Nonlocal-to-local limit in linearized viscoelasticity

Friedrich M, Seitz M, Stefanelli U (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Communications in Applied and Industrial Mathematics Società Italiana di Matematica Applicata e Industriale (SIMAI)

Book Volume: 15

Journal Issue: 1

DOI: 10.2478/caim-2024-0001

Abstract

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 Γ-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.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M., Seitz, M., & Stefanelli, U. (2024). Nonlocal-to-local limit in linearized viscoelasticity. Communications in Applied and Industrial Mathematics, 15(1). https://doi.org/10.2478/caim-2024-0001

MLA:

Friedrich, Manuel, Manuel Seitz, and Ulisse Stefanelli. "Nonlocal-to-local limit in linearized viscoelasticity." Communications in Applied and Industrial Mathematics 15.1 (2024).

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