Global/local and coupled FE-PD models for progressive failure analysis

Peridynamics is a non-local theory introduced by Silling in [1]. It is based on integro-differential equations, allowing the possibility of dealing with discontinuous displacement fields, such as in cracks. Nevertheless, the non-local nature of PD can lead to a high computational demand of the analysis, especially for 3D problems of practical interest. For this reason, researchers are investigating coupling strategies (i.e. [2]) between classical local elasticity models, such as Finite Element Method (FEM), and peridynamics domains, in order to exploit the advantages of both methods. In [3], the authors adopted a coupling method based on Lagrange multipliers for a progressive failure analysis. The 3D PD domain is here adopted only in regions where the crack is likely to develop, while the remaining portions are modelled through high-order one-dimensional models, based on Carrera Unified Formulation (CUF). In the present work, the authors propose the introduction of the aforementioned coupling strategy in a two-step Global\Local (G\L) framework for failure analysis. This G\L method has been first proposed in [4], where a 2D global analysis is carried out through a commercial FEM software, whereas the local refined analysis is performed on a critical region of the full structure by employing CUF-based high-order models. Displacements and rotations are retrieved from the global analysis and employed as boundary conditions in local model. The main novelty of the present research consists in the adoption of a coupled FE\PD model to analyze the local refined region. In such manner, an iterative process for progressive failure analysis is built, by updating the stiffness of the global structure whenever a damage occurs in the local PD region. Various test cases are discussed and results are compared with those obtained in literature with classical and coupled FE\PD three-dimensional models.