A model of elastoplastic reinforcing media with a tensor damageability parameter

A method of constructing models of elastoplastic reinforcing media taking account on the accumulation of defects and plastic incompressibility is proposed. The accumulation of defects is described by a symmetric positive definite second-rank tensor which is included in the number of governing parameters. The model of elastoplastic reinforcing media is formulated in the form of two alternative systems of partial differential equations. One of them is based on the free energy approximation and the other is based on the Gibbs potential approximation. It is shown that these systems satisfy the Hadamard–Legendre condition and inequalities following from the second law of thermodynamics.