Coupling approach of isogeometric analysis with non-ordinary state-based peridynamics

Abstract Isogeometric analysis (IGA) is an important mesh-free method for the integration of computer aided design (CAD) and computer aided engineering (CAE) but not suitable for crack propagation problems. A coupling model of IGA and non-ordinary state-based peridynamics (NOSB-PD) is proposed to solve crack initiation and propagation problems in IGA because peridynamics can deal with the discontinuities well. The NOSB-PD model is constructed from the control points of IGA model directly, and the stiffness of the NOSB-PD model is combined with the IGA model based on the force balance principle. This method relieves the boundary effect of NOSB-PD by setting the IGA model on the domain near boundaries. In addition, a precise volume correction algorithm is proposed in this study to correct the volume of NOSB-PD points at the boundary of horizon. Some examples of the dynamic simulation of crack propagation and the static simulation of a homogeneous square plate and a prenotched rectangular plate are given to prove the effectiveness of the proposed coupling method.