Theory and Simulation of the Structural and Damage Behaviour of Lightweight Structures Using Peridynamics

Abstract

The simulation of the structural behaviour and particularly damage response is a key instrument for the development of lightweight structures as required in aerospace engineering or wind rotor blade development. The prediction of damage initiation and propagation is a challenging task, even for state-of-the-art numerical procedures, such as the finite element method. The peridynamic theory presents a promising approach for these requirements. It is a non-local theory which takes long-range forces between material points into account. The theory assumes that a material point interacts with all its neighbouring particles within a finite radius. The formulation of its governing equations is based on integral equations, which are valid everywhere - whether a discontinuity such as a crack exists in the material or not. Damage is directly incorporated in the material response. In this thesis, the underlying theory and its numerical implementation are introduced. A multi-level validation of the theory is performed for exemplary problems. Firstly, the peridynamic theory is implemented for one-dimensional examples and compared to the analytical problem solution. Subsequently, a peridynamic code is investigated and further examples including damage are assessed and compared to finite element and extended _nite element method solutions.