Fracture propagation in brittle materials as a standard dissipative process: Effective crack tracking algorithms based on a viscous regularization

Abstract

Cracks propagation in brittle materials was framed into the theory of standard dissipative processes by several authors in many publications. Although the theoretical setting is sound, the derived crack tracking methods suffered from a major drawback that limited the interest in the method to its theoretical content. Specifically, the need of currently unavailable accurate approximations for weight functions made the approach numerically of minor interest. Such a drawback is overcome in the present note, where a viscous regularization of the fracture propagation in brittle materials as a standard dissipative process is formulated. Rate-dependency provided a simple and effective approximation of the crack front velocity, thus allowing to formulate crack tracking algorithms that seem to show promising potential.