The present paper provides details on the new trends in application of asymptotic
homogenization techniques to the analysis of composite materials and thin-walled …

This book uses asymptotic methods to obtain simple approximate analytic solutions to
various problems within mechanics, notably wave processes in heterogeneous materials …

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized
ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of …

We study the effective conductivity of equal unidirectional infinite circular cylinders randomly
distributed in a uniform host (disks on the plane). The problem is reduced to a boundary …

Maxwell's approach to calculate the effective constants of composites is discussed in many
recent works. There are also various modifications such as effective medium approximations …

In the current work we examine the application of the stochastic finite element method
(SFEM) to the modeling of representative volume elements for heterogeneous materials …

The paper presents applications of a new theory of the representative volume element
(RVE) based on the Mityushev-Eisenstein-Rayleigh sums (M-sums) to describe particle …

In the current work we apply the stochastic version of the FEM to the homogenization of
magneto-elastic heterogeneous materials with random microstructure. The main aim of this …

Uncertainties in the macroscopic response of heterogeneous materials result from two
sources: the natural variability in the microstructure's geometry and the lack of sufficient …

The computationally most expensive part of stochastic FEM based homogenization is the
inversion of the stochastic stiffness matrix. Previously we studied different combinations of …