Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 35, Issue 1, Pages 27-64Publisher
EUROPEAN MATHEMATICAL SOC-EMS
DOI: 10.1016/j.anihpc.2017.03.002
Keywords
Brittle materials; Variational fracture; Free discontinuity problems; Quasistatic evolution; Crack propagation
Categories
Funding
- Vienna Science and Technology Fund (WWTF) [MA14-009]
- Alexander von Humboldt Stiftung
- ERC [290888]
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In this paper we prove a two-dimensional existence result for a variational model of crack growth for brittle materials in the realm of linearized elasticity. Starting with a time-discretized version of the evolution driven by a prescribed boundary load, we derive a time-continuous quasistatic crack growth in the framework of generalized special functions of bounded deformation (GSBD). As the time-discretization step tends to zero, the major difficulty lies in showing the stability of the static equilibrium condition, which is achieved by means of a Jump Transfer Lemma generalizing the result of [19] to the GSBD setting. Moreover, we present a general compactness theorem for this framework and prove existence of the evolution without imposing a-priori bounds on the displacements or applied body forces. (C) 2017 Elsevier Masson SAS. All rights reserved.
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