Orthotropic Softening Material

Constitutive Law

This MPM softening material is an orthotropic, elastic material, but once it fails, it develops anisotropic damage. It will remain orthotropic, but properties in some dirrections will change. The constitutive law for this material is

      [math]\displaystyle{ \mathbf{\sigma} = \mathbf{C}(\mathbf{I} - \mathbf{D}) ( \mathbf{\varepsilon}- \mathbf{\varepsilon}_{res}) }[/math]

where C is stiffness tensor for the underlying orthotopic material and D is an anisotropic 4^th rank damage tensor appropriate for damage in orthotropic materials, and [math]\displaystyle{ \mathbf{\varepsilon}_{res} }[/math] is any residual strain (such as thermal or solvent induced strains).

The MPM implementation of softening isotropic materials is described in Nairn, Hammerquist, and Aimene. The extension to orthotropic materials is described in a paper on generalized damage mechanics methods.

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