Implementation of a bound-constrained solver in phase-field modelling of fracture

Resumo

In phase-field modelling of fracture, the cracking representation is conditioned by the relation between
the displacement field and a phase-field variable that measures the degradation of the material. In this sense, the
cracks are modelled as smooth and diffuse according to a group of functions that best represents the geometry of the
region where the phenomenon takes place and how the strain energy is degraded during crack propagation. Using
a variational formulation of Griffith’s criterion, these functions are combined in such a way to attend to the balance
laws and the crack irreversibility condition, as well as the bounds of the phase-field variable. The Department of
Structural Engineering of the Federal University of Minas Gerais (UFMG) has been currently incorporating, in its
open-source software INSANE (Interactive Structural Analysis Environment system), various phase-field models.
Nonetheless, the software still has some limitations as the use of some functions may extrapolate the phase-field
bounds during solving. The literature has described the use of a bound-constrained solver that can overcome this
issue. Therefore, this work proposes the implementation of this solution strategy without the use of any external
libraries.