<KINEMATIC> aniso_nonlinear

Description

This kinematic model implements anisotropic coefficients into a KINEMATIC behavior object. Note that this model does not include the 1.5 term in the modulus coefficients, so there are none in the evolution. The coefficients are to be entered into COEFFICIENT_MATRIX objects.

(443)\[\begin{split}\begin{aligned} &\ten m_{kin} = \ten n - \bf D\bf C^{-1}\bf X \\ &\ten \omega_{kin} = \bf C^{-1} \xi \bf Q:\bf X \left( \frac{\|\bf X\|_Q}{M} \right)^m \end{aligned}\end{split}\]

Any of the coefficients can of course be a function or table of the temperature, or other parameter.

The equivalent term \(\|\bf X\|_Q\) above is calculated as follows:

(444)\[\|\bf X\|_Q = \left[ \bf X:\bf Q:\bf X \right]^{1/2}\]

Syntax

**kinematic aniso_nonlinear [ name ] \(~\,~\,\) C <COEFFICIENT_MATRIX> \(~\,~\,\) D <COEFFICIENT_MATRIX> \(~\,\) [ xi <COEFFICIENT> ] % defines recovery exists \(~\,\) [ Q <COEFFICIENT_MATRIX> ] % overrides global \(~\,\) [ m <COEFFICIENT> ] % ditto \(~\,\) [ M <COEFFICIENT> ]

Example

*kinematic aniso_nonlinear  x1
    C  cubic C1111 20000.0 % 30000.0/1.5
             C1122 0.0
             C1212 20000.0
    D  cubic
       D1111 500.
       D1122 0.0
       D1212 500.