Point Interpolation Methods for phase-field modelling of brittle fracture

Resumo

The present work investigates the application of meshfree Point Interpolation Methods (PIM) to the
phase-field modelling of brittle fracture. The phase-field modelling is an efficient tool for the simulation of complex
cracks. Within this approach, a crack is modelled as a diffuse crack where a length scale parameter controls the
size of diffusive region and the value of phase-field indicates the integrity of the material. Point Interpolation
Methods can be based on polynomial or radial shape functions. These shape functions possess (i) the Kronecker
delta property, that allows a more simple imposition of essential boundary conditions, (ii) the compact support
property and (iii) the partition of unity property. This paper discusses the computational aspects of the application
of the PIM strategy to the phase-field modelling, and presents numerical simulations to illustrate the characteristics
of the proposed approach.