Aperiodic compression and reconstruction of real-world material systems based on Wang tiles

Abstract

The paper presents a concept to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a stochastic tiling algorithm. A substantial part of the study is devoted to the setup of optimal parameters of the automatic tile design by means of parametric studies with statistical descriptors at heart. The performance of the method is demonstrated on four two-dimensional two-phase target systems, monodisperse media with hard and soft disks, sandstone, and high porosity metallic foam.

Synthesized Enrichment Functions for Extended Finite Element Analyses With Fully Resolved Microstructure

“…This work supplements our previous results regarding efficient modelling of materials with stochastic heterogeneous microstructure, e.g., [3,4]. The microstructural geometry of a macro-scale model-as well as its finite element discretization-is synthesized using the Wang tiling concept, recalled in Section 2.…”

“…Procedures designed to compress a given microstructure into a SEPUC can be straightforwardly extended to take into account generalized periodicity occurring in the tiling concept, e.g., the standard optimization procedure based on minimizing discrepancy in the two-point probability function was used in [3]. We also adapted a sample-based approach originated in Computer Graphics in order to address the high computational cost of the optimization-based design [4]. Currently, a variety of material microstructures, ranging from particulate media to complex foam-like microstructures, can be represented with the framework of Wang tiling.…”

Microstructure synthesis using style-based generative adversarial networks

“…Also, the resulting artificial structure is regular while the natural materials mostly have random heterogeneous organization. There exists a modification of a single cell repetition, which is called Wang Tilings [7], and it overcomes the main drawback of PUC. It includes the following steps: sampling several pieces of the original structure; combining them via quilting procedure [5] to form a set of tiles; covering the plane with tiles randomly chosen from the prepared set.…”

Level-set Based Design of Wang Tiles for Modelling Complex Microstructures

“…However, the extension amplifies the major weakness of optimization approaches-their computational cost-making them prohibitively expensive for complex three-dimensional models. As a remedy, we have proposed a method motivated by Cohen et al [58] that combines a sample-based approach with quantitative spatial statistics [62]. While this method is by orders of magnitude faster than the optimization approach, it has difficulties handling complex, percolated microstructures such as foam, and produces corrupted ligaments in sample overlaps [45].…”