<POTENTIAL> 2M1C

Description

The potential of type 2M1C exists for the particular case where there are two flow mechanisms which act under a single criterion. This model also allows interaction between the isotropic hardening variable and the kinematic back stresses. The model is particularly useful for accurate modeling of ratcheting phenomenon [M31].

\[f = \left[ f^2_{1} + f^2_{2} \right]^{0.5}\]

Syntax

**potential 2M1C [ name ] \(~\,\) *criterion mises_2m1c \(~\,\) [ A1 <COEFFICIENT> ] \(~\,\) [ A2 <COEFFICIENT> ] [ *flow <FLOW> ] [ *kinematic <KINEMATIC> [ name ] ] [ *isotropic <ISOTROPIC> ] [ *coefficient ] \(~\,\) [ C12 <COEFFICIENT> ] \(~\,\) [ a <COEFFICIENT> ] \(~\,\) [ beta <COEFFICIENT> ]

• The model requires giving mises_2m1c as a criterion type. This criterion will accept coefficients A1 and A2 (scalar) to simulate a localization process in each of the two mechanisms. In this case the stress equivalent terms in the criterion will be calculated as:

  \[f_i=J({\tt A}_i\ten s -\ten X_j)~~i=1,2\]

  with \(j\) kinematic hardenings in each mechanism.

• In the event that the isotropic hardening variable is coupled to the kinematic back stress (type nonlinear_bsi), the radius will be calculated with kinematic interaction as:

  \[R (\bf \alpha_{1}, \bf \alpha_{2}) = R_o - \frac{1}{3}kb(\bf \alpha_{1}+\bf \alpha_{2}):(\bf \alpha_{1}+\bf \alpha_{2}) + Q r\]

  A corresponding isotropic interaction is introduced into the kinematic hardening variable:

  \[{\bf X}_{i} = \frac{2}{3}[C_{ij}^o + k(1-br)]\bf \alpha_{j}~~~i,j=1,N\]

  where \(i\) are the mechanisms and \(j\) are the kinematic variables in each mechanism.

• The coefficients a and b indicate that we desire the calculation of the coefficients C for the kinematic hardening and C12 (kinematic interaction) for special forms of the interaction matrix (e.g. zero determinant)