Wave dispersion and quantitative accuracy analysis of bond-based peridynamic models with different attenuation functions

Abstract

Peridynamics (PD) reformulates classical continuum mechanics in terms of spatial integral equations rather than partial differential equations. PD has successfully matched fracture patterns observed in experiments. However, issues remain, such as its dispersion characteristics, constant micromodules, and behavior at material boundaries. The introduction of attenuation functions can effectively address these three problems. In this study, we attempted to conduct a systematic investigation of bond-based peridynamics (BPD) with different attenuation functions. This mainly involved an analysis of the wave dispersion, surface effect, and quantitative accuracy of BPD models with different attenuation functions. Initially, a novel quartic polynomial attenuation function was proposed, and various types of functions were investigated. The corresponding expressions for non-constant micromodulus functions were determined, and attenuation bond-based peridynamic (ABPD) models that considered the effect of attenuation were established. Furthermore, the dispersion relationship of ABPD for the one-dimensional case was derived, and the effects of the horizon size, material point size, and attenuation functions on the dispersion properties were investigated. Finally, the surface effect and the effectiveness of different attenuation functions were examined by considering the attenuation functions and energy correction method in ABPD models under plane stress and plane strain conditions. Thus, the accuracy of ABPD was evaluated. The influence function proposed in this work and other several attenuation functions can be used to minimize wave dispersion for a fixed material point size or horizon size and to reduce the surface effect. The energy correction method had a remarkable influence on the computational accuracies of the classical BPD model and ABPD models. Practical recommendations for selecting the attenuation functions for coupling PD with other methods and for enhancing the accuracy of the BPD model were provided.