Hela Gmati, Olivier Lampron, Ludvik Martinu, Martin Lévesque
Polytechnique Montréal, 2500 Chemin de Polytechnique,
Montréal, QC H3T 1J4, Canada
The frictionless contact problem of a rigid sphere punch indenting a multilayer linear elastic material is investigated using phase-field modelling of fracture. The model uses a scalar damage variable to represent the progressive degradation of mechanical resistance. The spatial gradient of the damage variable, which is treated as an additional external state variable, serves regularization purposes and allow one to consider the surface energy associated with cracks. Crack growth is assumed to be driven by stress invariant. The numerical implementation is undertaken via the finite element method, where nodal degrees of freedom are the displacement and the damage variable. An implicit time integration scheme is considered. The mechanical equilibrium and the phase-field equations are solved in a staggered manner, usually used to solve the coupled damage-displacement governing equations. The proposed formulation is quite general and allows dealing with different damage mechanisms. To show the capabilities and limits of this formulation, representative numerical simulations are carried out. They allow investigating the impact of loading conditions on damage development as well as the impact of crack closures effects. Important aspects of crack nucleation and propagation including tension/compression asymmetry are discussed.