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

A canonical non-linear mathematical model of type-II (GN II) thermoelastic (TE) continuum with fine microstructure is discussed. The model is presented in terms of the canonical 4-covariant field theoretical formalism. The fine microstructure of the thermoelastic continuum is determined by d-vectors and d-tensors thus playing role of extra field variables. By virtue of proposed action density for type-II TE continuum with fine microstructure the least action principle is formulated. Virtual microstructural inertia is added to the action density. Corresponding 4-covariant field equations of type-II thermoelasticity are obtained. Constitutive equations of type-II microstructural thermoelasticity are discussed. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws. Following the usual procedure for type-II micropolar TE Lagrangians functionally independent rotationally invariant arguments are obtained. A formal proof of the completness of the system of rotationally invariant arguments is given. An alternative approach of constructuing a complete system of independent rotationally invariant arguments is discussed. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extra strain vectors and tensors.

Kovalev Vladimir Alexandrovich

e-mail: vlad_koval@mail.ru, DSc. (Phys.&Math.), Prof., Moscow City University of Management of Moscow Government, Moscow, Russia.

Radayev Yuri Nikolayevich

e-mail: radayev@ipmnet.ru, y.radayev@gmail.com, Leading Researcher, DSc., Prof., Institute for Problems in Mechanics of RAS, Moscow, Russia.