Discontinuous Galerkin isogeometric analysis with peridynamic model for crack simulation of shell structure

Abstract

A discontinuous Galerkin (DG) isogeometric analysis (IGA) formulation with peridynamic (PD) model is proposed for the simulation of cracks in shell structure. A micro-beam PD bond which considers the planar, bending and shearing deformations of shell is applied. Then, based on the micro-beam bond, the peridynamic integral equation is implemented via DG formulation of a conventional isogeometric element. The proposed DGIGA implementation of PD model (DGIGA PD) assures the analysis of crack propagation with spline based smooth geometric model, which is important in the simulation of shell structure. The DGIGA PD calculation improves the computational precision through multiple points based Gaussian integration and provides derivative fields such as strain and stress. To further improve the computational efficiency, the local/nonlocal coupling algorithm for the DGIGA PD model and IGA model is proposed. The computational domain is described fully by spline mesh of IGA, within which the PD domain is assigned where the cracks are propagating. The force and moment balance principal is applied, and an element based stiffness replacing technique is proposed for the coupling process. The performance of the proposed formulation is verified by benchmark examples.