Finite strains and extrastrains of type-ii thermoelastic continuum with fine microstructure

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.