Eigendamage: an eigendeformation model for the variational approximation of cohesive fracture - a one-dimensional case study

  • We study an approximation scheme for a variational theory of cohesive fracture in a one-dimensional setting. Here, the energy functional is approximated by a family of functionals depending on a small parameter 0<ε≪1 and on two fields: the elastic part of the displacement field and an eigendeformation field that describes the inelastic response of the material beyond the elastic regime. We measure the inelastic contributions of the latter in terms of a non-local energy functional. Our main result shows that, as ε→0, the approximate functionals Γ-converge to a cohesive zone model.

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Author:Veronika Auer-Volkmann, Lisa BeckGND, Bernd SchmidtGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/87412
Parent Title (Italien):Annali di Matematica Pura ed Applicata
Place of publication:Berlin
Year of first Publication:2022
Publishing Institution:Universität Augsburg
Release Date:2021/06/14
First Page:2161
Last Page:2195
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehr- und Forschungseinheit Angewandte Analysis
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)