Seamless coupling of bond- and state-based peridynamic and finite element analyses

Abstract

This study presents a variational approach to couple PeriDynamic (PD) and Finite Element (FE) analyses to take advantage of their salient features. The PD and FE domains share the same nodes along their interface without an overlap region and any constraint conditions. Therefore, this approach does not require a morphing or a blending function that facilitates coupling over a transition zone. Although this approach is general and not limited to any commercial FE software, the PD interactions for bond-based (BB), ordinary state-based (OSB) and non-ordinary state-based (NOSB) are modeled with MATRIX27 elements native to ANSYS, a commercial software, for the purpose of demonstration. It is a general framework to perform BB, OSB and NOSB PD coupled with traditional elements. It provides the ability to practicing engineers in industry for integrating PD into their FE based design tools. The PD domains can share a boundary with FE domains or be completely embedded in the FE domain. The resulting global system of equations includes the contributions arising from the PD nodes and FE nodes. These equations are solved simultaneously without requiring an iterative procedure through implicit methods. Therefore, it is a direct (seamless) coupling approach without an overlap zone. The results are free of displacement kinks; thus, unphysical stress concentrations do not appear near the interface between the PD and FE regions. Its accuracy is demonstrated by considering isotropic elastic plates subjected to various types of boundary conditions under quasi-static and dynamic loading conditions. Also, its accuracy is demonstrated for quasi-static crack propagation by considering double cantilever beam and three-point bend test specimens. The results from the coupled PD-FE approach agree well with those of FEM for all boundary and loading conditions.