An improved bond-based peridynamic model based on Timoshenko beam theory

Abstract

An improved constitutive model based on Timoshenko beam theory is proposed for bond-based peridynamics. The motion and force governing equations of the bond are established by introducing Timoshenko beam element to simulate the interaction between the particles including the bond tension-rotation-shear coupling effects. Since the axial displacement, transverse displacement and relative rotation angle of the bond are considered in the model, it can overcome the limitation of Poisson’s ratio in the classical bond-based peridynamics model. Three kinds of peridynamic parameters, corresponding to the compressive, shear and bending stiffness of the bond, are introduced to keep the consistence between the strain energy of the peridynamic model and that of the continuum mechanics under arbitrary deformation field. Moreover, an energy-based failure criterion, involving the maximum stretch, shear strain and rotation angle limits of the bond, is proposed to capture the progressive failure of general quasi-brittle materials. The validation of the proposed model is verified by comparing the simulation results to the experiment observations and analytical solution. Numerical results show that this improved model can be widely used to predict the nonlinear deformation, crack propagation and progressive failure of materials with variable Poisson’s ratio under complex loading conditions.