Coupling of Peridynamics with Finite Elements - an Overview and Results of an Arlequin Based Approach

Abstract

A continuum model fails, when the deformations are not smooth or discontinuous. Non-local models, such as the peridynamics (PD) could better solve fracture problems such as crack initiation, its growth and formation of crack patterns. Furthermore, it gives accurate representation of the crack profile and its propagating velocity. In PD the magnitudes of the bond forces depend on the collective deformations of all bonds withing a horizon. In addition, a relatively high resolution is required to describe continuous deformation functions and, consequently, calculation methods based on PD are computationally expensive. Therefore, the application of PD in undamaged regions requires an unnecessary high effort for receiving sufficient accurate results. In contrast, the finite element method (FEM) as a classical continuum mechanics-based approach, is very efficient, if continuous stress distributions can be assumed. Consequently, a computational cost reduction can be achieved, if the PD is applied in the local damaged zone only and the remaining area is modelled and analyzed with the classical FEM. The realization of such an approach requires a sufficient accurate coupling of the PD and the FEM subdomains. In the presentation a brief overview about different coupling approaches is given first. Then the general approach of an Arlequin based method is presented. Here the coupling is achieved via an overlapping of PD and FEM areas. The coupling equations are developed and realized with help of the Penalty method. The Penalty method is considered as an alternative procedure to the Lagrange multiplier strategy without creating new unknowns, which essentially simplifies the coupled PD-FEM approach. The validity and limits of the proposed technique are demonstrated through wave propagation analysis, where the choice of the Penalty number is discussed as well as artificial wave reflections caused by the coupling area.