Effective constitutive relations for inelastic composites / *V. I. Gorbachev.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 6. P. 37-42
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

The first special boundary value problem in the mechanics of deformable solids is considered to derive the effective constitutive relations for a heterogeneous inelastic solid. The problem is reduced to a number of auxiliary boundary value problems for functions dependent on the shape of a solid and the form of constitutive relations. In the case of a layer with nonuniform thickness, the problem of finding the effective constitutive relations is reduced to an operator equation whose solution is sought by an iterative method of successive approximations. An approximate analytical formula is proposed to find the effective constitutive relations for a laminated composite on the basis of known inelastic constitutive relations for its components. This approximate formula takes into account the character of structural anisotropy in a laminated composite and, in the elastic case, yields the exact values of the effective elastic modulus.

*Key words*:
mechanics of deformable solids, composite, inelasticity, effective constitutive relations.