A developed 3D peridynamic method incorporating non-conservative force for brittle materials

Abstract

A 3D peridynamic method involving the work done by the non-conservative force is developed, whose theoretical framework comprises two parts: the viscoelastic motion equation of material points and the rate-dependent fracture criterion of the bond. For the description of motion, a viscoelastic interaction model between material points is proposed based on the understanding deformation mechanism of concrete. Further, the viscoelastic motion equation is theorized by applying Hamilton's principle which considers the energy dissipation, as a result, the viscoelastic deformation of brittle material can be captured. The elastic and viscous parameters are calibrated by the energy density equivalence between the developed 3D peridynamic method and the classical continuum mechanics under the same deformation condition. For the control of strength and cracking, the dynamic uniaxial S strength criterion is introduced into the fracture criterion of the bond so that the rate-dependent behavior of strength and cracking failure can be reflected. The function and superiority of the developed 3D peridynamic method are discussed via numerical experiments. It is found that the developed peridynamic method can reasonably reflect the influence of loading rate on the deformation, strength, and cracking of brittle material.