Component-wise fracture analysis through coupled three-dimensional peridynamics and refined one-dimensional finite elements

Peridynamics (PD) is a non-local theory introduced by Silling in [1]. It is based on integro-differential equations, which means that PD could be employed for the investigation of problems with discontinuities, such as cracks. Nevertheless, the computational cost of a full 3D peridynamics analysis could be prohibitive. For this reason, researchers are working on coupling of local elasticity with peridynamics (i.e. [2,3]), in order to exploit the features of both theories. This work investigates crack propagation problems by combining local and non-local elasticity models. Specifically, the portion of the domain where the failure takes place is modelled via 3D peridynamics. On the other hand, the remaining part of the domain is modelled via refined 1D elements through the Carrera Unified Formulation (CUF) [4], which in recent years has proven to provide 3D-like results with a significant reduction of the computational cost. The coupling between the two domains is realized through the introduction of Lagrange multipliers, as presented in [5]. The present work is an extension of a previous one [6], where fracture in brittle material solid specimens was investigated through sequentially linear analysis. Particular attention is focussed on the crack propagation in multi-component structures (e.g., thin-walled reinforced structures) and multi-scale problems.