Monday, 18 November, 2013
SPEAKER: Prof. Tadele Mengesha, Penn State University
TITLE: "Multiscale analysis of a linearized peridynamic solid"
ABSTRACT: I will present a recent work on the homogenization of a nonlocal continuum model of a deformation of a heterogeneous solid. The model involves a multiscale nonlocal interaction in the form of long range forces with highly oscillatory (periodic) perturbations that represent the presence of heterogeneity on a smaller spatial length scale. The method of two-scale convergence is applied to establish homogenized nonlocal systems for the multiscale linear steady state variational problem as well as the system of nonlocal equations of motion. After proving some regularity results for solution of the homogenized nonlocal equation, we demonstrate a strong approximation of the actual field via a scaling of the two-scale homogenized solution.