A generalized bond-based peridynamic model for quasi-brittle materials enriched with bond tension–rotation–shear coupling effects

Abstract

A generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads. The mechanical behaviors of the material points are reformulated by incorporating the bond tension–rotation–shear coupling effects, which makes the model suitable for complex discontinuous problems in both three-dimensional spatial and two-dimensional plane conditions. The governing equations of the bond are established by employing the Timoshenko beam theory to simulate the interaction between material points as well as the bond coupling effect. Three kinds of peridynamic parameters, corresponding to the compressive, shear and bending stiffness of the bond, are introduced to keep the consistence of the strain energy obtained from the proposed peridynamic model and from the continuum mechanics under arbitrary deformation fields. Moreover, a novel energy-based failure criterion, involving the maximum stretch, shear strain and rotation angle limits of the bond, is proposed to describe the nonlinear behaviors and progressive failure for general quasi-brittle materials. The proposed model is verified by providing comparisons between its results and those from known analytical solutions and experimental observations. The influences of the bond tension–rotation–shear coupling effect as well as the applicability of the proposed model for the wave propagation, complex deformation and mix-mode fracture problems are also investigated. Results show that the proposed model with the bond coupling effect will greatly improve the simulation accuracy for dynamic problems of quasi-brittle materials under complex loading conditions. Results also indicate that the proposed model can well capture the nonlinear deformation, crack propagation, as well as progressive failure of materials with variable Poisson’s ratios under complex combined loads