Constitutive Equations with Dissipative Stresses

Abstract

A new class of constitutive equations for complex loading processes is obtained. It has three state functionals. A new method of mathematical modeling and mathematical principle is formulated. According to them, physically correct equations of state are changed by introducing gyroscopic terms that do not perform mechanical work. The constitutive equations of complex loading processes with two state functionals under conditions of force and kinematic loading are constructed. Their connection with the Il’yushin formula and modern theories of plastic flow is obtained. A mathematical model of the domain mechanism of plasticity is formulated. It represents a real deformable continuum as a mixture of an elastoplastic continuum and a Cosserat continuum—flat veinlets (domains of plastic deformation that are the zones of large relative rotations). A physical justification for the inclusion of the asymmetric part of the stress and rotation tensor in the composition of the thermodynamic parameters of the model is given.