Abstract
Peridynamics is a nonlocal model in Continuum Mechanics, and in particular Elasticity, introduced by Silling (2000). The nonlocality is reflected in the fact that points at a finite distance exert a force upon each other. If, however, those points are more distant than a characteristic length called horizon, it is customary to assume that they do not interact. We work in the variational approach of time-independent deformations, according to which, their energy is expressed as a double integral that does not involve gradients. We prove that the \(\Gamma \)-limit of this model, as the horizon tends to zero, is the classical model of hyperelasticity. We pay special attention to how the passage from the density of the non-local model to its local counterpart takes place.
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Communicated by L. Ambrosio.
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Bellido, J.C., Mora-Corral, C. & Pedregal, P. Hyperelasticity as a \(\Gamma \)-limit of peridynamics when the horizon goes to zero. Calc. Var. 54, 1643–1670 (2015). https://doi.org/10.1007/s00526-015-0839-9
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DOI: https://doi.org/10.1007/s00526-015-0839-9