Hypo‐Elasticity with Internal Variables and Derived Failure Condition

Abstract

AbstractA hypo‐elastic material with internal variables is proposed. The constitutive equations are composed of two types: the stress rate is a function for stress, stretching, and internal variables, and linear in stretching, and the evolutional equations with respect to scalar, vector, and symmetric tensor internal variables. By the requirement that all of the internal variables were vanished at a time, the vector variables can be eliminated. The failure criterion and the failure stretching are defined, respectively, by the singularity condition and the null space of the response function for stress rate. Then the failure depending on the internal variables may be supposed to show the work‐hardening plasticity. The following three constitutive assumptions are adopted: pressure‐insensitive, free of generalized Bauschinger effect, and of grade two. Two special cases are proposed: one is the Prandtl‐Reuss body with a scalar internal variable, and another is the T body with a tensor internal variable.