<DIRECT_KINEMATIC> non_symmetric#

Description#

This kinematic hardening model provides asymmetric behavior between tension and compression as recommended for cast iron materials [M7, M8].

This model takes the tensile coefficients for computing \(\ten X_i\) if the trace of the actual stress \(\ten 1:\ten \sigma\) is greater than the I1_trans value. The evolution is therefore:

(387)#\[\begin{split}\begin{aligned} &\dot{\boldsymbol{\alpha}_i}=\dot{\lambda}\left[\ten n - \frac{3}{2}\frac{D^*}{C^*}\ten X_i\right] \qquad \text{if}~ {\tt use\_alpha}~ \text{is set} \\ &\dot{\ten X_i} = C^* \dot{\lambda}\left[\ten n - \frac{3}{2}\frac{D^*}{C^*}\ten X_i\right] \qquad \text{if}~ {\tt use\_x}~\text{is set} \\ \end{aligned}\end{split}\]

where the coefficients \(C^*\) and \(D^*\) are either \(C_t\),\(D_t\) or \(C_c\),\(D_c\) depending on the above check on the stress. Note that in the use_x case the evolution is not the complete derivative where the terms involving the change in \(C^*\) with temperature are not taken into account.

Syntax#

The basic input syntax here is:

*kinematic non_symmetric [ I1_trans coef-value ] [ Ct coef-value ] [ Cc coef-value ] [ Dc coef-value ] [ Dc coef-value ] [ M coef-value ] [ m coef-value ] [ use_x | use_alpha ]

Only one choice of use_x or use_alpha can be used (default is use_x). The default value of I1_trans is 0. The coefficients M and m are the standard Norton-like static recovery coefficients.

Example#

The following example shows the use of this kinematic model in combination with the cast_iron yield criterion.

***behavior gen_evp
 **elasticity isotropic
   young 126000.
   poisson 0.265
 **potential gen_evp2 ev
   *criterion cast_iron
     ratio 3.
     associated 1
   *kinematic non_symmetric  x1
       I1_trans 50.
       Ct 300000.0
       Dt   5000.0
       Cc  30000.0
       Dc    500.0
   *isotropic constant
       R0 100.0
***return
../../_images/cast.svg