In the present work, a computationally efficient and explicit algorithm for the rigorous
enforcement of the irreversibility constraint in the phase-field modeling of brittle fracture is …

Variational models for cohesive fracture are based on the idea that the fracture energy is
released gradually as the crack opening grows. Recently, proposed a variational …

We consider a class of separately convex phase field energies employed in fracture
mechanics, featuring non-interpenetration and a general softening behavior. We analyze the …

In this paper, we derive a new 2D brittle fracture model for thin shells via dimension
reduction, where the admissible displacements are only normal to the shell surface. The …

In this paper, we focus on the finite-dimensional approximation of quasi-static evolutions of
critical points of the phase-field model of brittle fracture. In a space discretized setting, we …

We propose a phase–field model of dynamic fracture based on the Ambrosio–Tortorelli's
approximation, which takes into account dissipative effects due to the speed of the crack tips …

This contribution deals with the analysis of models for phase-field fracture in visco-elastic
materials with dynamic effects. The evolution of damage is handled in two different ways: As …

This thesis is devoted to the study of several mathematical problems in fracture mechanics
for brittle materials. In the first part, we prove existence, uniqueness, and continuous …

We consider the gradient flow of a quadratic non-autonomous energy under monotonicity
constraints. First, we provide a notion of weak solution, inspired by the theory of curves of …

This work is devoted to the analysis of convergence of an alternate (staggered) minimization
algorithm in the framework of phase field models of fracture. The energy of the system is …