A non incremental variational principle for brittle fracture

TL;DR

This paper introduces a unified, non-incremental variational principle for brittle fracture that models crack evolution over space and time using an internal variable approach, offering a more general framework than traditional methods.

Contribution

It presents a novel, non-incremental variational formulation for brittle fracture that treats static and dynamic cases within a single space-time framework, emphasizing internal variables and dissipation.

Findings

Unified treatment of static and dynamic fracture

Modeling of crack extension via internal variables

More general and flexible theoretical framework

Abstract

The aim of the paper is to propose a paradigm shift for the variational approach of brittle fracture. Both dynamics and the limit case of statics are treated in a same framework. By contrast with the usual incremental approach, we use a space-time principle covering the whole loading and crack evolution. The emphasis is given on the modelling of the crack extension by the internal variable formalism and a dissipation potential as in plasticity, rather than Griffith's original approach based on the surface area. The new formulation appears to be more fruitful for generalization than the standard theory.