Data di Pubblicazione:
2008
Abstract:
In this paper we study the crack initiation in a hyper-elastic body
governed by a Griffith's type energy.
We prove that, during a load process through a time dependent boundary datum of proportional type and in absence of strong singularities (this is the case of homogeneous isotropic materials) the crack initiation is brutal, i.e.,
a big crack appears after a positive time. On the contrary, in 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 (largely expected by the experts
of material science) 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 a Mumford Shah type functional.
governed by a Griffith's type energy.
We prove that, during a load process through a time dependent boundary datum of proportional type and in absence of strong singularities (this is the case of homogeneous isotropic materials) the crack initiation is brutal, i.e.,
a big crack appears after a positive time. On the contrary, in 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 (largely expected by the experts
of material science) 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 a Mumford Shah type functional.
Tipologia CRIS:
1.1 Articolo in rivista
Elenco autori:
Chambolle, A; Giacomini, Alessandro; Ponsiglione, M.
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