Calculus of Variations and Geometric Measure Theory

A. Giacomini - M. Ponsiglione

Non interpenetration of matter for $SBV$-deformations of hyperelastic brittle materials

created by ponsiglio on 09 Jan 2007
modified by giacomini on 13 Oct 2009


Published Paper

Inserted: 9 jan 2007
Last Updated: 13 oct 2009

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Volume: 138A
Pages: 1019-1041
Year: 2008


We prove that the Ciarlet-Necas non-interpenetration of matter condition can be extended to the case of $SBV$-deformations of hyperelastic brittle materials, and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an $SBV$-map by means of the approximately differentiable representative, and we prove some connected stability results under weak convergence. We provide an application to the case of brittle Ogden's materials.

Keywords: Brittle fracture, variational models, free discontinuity problems, energy minimization, a.e.-injectivity, measure-theoretical image