Microstructural enrichment functions based on stochastic Wang tilings

TL;DR

This paper introduces a novel method for creating microstructural enrichment functions using stochastic Wang tilings, enabling efficient modeling of non-periodic heterogeneous materials in finite element schemes.

Contribution

It develops a new approach leveraging aperiodic Wang tilings to generate microstructure-mimicking enrichment functions with minimal computational cost.

Findings

Successfully constructed stress enrichment functions for 2D particulate media.

Demonstrated the method's ability to produce non-periodic, morphologically similar microstructures.

Validated the approach's feasibility for complex heterogeneous materials.

Abstract

This paper presents an approach to constructing microstructural enrichment functions to local fields in non-periodic heterogeneous materials with applications in Partition of Unity and Hybrid Finite Element schemes. It is based on a concept of aperiodic tilings by the Wang tiles, designed to produce microstructures morphologically similar to original media and enrichment functions that satisfy the underlying governing equations. An appealing feature of this approach is that the enrichment functions are defined only on a small set of square tiles and extended to larger domains by an inexpensive stochastic tiling algorithm in a non-periodic manner. Feasibility of the proposed methodology is demonstrated on constructions of stress enrichment functions for two-dimensional mono-disperse particulate media.