general_tfa

Description

This material model implements a Transformation Field Analysis (TFA), which is a multi-material multi-scale model [M4]. Here the macroscopic stress or strain is localized into a number of sub-phases or sub-volumes \(s\), according to a localization scheme chosen by the user. Locally, this method integrates an eigenstrain, which is the strain measure of mismatch between subphases. Finally, the relevant quantities are homogeneized in a manner consistent with the selected localization scheme.

The special characteristic of this method is that the tensors of elasticity that are used in the localization step are kept constant after the start of the analysis, whereas all changes in moduli caused by (for instance) temperature changes or damage evolution are incorporated into the eigenstrain rule. With this, methods such as the self-consistent scheme, become computationally feasible, because the iterative localization solution does not have to be computed at each evaluation of the material law. For implicit integration, the model also provides a global consistent tangent matrix, and each sub-material has a consistant tangent as well.

Normally all mechanical ***behavior models can be used in this multi-mat model, including other multi-mat models themselves.

with \(\bf gamma_s\) being the “formal eigenstrain” and \(\bf xi_s\) is a constitutive correction term. The formal eigenstrain is simply found from the following definition: where \(\tilde{\bf L}_s\) is the current linear elastic modulus (possibly modified by damage, temperature or other parameter changes, etc), \(\bf L_s\) an effective fixed modulus tensor, \(\ten \varepsilon_s\) the total (observable) strain of phase \(s\), and \(\ten \sigma_s\) the value of the uniform stress acting on the material in phase or location \(s\). Inherent in

Syntax

***behavior general_tfa

Example

***behavior general_tfa
  **material 0.4 p
   *file mat3_tfa_tm.inp 2
   *integration theta_method_a 1.0 1.e-9 100
  **material 0.4 d
   *file mat3_tfa_tm.inp 3
  **material 0.2 e
   *file ../MAT/elastic
  **localization voigt
***return