Schlagwort(e):
Forschungsbericht
Beschreibung / Inhaltsverzeichnis:
This work provides a convergence analysis of a time-discrete scheme coupled with a finite-element approximation in space for a model for partial, rate-independent damage featuring a gradient regularization as well as a non-smooth constraint to account for the unidirectionality of the damage evolution. The numerical algorithm to solve the coupled problem of quasistatic small strain linear elasticity with rate-independent gradient damage is based on a Variable ADMM-method to approximate the nonsmooth contribution. Space-discretization is based on P1 finite elements and the algorithm directly couples the time-step size with the spatial grid size h. For a wide class of gradient regularizations, which allows both for Sobolev functions of integrability exponent r 2 (1;1) and for BV-functions, it is shown that solutions obtained with the algorithm approximate as h ! 0 a semistable energetic solution of the original problem. The latter is characterized by a minimality property for the displacements, a semistability inequality for the damage variable and an energy dissipation estimate. Numerical benchmark experiments confirm the stability of the method.
Materialart:
Online-Ressource
Seiten:
1 Online-Ressource (32 Seiten, 3,38 MB)
,
Illustrationen, Diagramme
Serie:
Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik no. 2707
URL:
https://doi.org/10.20347/WIAS.PREPRINT.2707
DOI:
10.20347/WIAS.PREPRINT.2707
Sprache:
Englisch
Anmerkung:
Literaturverzeichnis: Seite 28-30
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