Development of a non-ordinary state-based peridynamics solver

Abstract

Damage prediction is crucial in the design process of engineering structures to ensure structural integrity. The limitations of empirical methods and the high costs associated with experimental analyses have prompted the development of numerical methods to predict the initiation and/or propagation of cracks under prescribed loading conditions. While various methods exist for failure prediction, their formulations rely on partial differential equations with spatial derivatives. As a result, these methods require special treatments in order to accurately capture the underlying failure mechanisms. To overcome these limitations, the peridynamic theory has been introduced as a novel, nonlocal continuum formulation. In contrast to the other methods, it is expressed as an integro-differential equation devoid of spatial derivatives, hence applicable to structural analyses involving discontinuities. This project aims to elaborate on the development of a solver based on a specific variant of the peridynamic formulation to investigate the behavior of two- and three-dimensional structures under certain loading conditions. The current code is developed to solve quasi-static problems related to damage initiation and propagation. In addition, it is aimed to show that peridynamics can capture local, hyperelastic deformations. The overall structure of the code is reviewed and the potential extensions of the current work are discussed.