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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2015 Volume 15, Issue 4, Pages 451–461 (Mi isu613)

This article is cited in 2 papers

Mechanics

Micropolar thermoelastic continuum models with constrained microstructural parameters

V. A. Kovaleva, Yu. N. Radayevb

a Moscow City Government University of Management, 28, Sretenka st., 107045, Moscow, Russia
b Institute for Problems in Mechanics of RAS, 101, Vernadskogo ave., 119526, Moscow, Russia

Abstract: A new micropolar thermoelastic continuum model forrmulated by microstructural $d$-vectors and $d$-tensors of an arbitrary ranks is proposed. The microstructural vectorial and tensorial extra-field variables are restricted by holonomic or non-holonomic (differential) constraints. The study is carried out in the framework of the Lagrange field formalism as a $4$covariant field theory. Taking into consideration of holonomic or differential constraints involving microstructural parameters implies problem formulation as a problem of calculus of variations with constraints, namely as the variational Lagrange problem. The Lagrange multipliers technique is employed for derivation of field equations when microstructural parameters are restricted by the two types of constraints. Micropolar thermoelastic continuum model for the case of rigid rotations of the micropolar trihedron is considered as an example.

Key words: thermoelasticity, microstructure, micropolar continuum, field, action, $d$-tensor, constraint, Lagrange multiplier.

UDC: 539.374

DOI: 10.18500/1816-9791-2015-15-4-451-461



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