Computational modeling of the initiation and propagation of complex fracture is central to the
discipline of engineering fracture mechanics. This review focuses on two promising …

Phase-field models, sometimes referred to as gradient damage or smeared crack models,
are widely used methods for the numerical simulation of crack propagation in brittle …

In this paper we fully describe the trajectory of gradient flow over $2 $-layer diagonal linear
networks for the regression setting in the limit of vanishing initialisation. We show that the …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

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 …

In its numerical implementation, the variational approach to brittle fracture approximates the
crack evolution in an elastic solid through the use of gradient damage models. In this article …

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial
differential equations, inequalities, and systems. The exposition leads the reader through the …

Numerical methods for nonlinear partial differential equations Springer Series in Computational
Mathematics 47 Sören Bartels Numerical Methods for Nonlinear Partial Differential Equations …

A variational formulation is proposed for a family of elastic–plastic–damage models within
the framework of rate-independent materials. That consists first in defining the total energy …