Non-local energetics of random heterogeneous lattices

Details Non-local energetics of random heterogeneous lattices Non-local energetics of random heterogeneous lattices

2010-03-16

arxiv.org/abs/1003.3248v2

Journal of the Mechanics and Physics of Solids, 59 (6), 1214-1230, (2011)

Physics

Condensed Matter

Materials Science

32 pages, 8 figures

Scientific paper

10.1016/j.jmps.2011.03.006

In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in (Luciano and Willis, Journal of the Mechanics and Physics of Solids 53, 1505-1522, 2005), energetic bounds and estimates of the Hashin-Shtrikman-Willis type are developed for discrete systems with a heterogeneity distribution quantified by second-order spatial statistics. As illustrated by three numerical case studies, the resulting expressions for the ensemble average of the potential energy are fully explicit, computationally feasible and free of adjustable parameters. Moreover, the comparison with reference Monte-Carlo simulations confirms a notable improvement in accuracy with respect to approaches based solely on the first-order statistics.

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