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Asymptotic analysis of a coupled system of nonlocal equations with oscillatory coefficients. (English) Zbl 1453.35018

Summary: In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous media that additionally accounts for short-range forces. We consider the vanishing nonlocality limit on the same length scale as the heterogeneity and show that the system’s effective behavior is characterized by a coupled system of local equations that are elliptic in the sense of Legendre-Hadamard. This effective system is characterized by a fourth-order tensor that shares properties with Cauchy elasticity tensors that appear in the classical equilibrium equations for linearized elasticity.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35R09 Integro-partial differential equations
74Q05 Homogenization in equilibrium problems of solid mechanics
35J47 Second-order elliptic systems
35L53 Initial-boundary value problems for second-order hyperbolic systems
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References:

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