material models crack initiation and propagation through damage mechanics. The softening laws' properties tie the damage mechanics to toughness properties for the material. The scheme can handle interacting cracks (which become interacting damage zones) and 3D cracks. MPM modeling using this material is described in a recent paper<ref name="dmref"/>.
 == Material Properties ==
-When the material is undamaged, it response is identical to properties entered for the underlying [[Isotropic Material|isotropic material]]. Once those are specified, you have to attach one [[Damage Initiation Laws|damage initiation law]] and two [[Softening Laws|softening laws]] to define how the material responds after initiation of damage.
+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"
@@ Line 32: / Line 15: @@
 | ([[Isotropic Material#Material Properties|Isotropic Properties]]) || Enter all properties needed to define the underlying isotropic material response || varies || varies
 |-
-| Initiation || Attach [[Damage Initiation Laws|damage initiation law]] by name or ID that is compatible with isotropic materials. Once attached, enter all required material properties for that law. || none || MaxPrinciple
+| ([[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
 |-
-| SofteningI || Attach a [[Softening Laws|softening law]] (by name or ID) for propagation of tensile damage. Once attached, enter all required properties for that law by prefacing each property with "I-". || none || Linear
+| ([[Isotropic Softening Material#Material Properties|Isotropic Softening Properties]]) || Enter properties for initiation of damage and for two softening laws  || varies || varies
 |-
-| SofteningII || Attach a [[Softening Laws|softening law]] (by name or ID) for propagation of shear damage. Once attached, enter all required properties for that law by prefacing each property with "II-". || none || Linear
+| ([[Common Material Properties|other]]) || Properties common to all materials and must use the large rotation option || varies || varies
-|-
-| shearFailureSurface || Select failure surface assumed when modeling shear damage in 3D calculations. Use 1 for an elliptical failure criterion based on current degraded shear strengths. Use 0 for a rectangular failure surface that encloses the elliptical failure criterion. The elliptical surface is preferred, but rectangular is more efficient. || none || 1
-|-
-| coefVariation || This property assigns a coefficient of variation to failure properties. The property that is affected is determined by the <tt>coefVariationMode</tt> parameter. Each particle's relative property is set at the start of the simulation to have the same Gaussian distribution of values about their means, but will have no spatial correlations. A better approach to stochastic modeling would use Gaussian random fields with spatial correlation, but the feature is not yet implemented. || none || 0
-|-
-| coefVariationMode || The options are 1 = vary only strength, 2 = vary only toughness, and 3 = vary strength and toughness. Note that strength, toughness, and critical crack opening displacement (COD) are interrelated. Option 1 means COD will increase to keep toughness constant; 2 means COD will decreased to keep strength constant; 3 means COD will remain constant. || none || 1
-|-
-| ([[Common Material Properties|other]]) || Properties common to all materials || varies || varies
 |}
 == History Variables ==
-This material stores several history variables that track the extent of the damage and orientation of the damage plane:
+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.
-# 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.
+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:
-# δ<sub>n</sub> or the maximum normal cracking strain.
-# δ<sub>xy</sub> or the maximum x-y shear cracking strain.
-# δ<sub>xz</sub> or the maximum x-z cracking strain (zero for 2D).
-# d<sub>n</sub> or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.
-# 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).
+* 1 to P: Plastic law history variables
+* P+1 to P+S: [[Isotropic Softening Material]] history variable <tt>S</tt>
+* P+S+1: ε<sub>c,xx</sub> or x direction cracking strain normal to crack in the crack axis system
+* P+S+2: γ<sub>c,xy</sub> or x-y direction shear cracking strain in the crack axis system
+* P+S+3: γ<sub>c,xz</sub> or x-z direction shear cracking strain in the crack 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.
+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.
+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 ==
-  Material "isosoft","Isotropic Softening Material",50
+  Material "isoplastsoft","Isotropic Plastic Softening Material",53
     E 1000
     nu .33
@@ Line 83: / Line 54: @@
     SofteningII Linear
     II-Gc 10000
+   Hardening Linear
+   yield 20
+   Ep 200
   Done
-== References ==
-<references/>

Difference between revisions of "Isotropic Plastic Softening Material"

Latest revision as of 10:48, 18 November 2023

Contents

Constitutive Law

Material Properties

History Variables

Examples

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