Difference between revisions of "Isotropic Softening Material"
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This material stores several history variables that track the extent of the damage and orientation of the damage plane: | This material stores several history variables that track the extent of the damage and orientation of the damage plane: | ||
# δ<sub>n</sub> or the | # δ<sub>n</sub> or the maximum normal cracking strain. | ||
# δ<sub>t</sub> or the | # δ<sub>t</sub> or the maximum tangential cracking strain. | ||
# 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>n</sub> or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure. | ||
# d<sub>t</sub> or damage variable for tangential loading. It varies from 0 to 1 where 1 is complete damage or failure. | # d<sub>t</sub> or damage variable for tangential loading. It varies from 0 to 1 where 1 is complete damage or failure. | ||
| Line 50: | Line 50: | ||
# For 2D it is sin(θ), but for 3D it is Euler angle β. | # 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. | # 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. | # ''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. | ||
Variables 5-7 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. | Variables 5-7 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. | ||
Revision as of 17:59, 25 December 2016
Constitutive Law
This MPM Material is an isotropic, elastic material, but once it fails, it develops anisotropic damage. The material is available only in OSParticulas.The constitutive law for this material is
[math]\displaystyle{ \mathbf{\sigma} = (\mathbf{I} - \mathbf{D}) \mathbf{C} \mathbf{\varepsilon} }[/math]
where C is stiffness tensor for the underlying isotropic material and D is an anisotropic 4th rank damage tensor appropriate for damage in isotropic materials.
The appropriate damage tensor was first proposed by Chaboche[1]. This fourth rank tensor depends on two damage variables, which can be shown to relate to tensile and shear damage along the crack plane. These two 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 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 laws to predict degradation of normal and shear tractions across the crack plane. Because an underlying isotropic material has two damage parameters, you need to attach two softening laws to this material. These two laws handle tensile and shear damage and the areas under the laws correspond to fracture toughnesses GIc and GIIc 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 (really interacting damage zones) and 3D cracks. MPM modeling using this material is described in a recent paper [2]
Material Properties
When the material is undamaged, it response is identical to properties entered for the underlying isotropic material. Once those are specified, you have to attach one damage initiation law and two softening laws to define how the material responds after initiation of damage.
| Property | Description | Units | Default |
|---|---|---|---|
| (Isotropic Properties) | Enter all properties needed to define the underlying isotropic material response | varies | varies |
| Initiation | Attach 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 |
| SofteningI | Attach a 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 |
| SofteningII | Attach a 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 |
| (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:
- δn or the maximum normal cracking strain.
- δt or the maximum tangential cracking strain.
- dn or damage variable for normal loading. It varies from 0 to 1 where 1 is complete damage or failure.
- dt or damage variable for tangential loading. It varies from 0 to 1 where 1 is complete damage or failure.
- 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.
- Ac/Vp where Ac is crack area within the particle and Vp is particle volume.
Variables 5-7 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 damagenormal archiving option to save enough information for plotting the normal.
This material also tracks the cracking strain which can be saved by using the plasticstrain archiving option. The 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
References
- ↑ 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.
- ↑ J. A. Nairn, C. Hammerquist, and Y. E. Aimene (2016), Numerical Implementation of Anisotropic Damage Mechanics, submitted.