Semicontinuity theorem in the micropolar elasticity

Abstract

Abstract. In this paper we investigate the equivalence of the sequential weak lower semicontinuity of the total energy functional and the quasiconvexity of the stored energy function of the nonlinear micropolar elasticity. Based on techniques of Acerbi and Fusco [Arch. Rational Mech. Anal. 86 (1984)

Exact Solution for Lord-Shulman Generalized Coupled Thermoporoelasticity in Cylindrical Coordinates

“…From (38)- (40), the constants U k , F k , and W k can be obtained. The stress components can be evaluated by substituting (36) into (15) and (18), and then into (19).…”

“…By comparing (30) and (40), it is found that e à ij j ð Þ in (40) denote the densities in j-space of the amplitude. From (40), the displacements due to the eigenstrains may be expressed as…”

“…In the similar way, we neglect the terms due to micropolar effects in (39,40) to arrive Eshelby tensors for microelongation. Then, we find …”

“…The initial conditions (7) are considered only for the general solutions (40) and the initial conditions of G 1n ðtÞ to G 6n ðtÞ for the particular solutions are considered equal to zero. Here, G 1n ðtÞ to G 6n ðtÞ are calculated.…”

“…For related work on existence theorems in the case where coercivity is postulated from the beginning as a constitutive assumption, we refer the reader to [18,39,40]. In addition, coercivity turns out to be a delicate problem related to the possible fracture of the material.…”