A vector form conjugated-shear bond-based peridynamic model for crack initiation and propagation in linear elastic solids

Abstract

A vector form conjugated-shear bond-based peridynamic model is proposed to overcome the limitation of the fixed Poisson’s ratio based on the assumption of central force between material points in bond-based peridynamic theory. In the virtue of this proposed approach, the angle variation of a pair of conjugated-shear bonds is derived as a vector in terms of the displacements at three points located at the conjugated-shear bonds instead of the direct use of the angle, which improves the computational efficiency in both two and three dimensional conditions. Emphasis is placed on deriving the relationship between micro moduli in the proposed model and macro constants by equating peridynamic strain energy to the macroscopic strain energy. It is found that the micro moduli in this proposed approach can reduce to classical bond-based peridynamic parameters when the rotation effect of conjugated-shear bonds is not considered. A comparative study of the proposed approach and the FEM or analytical solutions on a square isotropic plate and a three-dimensional rectangular block under uniaxial tension shows that this proposed approach can well investigate the behavior of elastic solids under both two and three dimensional conditions. We test the numerical convergence behavior of the proposed model to classical solutions in the varying horizon/grid spacing ratios or horizon sizes. Moreover, the improvement of computational efficiency of the proposed model is verified by comparison of the CPU time computed from the scalar form conjugated bond-based peridynamic model. The capability of the proposed model in simulating dynamic brittle fracture problems is demonstrated by comparing the results obtained by the proposed model with the previous numerical results in the case of Kalthoff-Winkler experiment.