The quasi-static fracture propagation problem has been extensively investigated in analogy with standard dissipative systems [1]. An associative ow rule, dening the rate of the internal variable conjugated to the stress intensity factors, descend from the maximum dissipation principle, together with loading/unloading conditions, the satisfaction of the Clausius-Duhem inequality and the convexity of the safe equilibrium domain.
Variational formulations descend, characterizing the crack front quasi-static velocity as minimizer of constrained quadratic functionals. The resoluteness of the established theoretical framework is counterbalanced by a poor numerical validation because of the need of currently unavailable accurate approximation for weight functions [2].
In the present study, a viscous regularization of the quasi-static fracture propagation problem is formulated. It allows to derive a simple, explicit expression for the crack front velocity. As usually done in plasticity, where viscosity is interpreted as a regularization of the rate-independent formulation [3], the adopted viscous regularization allows to formulate explicit in time crack tracking algorithms, which enable to compute nite elongations along the crack front.
Three-dimensional fractures path has been investigated, this last caused by the increment of the external mechanical load. Performed numerical benchmarks allow to assess the capabilities of the proposed formulation, demonstrating its potential also for real-life complex geometries.
REFERENCES
[1] Salvadori, A. and Fantoni, F. Minimum theorems in 3D incremental linear elastic fracture mechanics. Int. J. Fracture (2013) 184:57{74.
[2] 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 (2016) 95:681{696.
[3] Simo, J.C. and Hughes, T.J.R. Computational inelasticity. Springer-Verlag, New York, (1998).