Microstructural enrichment functions based on stochastic Wang tilings

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.

27 pages, 12 figures; v2: completely re-written after the first review

References in corpus (4)

• Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
• Compressing Random Microstructures via Stochastic Wang Tilings
• A micromechanics-enhanced finite element formulation for modelling heterogeneous materials
• Effective-medium theory for infinite-contrast, 2D-periodic, linear composites with strongly anisotropic matrix behavior: dilute limit and cross-over behavior

Cited by in corpus (7)

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• Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials
• Level-set based design of Wang tiles for modelling complex microstructures
• Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method