voigt/voigt_fs

This behavior provides the Voigt/Taylor homogenization scheme, applied to multi-phase or multi-constituent heterogeneous materials. This model, which is also referred to as the uniform strain model, assumes a uniform total strain field among each sub-volume and the homogeneous macroscopic medium:

(587)\[\begin{split}\begin{aligned} \boldsymbol{E} & = & \boldsymbol{\epsilon}_1= \boldsymbol{\epsilon}_2 = \ldots = \boldsymbol{\epsilon}_n \nonumber\\ \\\boldsymbol{\Sigma} & = & f_1 \boldsymbol{\sigma}_1 + f_2 \boldsymbol{\sigma}_2 + \ldots + f_n \boldsymbol{\sigma}_n \nonumber \end{aligned}\end{split}\]

where \(\boldsymbol{E}\) and \(\boldsymbol{\Sigma}\) are respectively the macroscopic strain and stress tensors. \(\boldsymbol{\epsilon}_i\) and \(\boldsymbol{\sigma}_i\) are respectively the local total strain and stress in the sub-volume \(i\). The volume fraction of sub-volume \(i\) is denoted by \(f_i\) and \(n\) is the number of sub-volumes.

Syntax

***behavior voigt \(~\,\) **material  volume_fraction name |   **material_in_file <file> *file file_name \(~\,\) [ *integration method ] \(~\,\) [ *rotation ROTATION ] | [ *rotation_list <ROTATION> ] \(~\,\) [ *volume_fraction_file <file> ] \(~\,~\,\) *material etc … ***return

Example

***behavior voigt
%%%%%%%%%% Large deformation %%%%%%%%%%
%***behavior voigt_fs
%For the large deformation, the keyword "voigt\_fs" must be used instead of "voigt".
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 **material 0.5  m1
  *file voigt_elas2.inp 2
 **material 0.5 m2
  *file voigt_elas2.inp 3
 ***return

***behavior linear_elastic
 **elasticity young 200000. poisson 0.3
***return
***behavior linear_elastic
 **elasticity young 100000. poisson 0.3
***return