Authors
Antonin Chambolle, Alessandro Giacomini, Marcello Ponsiglione
Publication date
2008/5
Journal
Archive for rational mechanics and analysis
Volume
188
Issue
2
Pages
309-349
Publisher
Springer-Verlag
Description
In this paper we study the crack initiation in a hyper-elastic body governed by a Griffith-type energy. We prove that, during a load process through a time-dependent boundary datum of the type t → t g(x) and in the absence of strong singularities (e.g., this is the case of homogeneous isotropic materials) the crack initiation is brutal, that is, a big crack appears after a positive time t i > 0. Conversely, in the presence of a point x of strong singularity, a crack will depart from x at the initial time of loading and with zero velocity. We prove these facts for admissible cracks belonging to the large class of closed one-dimensional sets with a finite number of connected components. The main tool we employ to address the problem is a local minimality result for the functional where , k > 0 and f is a suitable Carathéodory function. We prove that if the uncracked …
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A Chambolle, A Giacomini, M Ponsiglione - Archive for rational mechanics and analysis, 2008