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In this paper we prove a two-dimensional existence result for a variationalmodel of crack growth for brittle materials in the realm of linearizedelasticity. Starting with a time-discretized version of the evolution driven bya prescribed boundary load, we derive a time-continuous quasistatic crackgrowth in the framework of generalized special functions of bounded deformation(GSBD). As the time-discretization step tends to $0$, the major difficulty liesin showing the stability of the static equilibrium condition, which is achievedby means of a Jump Transfer Lemma generalizing the result of Francfort andLarsen [Comm. Pure Appl. Math., 56 (2003), 1465--1500] to the GSBD setting.Moreover, we present a general compactness theorem for this framework and proveexistence of the evolution without the necessity of a-priori bounds on thedisplacements or applied body forces.

Quasistatic crack growth in 2d-linearized elasticity