Construction of peridynamic beam and shell models on the basis of the micro-beam bond obtained via interpolation method

Abstract

Peridynamic (PD) theory is suitable for predicting structural damages, such as crack propagation and multiple crack growths. However, it is computationally more expensive than finite element method (FEM). Structural idealization is an useful method to improve computational efficiency, especially for complex structures. This study presents a new strategy for general PD beam and shell models on the basis of the micro-beam bond; in this strategy, the bond deformation is obtained directly through the interpolation method, the micro potential energy of the bond can be built, and the micro moduli of the beam and shell models can be solved spontaneously. The Euler beam and Kirchhoff plate theory are used for bending deformation in this study. Each endpoint of the micro-beam bond has three translational degrees of freedom (DOFs) and three rotational DOFs simultaneously. The force and displacement formulations of the micro-beam bond are completely similar to the FEM beam element, which is naturally suitable for the coupling of PD and FEM. Transversal deformation is captured accurately due to the high-order relationship with the transversal forces/moments and transversal displacements of the micro-beam bond. Moreover, no material parameters are limited in the model. Simulation results show the precision of the presented PD beam and shell models on the basis of the micro-beam bond.