A stability augmentation technique for state-based peridynamics

Abstract

State-based peridynamics (SPD) is an effective method for simulating the fracture and damage behaviors of various materials. However, SPD may suffer from zero-energy mode problems, leading to numerical instabilities, e.g., response oscillations in displacement or stress, due to its nodal integration scheme. The issues are particularly pronounced under highly non-uniform external loading conditions, such as single point loads. This paper presents a novel stability augmentation technique (SAT) for SPD under varied loading conditions. The SAT identifies points causing zero-energy mode problems and applies corrective forces at these points by replacing nodal integration with multi-point integration: it involves adding auxiliary points at the midpoints between each peridynamic (PD) point and its neighbors within the horizon, calculating the strain at each auxiliary point with a newly defined sub-horizon similar to SPD methods, computing the stresses at these points and integrating them to determine the internal force at the PD point. This innovative approach not only eliminates zero-energy modes but also preserves computational efficiency by selectively applying corrections at critical points. Moreover, it simplifies the integration process with predetermined coefficients and ensures versatility under diverse static and dynamic loading conditions. The calculations are streamlined by using existing PD horizons to define sub-horizons. Implemented in the open-source software OpenSees, the SAT is evaluated across three applications and confirmed its effectiveness in addressing stability issues in SPD.