thermoelasticity, microstructure, field, extra field, action, covariance, conservation law,rnd-tensor, 4-current, energy–momentum tensor, kinematic constraint, Lagrange multiplier, rotation,rnframe indifference principle, extrastrain tensor

A new non-linear mathematical model of type-II thermoelastic continuum with finernmicrostructure is developed. The model is described in terms of 4-covariant field theoreticalrnformalism. Fine microstructure is represented by d-vectors and d-tensors, playing role of extrarnfield variables. A Lagrangian density for type-II thermoelastic continuum with fine microstructurernis given and the least action principle is formulated. Virtual microstructural inertia is added to thernconsidered action density. Corresponding 4-covariant field equations of type-II thermoelasticityrnare derived. Constitutive equations of type-II microstructural thermoelasticity are discussed.rnVariational symmetries of the thermoelastic action are used to formulate covariant conservationrnlaws in a plane spacetime. Following the usual procedure for type-II micropolar thermoelasticrnLagrangians functionally independent rotationally invariant arguments are obtained. A formalrnproof of the completness of the system of rotationally invariant arguments is given. An alternativernapproach of constructuing a complete system of independent rotationally invariant arguments isrndiscussed. Objective forms of the Lagrangians satisfying the frame indifference principle are given.rnThose are derived by using extra strain vectors and tensors.

Kovalev, Vladimir Aleksandrovich

Dr. Sci. Phys. & Math., Professor, Moscow City Government University of Management, Moscow

Radayev, Yuri Nickolaevich

Dr. Sci. Phys. & Math., Professor, Leading Researcher, Institute for Problems in Mechanics of RAS, Moscow