The Coupling Approach of Isogeometric Analysis and Peridynamics for Plane Problem with Non-Uniform Control Net

Isogeometric analysis (IGA) is an important mesh-free method which utilizes the splines basis functions and control net in the CAD geometry for simulation. Its theoretical basis is continuum mechanics, and it is not suitable for fracture problems. Peridynamics (PD) is a non-local theory based on integral equations, which is suitable for discontinuous problems such as cracks, while the non-local property of PD increases the computational effort. The coupling of IGA and PD promotes the simulation of cracks with the precise CAD geometry and improves the computational efficiency compared with that of pure PD model. In this paper, the coupling approach of IGA and PD (IGA-PD) for plane problems with non-uniform control net is introduced, and the main contribution is a system of algorithms to convert the non-uniform control net into IGA-PD coupling model. A volume division method is proposed to calculate the occupied volumes for the PD nodes. To account for the non-uniform control net, the search range correction method, volume and centroid correlation methods of family nodes and dual-horizon method are applied to improve the computational precision. An exponential gradual constitutive model (EGCM) is applied to calculate the crack propagation of materials. The proposed IGA-PD model with non-uniform control net makes full use of the advantages of the non-local continuum theory, which can solve the fracture problem and alleviate the surface effect of PD. The processing algorithms for the non-uniform control net improve the computational accuracy. Numerical examples of static problems and crack propagations are given. The results prove that the search range, centroid and volume correction methods are important for improving the numerical precision. The plate under stretch and bending, Kalthoff–Winkler impact problem and simulation of concrete material are carried out to show the effectiveness of the proposed IGA-PD model.