Calculus of Variations and Geometric Measure Theory

G. Del Piero - G. Lancioni - R. March

A variational model for fracture mechanics: numerical experiments

created by march on 21 Dec 2006
modified on 05 Feb 2008


Published Paper

Inserted: 21 dec 2006
Last Updated: 5 feb 2008

Journal: J. Mech. Phys. Solids
Volume: 55
Pages: 2513-2537
Year: 2007


In the variational model for brittle fracture proposed by Francfort and Marigo, the minimum problem is formulated as a free discontinuity problem for the energy functional of a linear elastic body. A family of approximating regularized problems is then defined, each of which can be solved numerically by a finite element procedure. Here we re-formulate the minimum problem within the context of finite elasticity. The main change is the introduction of the dependence of the strain energy density on the determinant of the deformation gradient. This change requires new and more general existence and $\Gamma$-convergence results. Some two-dimensional numerical simulations are illustrated, and compared with corresponding simulations made by Bourdin, Francfort and Marigo for the linear elastic model.