Microstructural enrichment functions based on stochastic Wang tilings

Details Microstructural enrichment functions based on stochastic Wang tilings Microstructural enrichment functions based on stochastic Wang tilings

2011-10-19

arxiv.org/abs/1110.4183v1

Physics

Condensed Matter

Materials Science

23 pages, 12 figures

Scientific paper

This paper presents a new approach to determining 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 tiling 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, thereby circumventing the need for simulations of large heterogeneous bodies. Feasibility of the proposed methodology is demonstrated on local constructions of the stress fields in two-dimensional particulate media.

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