A bound-constrained solver for phase-field modelling of diffuse fracture

Resumo

In a structural analysis it is important to know the propagation of cracks to prevent a possible failure
of the material or the structure. One way to model a crack is by the phase-field strategy. Within this approach,
the problem is described by the displacements field and by an additional variable, the phase-field, that measures
the degradation of the material, like a damage variable. Using this variable, a crack is represented in a smooth
and diffuse way. In the current version of the INSANE (INteractive Structural ANalysis Environment system),
an open-source software developed at the Department of Structural Engineering (DEES) of the Federal University
of Minas Gerais (UFMG), some phase-field models have been implemented. However such models have certain
limitations, due to how the crack irreversibility condition is handled. The present work proposes to remove these
limitations with the implementation of a bound-constrained solver that, as pointed out in the literature, constitutes
a more general approach to deal with the irreversibility condition. In the implementation, the library PETSc
(Portable, Extensible Toolkit for Scientific Computation) is used. Numerical simulations are presented to illustrate
the characteristics of the implementation.