Publisher Summary Multifield theories indicate the wide range of models in which some
graphic fields must be introduced to describe the influence of material substructures on the …

This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

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 …

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 …

Phase-field models of brittle fracture can be regarded as gradient damage models including
an intrinsic internal length. This length determines the stability threshold of solutions with …

In this paper, the cohesive fracture is revisited as an energy minimization problem. The
energy functional is rigorously derived based on a pair of integral transformations and a …

In this paper the existence of minimizers in nonlinear elasticity is established under
assumptions on the stored energy that permit the formation of new holes in the body. Such …

Due to its computational robustness and versatility, the phase field fracture model has
become the preferred tool for predicting a wide range of cracking phenomena. However, in …

The newly proposed nonlocal macro-meso-scale consistent damage model (NMMD) is
extended to compression/shear-dominate failure problems. For this purpose, the nonlocal …

Phase-field models of brittle fracture are typically endowed with a decomposition of the
elastic strain energy density in order to realistically describe fracture under multi-axial stress …