Mesh-free discretization of peridynamic shell structures and coupling model with isogeometric analysis

Abstract

Peridynamic (PD) theory applies nonlocal framework to reform the equilibrium equation in fracture analysis. The mesh-free formulation of the PD model performs well in two- and three-dimensional formulations. A mesh-free discretization of the PD shell using Reissner–Mindlin theory is proposed to meet the demands of crack simulation in shell structures. A micro-beam bond with three translatory and three rotational degrees of freedom is applied to describe the in-shell planar, shearing, and bending deformations. A particle-based method for the coupling of isogeometric analysis (IGA) and PD shells is proposed to improve the computational efficiency. The smooth geometry of the shell structure is precisely described by nonuniform rational B-splines (NURBS). The zone around the crack is transformed from IGA mesh into PD particles by applying mesh-free PD discretization to account for the crack propagation. A particle equilibrium-based method is used for the coupling of IGA and PD zones. The proposed coupling model combines the advantages of both methods and successfully simulates crack growth in shell structures with better computational efficiency compared with the pure PD model. Numerical examples are conducted wherein the complex propagation and intersecting of cracks can be captured, thus proving the accuracy and effectiveness of the proposed method.