Wang tiling for particle heterogeneous materials: Algorithms for generation of tiles/cubes via molecular dynamics

David Šedlbauer,Matěj Lepš

doi:10.24132/acm.2019.537

Abstract

This paper aims at a reduction of periodicity artefacts during a generation of random heterogeneous material models. The traditional concept of the Periodic Unit Cell is compared with a novel approach of the stochastic Wang tiling. Since modelled structures consist of hard circular/spherical particles in a matrix, the algorithm for placement of inclusions is based on the modified molecular dynamics. We introduce two types of Wang tile boundary conditions to decrease periodicity artefacts. Tested samples for 2D applications form sets of both monodisperse and polydisperse microstructures. The overall volume fractions of these samples are approximately 0.2, 0.4, and 0.6, respectively. The generated sets are analysed both visually and statistically via a two-point probability function. An extension of the stochastic Wang tiling enables to create 3D structures, as well. Therefore, artificial periodicity is also investigated on a 3D sample consisting of spherical particles of identical radii distributed in a continuous phase.

Highlights

The most of real-world materials can be considered as heterogeneous at least on the micro or nanoscale level
The present paper aims at modelling of random heterogeneous material samples composed of discrete hard circular or spherical particles in a matrix
If we focus on the secondary extremes of the probability function, we gain a considerable reduction in the Wang tiling case compared to the Periodic Unit Cell (PUC) one

Summary

Introduction

The most of real-world materials can be considered as heterogeneous (composed of different materials or the same material in different states [29]) at least on the micro or nanoscale level. The homogenisation approaches together with the concepts of the Periodic Unit Cell (PUC) or the Statistically Equivalent Periodic Unit Cell (SEPUC) [15] or [28], and the Representative Volume Element (RVE) [10, 20, 24] or [1], are applied to determine the effective properties at higher microstructure levels. The above methods can be used for both tasks of reconstruction and compression of the random heterogeneous materials. We do not avoid the loss of information about the randomness of the domain, thereby characteristics or properties of the material samples are distorted. The generalized main advantage for such a tiling is the ability to create infinite random heterogeneous domains via a finite set of basic building blocks – Wang tiles

Objectives

Methods

Conclusion