At the risk of being unfair, we credit first and foremost AA Griffith for developing the field of
brittle fracture. His views were that cracks are the macroscopic manifestation of putative …

The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for
the description of the asymptotic behaviour of variational problems. Its applications range …

Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …

We obtain a cohesive fracture model as Γ-limit, as ε→ 0, of scalar damage models in which
the elastic coefficient is computed from the damage variable v through a function f ε of the …

In this paper, we explore the convergence of the semi-discrete Scharfetter–Gummel scheme
for the aggregation-diffusion equation using a variational approach. Our investigation …

Many materials can be modeled either as discrete systems or as continua, depending on the
scale. At intermediate scales it is necessary to understand the transition from discrete to …

We study fracture and debonding of a thin stiff film bonded to a rigid substrate through a thin
compliant layer, introducing a two-dimensional variational fracture model in brittle elasticity …

We prove an integral representation result for functionals with growth conditions which give
coercivity on the space SBD^ p (Ω) SBD p (Ω), for Ω ⊂ R^ 2 Ω⊂ R 2, which is a bounded …

It is shown that the relaxed energy [Formula: see text] admits the representation [Formula:
see text] where f is a convex, Carathéodory integrand satisfying a nonstandard “α–β” growth …

We prove a stability result for a large class of unilateral minimality properties which arise
naturally in the theory of crack propagation proposed by Francfort & Marigo in [14]. Then we …