Difference between revisions of "Isotropic Softening Material"
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== Constitutive Law == | == Constitutive Law == | ||
This [[Material Models|MPM Material]] is an isotropic, elastic material, but once it fails, it develops anisotropic damage. The constitutive law for this material is | This [[Material Models|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>\mathbf{\sigma} = (\mathbf{I} - \mathbf{D}) \mathbf{C} \mathbf{\varepsilon}</math> | <math>\mathbf{\sigma} = (\mathbf{I} - \mathbf{D}) \mathbf{C} \mathbf{\varepsilon}</math> | ||
where | where '''C''' is stiffness tensor for the underlying isotropic material and ''D'' is an anisotropic 4<sup>th</sup> rank damage tensor. The important questions for implementing this material are: | ||
# When does damage initiate? | |||
# Once damage is form, what damage tensor, D, should be used to describe the anisotropic response after failure? | |||
# How does damage evolve? | |||
The first question is answered by attaching a failure criterion to this law. | |||
Chaboche, J. (1982). 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. | |||
Revision as of 12:59, 13 January 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. The important questions for implementing this material are:
- When does damage initiate?
- Once damage is form, what damage tensor, D, should be used to describe the anisotropic response after failure?
- How does damage evolve?
The first question is answered by attaching a failure criterion to this law.
Chaboche, J. (1982). 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.