Quasistatic crack growth in 2d-linearized elasticity

Friedrich, Manuel; Solombrino, Francesco

doi:10.1016/j.anihpc.2017.03.002

Friedrich, Manuel ; Solombrino, Francesco

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 1, pp. 27-64.

Résumé

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 ( $G S B D$ ). 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 $G S B D$ 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.

MR Zbl

DOI : 10.1016/j.anihpc.2017.03.002

Classification : 74R10, 49J45, 70G75
Mots clés : Brittle materials, Variational fracture, Free discontinuity problems, Quasistatic evolution, Crack propagation

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     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},
     publisher = {Elsevier},
     volume = {35},
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     doi = {10.1016/j.anihpc.2017.03.002},
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     zbl = {1386.74124},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2017.03.002/}
}

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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. http://www.numdam.org/articles/10.1016/j.anihpc.2017.03.002/

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