A novel kinematic-constraint-inspired non-ordinary state-based peridynamics

Abstract

The non-ordinary state-based peridynamics (NOSBPD) is attractive because of its ability to incorporate available constitutive models. However, conventional NOSBPD suffers from numerical oscillation induced by zero-energy mode. Although the recently proposed bond-associated deformation gradient performs well with controlling the issues, the size of the bond-associated horizon is undetermined. The work is aimed to introduce kinematic constraints to redefine the classical bond-associated deformation gradient. Based on the kinematic constraints imposed by the symmetry of the bond-associated deformation gradient and non-local kinematic measures, a well-defined bond-associated horizon is derived for 1D, 2D, and 3D structures. In this way, a novel kinematic-constraint-inspired non-ordinary state-based peridynamics (KC-NOSBPD) is proposed, which completely differs from the previous continuum-kinematics-inspired peridynamics (CPD) extended from classical bond-based peridynamics (BBPD). The linear and angular momentum conservation is firstly and rigorously proved. The novel proposed model is proved capable of avoiding unphysical deformation modes that typically beset conventional formulation through several analytical examples. In addition, bond-associated stress-state-based failure criteria are proposed for fracture analysis. Several benchmarking tests verify the effectiveness of the proposed formulation in eliminating spurious oscillation of numerical solution and highlight the significance of kinematic constraints. The final crack pattern of sandstone specimens coincides with experimental observation, illustrating its suitability for solving crack propagation.