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Abstract: In this paper, we study the mechanics of statistically non-uniform two-phaseelastic discrete structures. In particular, following the methodology proposedin Luciano and Willis, Journal of the Mechanics and Physics of Solids 53,1505-1522, 2005, energetic bounds and estimates of the Hashin-Shtrikman-Willistype are developed for discrete systems with a heterogeneity distributionquantified by second-order spatial statistics. As illustrated by threenumerical case studies, the resulting expressions for the ensemble average ofthe potential energy are fully explicit, computationally feasible and free ofadjustable parameters. Moreover, the comparison with reference Monte-Carlosimulations confirms a notable improvement in accuracy with respect toapproaches based solely on the first-order statistics.



Author: Jan Zeman, Ron H.J. Peerlings, Marc G.D. Geers

Source: https://arxiv.org/







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