Quasistatic crack growth in 2d-linearized elasticity - Solombrino, Francesco; Friedrich, Manuel (Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 2018)
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.
CRIS-Team Scopus Importer:2021-10-21
Keywords: Brittle materials; Crack propagation; Free discontinuity problems; Quasistatic evolution; Variational fracture