Isogeometric analysis of cracks with peridynamics

Abstract Isogeometric analysis (IGA) is an important mesh-free method that provides the technique for the integration of computer-aided design and analysis. However, its formulation is based on classical continuum mechanics and is not suitable for crack propagation problems. The peridynamics (PD) theory is based on the non-local integral equation, which avoids the discontinuous problem of classical continuum mechanics and can solve the crack problems. In this paper, a coupling model of IGA and bond-based PD (IGA-PD) is proposed to provide the solution to crack problem of model with exact geometry. We prove that in the IGA-PD coupling model, the PD nodes can be constructed by using the control net from IGA. The implicit and explicit formulas of the PD model are combined with IGA formulations based on the force balance principle . Through setting the isogeometric model on the domain near the boundaries, the surface effect of the PD model can be relieved. The IGA-PD model fully utilizes the advantages of non-local continuum theory and improves the precision and computational efficiency in calculation of crack problems. The coupling method is straightforward and effective, and can be integrated within existing IGA codes. Examples of static problems and crack propagations are given to prove the effectiveness of the proposed method.