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 (). 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 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.
Keywords: Brittle materials, Variational fracture, Free discontinuity problems, Quasistatic evolution, Crack propagation
@article{AIHPC_2018__35_1_27_0,
author = {Friedrich, Manuel and Solombrino, Francesco},
title = {Quasistatic crack growth in 2d-linearized elasticity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {27--64},
year = {2018},
publisher = {Elsevier},
volume = {35},
number = {1},
doi = {10.1016/j.anihpc.2017.03.002},
mrnumber = {3739927},
zbl = {1386.74124},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.03.002/}
}
TY - JOUR AU - Friedrich, Manuel AU - Solombrino, Francesco TI - Quasistatic crack growth in 2d-linearized elasticity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 27 EP - 64 VL - 35 IS - 1 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.03.002/ DO - 10.1016/j.anihpc.2017.03.002 LA - en ID - AIHPC_2018__35_1_27_0 ER -
%0 Journal Article %A Friedrich, Manuel %A Solombrino, Francesco %T Quasistatic crack growth in 2d-linearized elasticity %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 27-64 %V 35 %N 1 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.03.002/ %R 10.1016/j.anihpc.2017.03.002 %G en %F AIHPC_2018__35_1_27_0
Friedrich, Manuel; Solombrino, Francesco. Quasistatic crack growth in 2d-linearized elasticity. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 27-64. doi: 10.1016/j.anihpc.2017.03.002
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