Nonlocal-to-local limit in linearized viscoelasticity

Manuel Friedrich; Manuel Seitz; Ulisse Stefanelli

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Nonlocal-to-local limit in linearized viscoelasticity

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arxiv 2402.16386 v1 pith:HP6RCSFK submitted 2024-02-26 math.AP

Nonlocal-to-local limit in linearized viscoelasticity

Manuel Friedrich , Manuel Seitz , Ulisse Stefanelli This is my paper

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keywords nonlocallimitnonlocal-to-localperidynamicproblemapproachconsiderconverge

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We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an evolutionary $\Gamma$-convergence approach, we prove that the solutions of the nonlocal problem converge to the solution of the local problem, when the peridynamic horizon tends to $0$, that is, in the nonlocal-to-local limit.

Nonlocal-to-local limit in linearized viscoelasticity

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