Peridynamic and Finite Element Coupling Strategies for the Simulation of Brittle Fracture

Abstract

The Peridynamic theory is a nonlocal approach, based on an integral formulation that avoids the use of spatial derivatives. This attribute is very desirable in fracture simulations, making Peridynamics a versatile tool for failure analyses. A major disadvantage however is the high computational cost associated with its numerical implementation. The aim of this study is to propose coupling strategies between standard Finite Element methodologies and Peridynamic grids in order to simultaneously exploit the inherent ability of the latter to simulate crack initiation and propagation with the computational efficiency of the former. Initially a coupling technique, where the thermal field is approximated using Finite Elements and the mechanical field using Peridynamics, is applied to a thermal shock problem for refractory ceramics. The results, although very accurate, verify the increased computational cost of Peridynamic simulations. To remedy this, a methodology to couple Peridynamics with finite element solvers for classical continuum theories, restricting the use of particles at the vicinity of the crack tip, is developed. The coupling method introduces fictitious particles inside the finite elements near the coupling interface. This method is selected after comparing three different methodologies with respect to spurious reflections observed during pulse propagation in a 1D bar. A crack tip tracking algorithm and an adaptive expansion/contraction methodology are developed for the dynamic relocation of the Peridynamic patch around the emerging crack fronts. This methodology also employs enrichment of the Finite Elements with Heaviside functions (Extended Finite Element Method) to limit the use of Peridynamics only near the crack tip. The proposed method is used for the simulation of several fracture problems, including the complex case of dynamic crack branching. The results are in close agreement with those obtained using a Peridynamic only approach while featuring significant computational savings.