Quasistatic crack growth in 2d-linearized elasticity

Solombrino F, Friedrich M (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Book Volume: 35

Pages Range: 27-64

Journal Issue: 1

DOI: 10.1016/j.anihpc.2017.03.002

Abstract

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.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Technische Universität München (TUM)

Germany (DE) Universität Wien / University of Vienna

Austria (AT)

How to cite

APA:

Solombrino, F., & Friedrich, M. (2018). Quasistatic crack growth in 2d-linearized elasticity. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 35(1), 27-64. https://doi.org/10.1016/j.anihpc.2017.03.002

MLA:

Solombrino, Francesco, and Manuel Friedrich. "Quasistatic crack growth in 2d-linearized elasticity." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 35.1 (2018): 27-64.

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