A viscoelastic micropolar peridynamic model for quasi-brittle materials incorporating loading-rate effects

A viscoelastic micropolar peridynamic (VMPD) model is proposed to describe the nonlinear deformation and fracture behaviors of quasi-brittle materials considering loading-rate effects. The governing equations of bonds connecting material points are reformulated by introducing the definition of bond deformation rates. Two peridynamic parameters, corresponding to the normal stiffness and the tangential stiffness of the bond, respectively, are introduced to ensure that the strain energy obtained from the proposed peridynamic model is consistent to that from the continuum viscoelastic mechanics. A novel failure criterion is developed to describe the dynamic progressive fracture of quasi-brittle materials. Damage functions and dynamic strengths of the bond are introduced to capture loading-rate effects for solid materials. The proposed model is verified by comparing its predictions with those from experimental observations. Numerical examples demonstrate that the nonlinear viscoelastic behaviors of quasi-brittle materials such as relaxation, softening–hardening behaviors as well as mix-mode fractures under dynamic loads with different loading rates are well captured by the proposed model.