Fracture propagation in brittle materials as a standard dissipative process: General theorems and crack tracking algorithms

The present work frames the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes. Variational formulations are stated. They characterize the three dimensional crack front ``quasi-static velocity" as minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm that computationally handles the constraint via the penalty method algorithm is introduced and proof of concept provided.