orthogonality, plasticity, creep, balance equation, heat transfer, thermoelasticity, metamaterial.

The present study is devoted to formulations of constitutive equations for dissipative continua. The consistence of the principle of thermomechanical orthogonality and deformation processes is assumed. The application of orthogonality principle is physically and geometrically reasonable for simulation problems of plasticity, creep, elasticity and thermoconductivity.

Consequent applying of orthogonality principle and Furie’s and Fick’s laws for derivation of constitutive equations in heat and mass transfer leads to conventional equations of thermoconductivity and diffusion. The Murnaghan constitutive equations in elasticity can be obtain by the principle of thermomechanical orthogonality. This principle in the frameworks of mathematical plasticity theory akin to R. von Mises. The principle manifestation for plastic solids provides the convexity of yield surface and satisfaction of associated plastic flow rule. It should be noted that the creep and plastic potentials are need to be conjugated for coupled deformation processes. The procedure of constitutive equations derivations in frameworks of plastic flow, creep, coupled thermoelasticity, type-III thermoconductivity are discussed at present study as an example of the thermomechanical orthogonality principle application.

Kovalev Vladimir Alexandrovich,

e-mail: vlad_koval@mail.ru, Dr. Sci. Phys. & Math., Professor, Moscow City University of Management, Moscow, Russia.

Murashkin Evgenii Valeryevich,

e-mail: murashkin@ipmnet.ru, Cand. Sci. Phys. & Math., Senior Researcher, Institute for Problems in Mechanics of RAS, Moscow, Russia.