Calculus of Variations and Geometric Measure Theory

F. Iurlano

Fracture and plastic models as Gamma-limits of damage models under different regimes

created by iurlano on 04 Nov 2011
modified on 25 Nov 2013


Published Paper

Inserted: 4 nov 2011
Last Updated: 25 nov 2013

Journal: Adv. Calc. Var.
Volume: 6
Pages: 165--189
Year: 2013
Doi: 10.1515/acv-2011-0011
Links: online publication


We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

Keywords: Gamma-convergence, fracture mechanics, Damage problems, cohesive zone models, Hencky's plasticity model