A Practical Stress Correction Method for Improving Stability of State-Based Peridynamics Based on Stress Equilibrium Equation

Abstract

State-based peridynamics (SPD) is effective for simulating fracture and damage in different materials. However, the solutions may suffer from numerical instabilities, particularly for strong nonlinearity cases or large displacement cases, leading to inaccurate predictions or oscillation in responses. This paper proposed a novel practical method to solve the instability problem of SPD based on stress equilibrium equation, referred to herein as the stress correction method (SCM). A correction force is applied on each SPD point surrounding the loading points. The correction force is defined as the difference between an internal force obtained by the stress equilibrium equation and that obtained by the force states of the SPD. Four examples are presented herein to verify the accuracy and stability of the proposed method in various conditions, e.g. static and dynamic analyses of elastic and plastic models subjected to force and displacement boundary conditions.

Refined Simulation of Reinforced Concrete Beam Based on a Hybrid Peridynamic Method

“…However, there is currently insufficient utilization of SPD in the simulation of RC structures. In addition, the SPD may suffer from the so-called "zero-energy mode" (i.e., the predicted responses by SPD, such as displacements, stresses, and strains, may be inaccurate or have spatial oscillation) [5,[22][23][24][25]. To mitigate the zeroenergy mode, several solutions have been proposed in the literature.…”