Communications in Mathematical Sciences
Volume 13 (2015)
Multiscale analysis of linearized peridynamics
Pages: 1193 – 1218
In this paper, we study the asymptotic behavior of a state-based multiscale heterogeneous peridynamic model. The model involves nonlocal interaction forces with highly oscillatory perturbations representing the presence of heterogeneities on a finer spatial length scale. The two-scale convergence theory is established for a steady state variational problem associated with the multiscale linear model. We also examine the regularity of the limit nonlocal equation and present the strong approximation to the solution of the peridynamic model via a suitably scaled two-scale limit.
multiscale analysis, peridynamics, nonlocal equations, elasticity, Navier equation, homogenization, heterogeneous materials, two-scale convergence
2010 Mathematics Subject Classification
45F99, 45P05, 74E05, 74H10, 74Q05