Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials
arXiv:1709.05926 · doi:10.1016/j.euromechsol.2017.12.002
Abstract
Wang tile based representation of a heterogeneous material facilitates fast synthesis of non-periodic microstructure realizations. In this paper, we apply the tiling approach in numerical homogenization to determine the Representative Volume Element size related to the user-defined significance level and the discrepancy between bounds on the apparent properties. First, the tiling concept is employed to efficiently generate arbitrarily large, statistically consistent realizations of investigated microstructures. Second, benefiting from the regular structure inherent to the tiling concept, the Partition theorem, and statistical sampling, we construct confidence intervals of the apparent properties related to the size of a microstructure specimen. Based on the interval width and the upper and lower bounds on the apparent properties, we adaptively generate additional microstructure realizations in order to arrive at an RVE satisfying the prescribed tolerance. The methodology is illustrated with the homogenization of thermo-mechanical properties of three two-dimensional microstructure models: a microstructure with mono-disperse elliptic inclusions, foam, and sandstone.
19 pages, 22 figures, post-print version
References in corpus (5)
- Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
- Power-law cosmic expansion in f(R) gravity models
- Compressing Random Microstructures via Stochastic Wang Tilings
- Aperiodic compression and reconstruction of real world material systems based on Wang tiles
- A jigsaw puzzle framework for homogenization of high porosity foams
Cited by in corpus (10)
- Modular-topology optimization of structures and mechanisms with free material design and clustering
- Extracting Geometry and Topology of Orange Pericarps for the Design of Bioinspired Energy Absorbing Materials
- A jigsaw puzzle metamaterial concept
- Modular-topology optimization with Wang tilings: An application to truss structures
- Convergence and Error Analysis of FE-HMM/FE for Energetically Consistent Micro-Coupling Conditions in Linear Elastic Solids
- Wang tiles enable combinatorial design and robot-assisted manufacturing of modular mechanical metamaterials
- Level-set based design of Wang tiles for modelling complex microstructures
- On the generation of periodic discrete structures with identical two-point correlation
- On bounded Wang tilings
- Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method