A Variational Approach to Non-Local Energy Minimization of Random Elastic Lattices

摘要

The purpose of this paper is to establish variational principles for the mechanical behaviorrnof two-phase random elastic lattices. By restricting the attention to the systemsrncharacterized by second-order statistics, the variational bounds on the stored energy ofrnthe Hashin-Shtrikman-Willis type are established using basic tools of structural staticsrnand linear algebra. Accuracy of the improved bounds is verified against elementaryrnestimates as well as detailed Monte-Carlo simulations. Finally, selected numericalrnresults related to the accuracy of the bounds are presented.