The present work frames the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes [1].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. 3D crack tracking methods, which arise from visco-plastic regularizations, will be discussed.

**References:**

[1] Salvadori, A. and Fantoni, F., Fracture propagation in brittle materials as a standard dissipative process: general theorems and crack tracking algorithms, J MECH PHYS SOLIDS, 681-696, 95, 2016