<DIRECT_KINEMATIC> asaro

Description

This kinematic hardening model provides nonlinear modulus behavior forming a hysteresis loop with slight S shape. Normally this kinematic type would be combined with other linear and nonlinear hardenings to fine tune cyclic behavior.

(386)\[\begin{split}\begin{aligned} &\alpha_{eq} = \left[\dfrac{3}{2}\ten \alpha:\ten \alpha \right]^{1/2} \\ &\ten X_i = \frac{C~\tanh(D\,\alpha_{eq})}{D\,\alpha_{eq}} \ten{\alpha}_i \\ &\dot{\ten{\alpha}}_i = \dot{\lambda}\ten n \end{aligned}\end{split}\]

Syntax

The basic input syntax here is:

*kinematic asaro name [ C coef-value ] [ D coef-value ] [ M coef-value ] [ m coef-value ]

Example

The following example shows the use of this kinematic model in combination with a number of other kinematic hardenings, with the separate terms plotted below.

***behavior gen_evp
 **elasticity isotropic
   young 69000.00
   poisson 0.3
 **potential gen_evp2 ev
  *store_all
  *criterion mises
  *isotropic nonlinear
    R0 340.0
    b  900.0
    Q -210.0
  *kinematic nonlinear 1_
    C  187500.
    D  1250.0
  *kinematic armstrong_frederick 2_
    C  11250.0
    D  150.0
  *kinematic linear    3_
    C  1000.0
  *kinematic asaro     4_
    C  56250.0
    D  750.0
***return