Non-local energetics of random heterogeneous lattices

作者：Zeman Jan^*; Peerlings Ron H J; Geers Marc G D

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

DOI：10.1016/j.jmps.2011.03.006

• Inhomogeneous material
• Structures
• Energy methods
• Probability and statistics
• Hashin-Shtrikman-Willis variational principles

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 (2005) [Journal of the Mechanics anti Physics of Solids 53, 1505-1522], 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.

• 出版日期2011-6