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This article is cited in 1 scientific paper (total in 1 paper)
Mechanics of Solids
On frame indifferent Lagrangians of micropolar thermoelastic continuum
V. A. Kovaleva, Yu. N. Radayevb a Moscow City Government University of Management Moscow, Moscow, 107045, Russian Federation
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
A 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 attributed to field theories of continuum mechanics. Fine microstructure is introduced by $d$-vectors and tensors playing role of extra field variables. A Lagrangian density for type-II thermoelastic continuum with fine microstructure is proposed and the least action principle is formulated. Virtual microstructural inertia is added to the considered action density. It is also valid for the thermal inertia. Corresponding $4$-covariant field equations of type-II thermoelasticity are obtained. Constitutive equations of type-II microstructural thermoelasticity are discussed. Following the usual procedure for type-II micropolar thermoelastic Lagrangians functionally independent rotationally invariant arguments are obtained. Those are proved to form a complete set. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extrastrain vectors and tensors.
Keywords:
thermoelasticity, microstructure, action, thermodynamical basis, rotational invariance, frame indifference principle, extrastrain tensor, constitutive equation.
Original article submitted 25/II/2015 revision submitted – 11/III/2015
Citation:
V. A. Kovalev, Yu. N. Radayev, “On frame indifferent Lagrangians of micropolar thermoelastic continuum”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:2 (2015), 325–340
Linking options:
https://www.mathnet.ru/eng/vsgtu1413 https://www.mathnet.ru/eng/vsgtu/v219/i2/p325
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