Carrying out homogenization in viscoelastic heterogeneous media taking into account the collective influence of boundaries

A. V. Mishin<sup>ab

a</sup> Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
^b Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, ul. Institutskaya 4/1, Novosibirsk 630090, Russia

Abstract: The effective coefficients of viscoelasticity of a heterogeneous medium are obtained on the basis of the generalized derivative formalism, which reflects the internal boundaries of a heterogeneous medium. A solution is sought for the averaged Green's function for the found modified operator, taking into account the averaging and subsequent analysis of the operator. The effective viscoelasticity coefficients integrally take into account the microstructure of the system (physical properties and characteristic phase sizes) in an explicit form, that is a consequence of the solution obtained, which expresses the solution of the many-body problem in a heterogeneous medium.

Keywords: heterogeneous medium, microstructure, transition layer, generalized derivative, Green's function, averaging, viscoelasticity. .

UDC: 539.3

Received: 06.07.2022
Revised: 16.09.2022
Accepted: 29.09.2022

DOI: 10.33048/SIBJIM.2023.26.109

 English version: Journal of Applied and Industrial Mathematics, 2023, 17:1, 131–137