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 …

Our starting point is a parameterized family of functionals (a 'theory') for which we are
interested in approximating the global minima of the energy when one of these parameters …

Discrete fine-scale models, in the form of either particle or lattice models, have been
formulated successfully to simulate the behavior of quasi-brittle materials whose mechanical …

In this work, a novel multiscale cohesive zone model is proposed, in which the bulk material
is modeled as a local quasi-continuum medium that obeys the Cauchy–Born rule while the …

We consider a system of parallel straight edge dislocations and we analyse its asymptotic
behaviour in the limit of many dislocations. The dislocations are represented by points in a …

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 provide a variational description of nearest-neighbours and next-to-nearest neighbours
binary lattice systems. By studying the Γ-limit of proper scaling of the energies of the …

This article is devoted to the study of the asymptotic behavior of a class of energies defined
on stochastic lattices. Under polynomial growth assumptions, we prove that the energy …

Two different free discontinuity finite element models for studying crack initiation and
propagation in 2D elastic problems are presented. Minimization of an energy functional …

In this paper, we present an atomistic-based interphase zone model (AIZM), discuss its
physical foundation, and apply it to simulate fractures at small scales. The main technical …