Calculus of Variations and Geometric Measure Theory

F. Freddi - G. Royer Carfagni

Regularized variational theories of fracture: A unified approach

created by royercarfagni on 25 Apr 2016


Published Paper

Inserted: 25 apr 2016

Journal: Journal of the Mechanics and Physics of Solids
Volume: 58
Number: 8
Pages: 1154–1174
Year: 2010
Doi: 10.1016/j.jmps.2010.02.010
Links: sciencedirect


The fracture pattern in stressed bodies is defined through the minimization of a two-field pseudo-spatial-dependent functional, with a structure similar to that proposed by Bourdin–Francfort–Marigo (2000) as a regularized approximation of a parent free-discontinuity problem, but now considered as an autonomous model per se. Here, this formulation is altered by combining it with structured deformation theory, to model that when the material microstructure is loosened and damaged, peculiar inelastic (structured) deformations may occur in the representative volume element at the price of surface energy consumption. This approach unifies various theories of failure because, by simply varying the form of the class for admissible structured deformations, different-in-type responses can be captured, incorporating the idea of cleavage, deviatoric, combined cleavage-deviatoric and masonry-like fractures. Remarkably, this latter formulation rigorously avoid material overlapping in the cracked zones. The model is numerically implemented using a standard finite-element discretization and adopts an alternate minimization algorithm, adding an inequality constraint to impose crack irreversibility (fixed crack model). Numerical experiments for some paradigmatic examples are presented and compared for various possible versions of the model.

Keywords: fracture, Structured deformations, damage mechanics, free-discontinuity problem