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

A new non-linear mathematical model of type-II thermoelastic continuum with fine microstructure is developed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-vectors and d-tensors, playing role of extra field variables. A Lagrangian density for type-II thermoelastic continuum with fine microstructure is given and the least action principle is formulated. Virtual microstructural inertia is added to the considered action density. Corresponding 4-covariant field equations of type-II thermoelasticity are derived. Constitutive equations of type-II microstructural thermoelasticity are discussed. Variational symmetries of the thermoelastic action are used to formulate covariant conservation laws in a plane spacetime. Following the usual procedure for type-II micropolar thermoelastic 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.