<CRITERION> cast_iron

Description

This criterion provides asymmetric tension/compression behavior which is suggested for cast iron modeling [M9, M10]. In general this model would be used with behavior gen_evp potential gen_evp2 and includes one or more non_symmetric kinematic hardening terms (and possibly others as well).

You can have either isotropic hardening scaling both the compressive and tensile behavior (with a given ratio relating them), or use isotropic hardening in only the tensile, or only the compressive with extra coefficients given for the non-hardening one. Probably the calling application requires that an R be given, so defining both Rt and Rc is not allowed.

\[\begin{split}\begin{aligned} &R_c = {\tt ratio}~R\qquad & R_t = R &{\rm \quad if~ {\tt ratio} \quad is entered} \\ &R_c = {\tt Rc} & R_t = R &{\rm \quad if ~ {\tt Rc} \quad is entered} \\ &R_c = R & R_t = {\tt Rt} &{\rm \quad if ~ {\tt Rt} \quad is entered} \\ \end{aligned}\end{split}\]

The different tension and compression yield values \(R_c\) and \(R_t\) are applied to two distinct different yield functions as follows.

\[\begin{split}\begin{aligned} &F_1 = \left[\dfrac{3}{2}\ten s:\ten s + \hbox{Tr}(\ten \sigma)(R_c-R_t) \right]^{1/2} - (R_c R_t)^{1/2} \\ &F_2 = \left[\dfrac{3}{2}\ten s:\ten s \right]^{1/2} - R_c \\ \end{aligned}\end{split}\]

The transition from the tension yield \(F_1\) to the compression yield \(F_2\) is determined if the trace of the effective stress \(\ten \sigma - \sum \ten X\) is less than \(-R_c\). See the section for the non_symmetric direct kinematic model for a demonstration of the model’s effect.

Syntax

The basic input syntax here is:

*criterion cast_iron [ ratio value ] [ Rc value ] [ Rt value ] [ associated 0 | 1 ]

Only one choice of ratio Rc or Rt may be given as described above. If the associated is set to 1, the \(F_1\) yield function will be used all the time. The default is associated behavior.

Example

*criterion cast_iron
  ratio 3.
  associated 1