Abstract
An adaptive relocation strategy for a coupled XFEM–Peridynamic (PD) model is introduced. The motivation is to enhance the efficiency of the coupled model and demonstrate its applicability to complex brittle fracture problems. The XFEM and PD approximation domains can be redefined during the simulation, to ensure that the computationally expensive PD model is applied only where needed. To this end a two-step expansion/contraction process, allowing the PD patch to adaptively change its shape, size and location, following the propagation of the crack, is employed. No a priori knowledge of the crack path or re-meshing is required, and the methodology can automatically switch between PD and XFEM. Three 2D fracture examples are presented to highlight the performance of the methodology and the ability to follow multiple crack tips. Results indicate significant computational savings. Furthermore, the characteristic length scale of PD theory bestows a nonlocal and multiscale component to the methodology.
Highlights
Many studies have been devoted to the coupling of FE meshes and PD grids, for the mitigation of the computational restrictions associated with the numerical implementation of the PD theory
Coupling is enforced through the introduction of ghost nodes and particles and it is similar to the coupling approach employed here
A similar procedure was used by Han et al [2] where the ‘morphing’ strategy was used to couple classical elasticity with the PD theory [2], [5]
Summary
Many studies have been devoted to the coupling of FE meshes and PD grids, for the mitigation of the computational restrictions associated with the numerical implementation of the PD theory. This requirement is removed with the expansion process used [1] and [2] that adaptively expands PD This has been proven to be an efficient procedure to simulate complex problems such as dynamic crack branching. The present contribution is an attempt towards the efficient combination of local and non-local models, with dynamic relocation capabilities, aiming at true multiscale simulations. An adaptive refinement process redefines the location where the coarse (FE) and fine scale (atomistic) models are used while the phantom node method is implemented to model the discontinuity within the continuum domain. 2 the implementation of the XFEM–PD model for dynamic fracture problems with multiple or intersecting cracks is presented. The expansion and contraction steps of the adaptive relocation strategy are presented in Sect.
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