Simulation of highly nonlinear materials based on a stabilized non-ordinary state-based peridynamic model

Peridynamics (PD) is an effective method to solve discontinuity problems that involve cracking or crushing behaviors. In the non-ordinary state-based PD (NOSBPD), the so called zero-energy mode may cause inaccuracy particularly when the material is highly nonlinear. This paper proposed a novel stabilized NOSBPD modeling method to mitigate the inaccuracy and instability of NOSBPD solutions. A correction force for a PD point is defined as the difference between an internal force obtained by stress equilibrium equation and that obtained by the force states of the points within its horizon. The correction force is applied on the PD points to be corrected, e.g., that on the boundary of a PD model. Three examples are presented demonstrating the proposed method's effectiveness in static and dynamic analyses of both linear or highly nonlinear models, i.e., 3D cap plasticity concrete model and 2D multi-yield surface soil model. The predicted responses (e.g., displacements, stresses, strains at representative points) are analyzed and compared with those without force correction for both linear and highly nonlinear cases. The proposed method is demonstrated to be an effective method for mitigating the inaccuracy and instability of the NOSBPD solutions.