A Quasi-Brittle damage model in the framework of Bond-based Peridynamics with Adaptive Dynamic Relaxation method

Abstract

Peridynamics (PD) is a new tool, based on the non-local theory for modelling fracture mechanics, where particles connected through physical interaction used to represent a domain. By using the PD theory, damage or crack in a material domain can be shown in much practical representation. This study compares between Prototype Microelastic Brittle (PMB) damage model and a new Quasi-Brittle (QBR) [4] damage model in the framework of the Bond-based Peridynamics (BBPD) in terms of the damage plot. An in-house code using Matlab was developed for BBPD with the inclusion of both damage models, and tested for a quasi-static problem with the implementation of Adaptive Dynamic Relaxation (ADR) method in the theory in order to get a faster steady state solutions [1]. This paper is the first attempt to include ADR method in the framework of BBPD for QBR damage model. A numerical problem with the absence of failure is analysed, and the displacement is compared with literature result that utilised Finite Element Method (FEM). The obtained numerical results are in good agreement with the result from FEM. The problem was extended by allowing the failure to happen for both of the damage models; PMB and QBR, to observe the damage patterns between these two damage models. PMB damage model produced damage value of roughly twice compared to the damage value from QBR damage model. It is found that the QBR damage model with ADR under quasi-static loading shows a more uniform damage pattern through the crack path compared to the PMB damage pattern.