On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization

TL;DR

This paper introduces efficient algorithms for generating representative volume elements (RVEs) with spherical and cylindrical inclusions, enhancing stochastic homogenization analysis of composite materials.

Contribution

It presents two explicit methods for RVE generation based on Random Sequential Adsorption and Molecular Dynamics, optimized for different inclusion densities.

Findings

Random Sequential Adsorption is efficient for low volume fractions.

Molecular Dynamics allows denser RVE configurations.

Algorithms are explicitly provided for direct implementation.

Abstract

In this paper we describe efficient methods of generation of representative volume elements (RVEs) suitable for producing the samples for analysis of effective properties of composite materials via and for stochastic homogenization. We are interested in composites reinforced by a mixture of spherical and cylindrical inclusions. For these geometries we give explicit conditions of intersection in a convenient form for verification. Based on those conditions we present two methods to generate RVEs: one is based on the Random Sequential Adsorption scheme, the other one on the time driven Molecular Dynamics. We test the efficiency of these methods and show that the first one is extremely powerful for low volume fraction of inclusions, while the second one allows us to construct denser configurations. All the algorithms are given explicitly so they can be implemented directly.