Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials

0507079 - ÚTIA 2020 RIV FR eng J - Journal Article
Doskar, M. - Zeman, Jan - Jaruskova, D. - Novák, J.
Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials.
European Journal of Mechanics A-Solids. Roč. 70, č. 1 (2018), s. 280-295. ISSN 0997-7538. E-ISSN 1873-7285
R&D Projects: GA ČR GA17-04301S
Institutional support: RVO:67985556
Keywords : Wang tiling * Numerical homogenization * Representative Volume Element size
OECD category: Statistics and probability
Impact factor: 2.931, year: 2018
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/MTR/zeman-0507079.pdf https://www.sciencedirect.com/science/article/pii/S0997753817305673

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.
Permanent Link: http://hdl.handle.net/11104/0298166