Convergence of alternate minimization schemes for phase-field fracture and damage-Reference-Cited by-同舟云学术

Convergence of alternate minimization schemes for phase-field fracture and damage

Published:2017-05-23 Issue:09 Volume:27 Page:1743-1794
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Knees Dorothee¹,Negri Matteo²

Affiliation:

1. Institut für Mathematik, Universität Kassel, Heinrich-Plett Str. 40, D-34132 Kassel, Germany

2. Department of Mathematics, University of Pavia, Via A. Ferrata 1, I-27100 Pavia, Italy

Abstract

We consider time-discrete evolutions for a phase-field model (for fracture and damage) obtained by alternate minimization schemes. First, we characterize their time-continuous limit in terms of parametrized [Formula: see text]-evolutions, introducing a suitable family of “intrinsic energy norms”. Further, we show that the limit evolution satisfies Griffith’s criterion, for a phase-field energy release, and that the irreversibility constraint is thermodynamically consistent.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202517500312

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