A Generalized Micropolar Peridynamic Model and Its Simulation of Three-Dimensional Fracture Behaviors

Abstract:

The fracture of solid is still a long-standing problem in engineering and computational mechanics， which is an extremely complex phenomenon. A generalized micropolar peridynamic （GMPD） model is proposed for the three-dimensional fracture problem of quasi-brittle materials. First， the governing equations of the bonds are established by employing the Timoshenko beam theory to simulate the interaction between material points， which considers axial deformation， tangential deformation， and the relative rotational angle of bonds. Then， three kinds of peridynamic parameters， corresponding to the tensile， the shear， and the 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 complex loading conditions. Moreover， a novel energy-based failure criterion， involving the maximum stretch， the shear strain， and the rotation angle limits of the bond， is proposed to describe the dynamic failure for quasi-brittle materials. Finally， the three-dimensional fracture processes of the quasi-brittle materials under axial compression loads are simulated by the proposed model. The proposed model is verified by comparisons of its results and those from experimental observations， which can accurately simulate the initiation and propagation processes of different types of cracks， such as wing crack， anti-wing crack， and secondary crack.