1 research outputs found
Non-local energetics of random heterogeneous lattices
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.Comment: 32 pages, 8 figure