Quasistatic crack growth in 2d-linearized elasticity

  • Manuel Friedrich

    Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • Francesco Solombrino

    Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching, Germany; Dipartimento di Matematica e Applicazioni, Universita di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy


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.

Cite this article

Manuel Friedrich, Francesco Solombrino, Quasistatic crack growth in 2d-linearized elasticity. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 1, pp. 27–64

DOI 10.1016/J.ANIHPC.2017.03.002