BETA_TFA

Description

This object class is used for specifying the evolution laws of \(\ten{\beta}\) variable. This variable has the dimension of a strain and is to be considered as an internal variable in each sub-volume.

The following types of evolution laws of \(\ten{\beta}\) variable may be chosen:

CODE	DESCRIPTION
beta_d	\(\displaystyle{\boldsymbol{\dot \beta_s} = \boldsymbol{\dot \epsilon^p_s} - D_s \dot p_s \boldsymbol{\beta_s} - \frac{\det(\boldsymbol{\dot \epsilon^p_s}) \,\,\boldsymbol{P}}{\dot p_s^2} \boldsymbol{I}}\)
beta_matrix	\(\displaystyle{\boldsymbol{\dot \beta_s} = \boldsymbol{\dot \epsilon^p_s} - D_s \dot p_s \boldsymbol{S}_s:\boldsymbol{\beta_s}}\)
kroner	\(\displaystyle{\boldsymbol{\dot \beta_s} = \boldsymbol{\dot \epsilon^p_s}}\)
delta	\(\displaystyle{\boldsymbol{\dot \beta_s} = \boldsymbol{\dot \epsilon^p_s} - D \dot p_s (\boldsymbol{\beta_s} - \delta \boldsymbol{\epsilon^p_s}) - \frac{\det(\boldsymbol{\dot \epsilon^p_s})\,\, \boldsymbol{P}}{\dot p_s^2} \boldsymbol{I}}\)
free	\(\displaystyle{\boldsymbol{\dot \beta_s} = \boldsymbol{\dot \epsilon^p_s} - C_b \dot p_s \boldsymbol{\beta_s} + \frac{\det(\boldsymbol{\dot \epsilon^p_s}) C_{e3}}{\dot p_s^2} \boldsymbol{I}}\)

where \(\det(A)\) represents the determinant of a matrix A. \(\boldsymbol{P}\) is the extreme pressure and \(\dot p_s\) is the rate of accumulated plastic strain \(\displaystyle{\dot p_s = \sqrt{\frac{2}{3}(\boldsymbol{\dot \epsilon^p_s}:\boldsymbol{\dot \epsilon^p_s)}}}\).

Syntax

The syntax for a BETA\(\_\)TFA object requires that a name of the sub-volume must be given, followed by the type and whatever coefficients are allowed for the corresponding model.

beta_d

**beta  name beta_d \(~\,~\,\) D <double> \(~\,\) [ pressure <double> ]

beta_matrix

**beta  name beta_matrix double \(~\,~\,\) poisson <double> \(~\,~\,\) ratio <double>

kroner

**beta  name kroner

delta

**beta  name delta \(~\,~\,\) D <double> \(~\,~\,\) delta <double> \(~\,~\,\) [ pressure <double> ]

free

**beta  name free \(~\,~\,\) Ce3 <double> \(~\,~\,\) Cb <double>