An energy based peridynamic state-based failure criterion

Abstract

The simulation of the structural behavior 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 in structural elements 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. Utilizing the state-based formulation arbitrary materials can be modeled and analyzed.

Proper failure criteria are needed for this formulation. The majority of publications use the so-called critical stretch model. Therein, a ``bond'' between two points breaks when its stretch exceeds a critical value. However, this model reaches its limits when convergence is considered.

Therefore, in this paper a mode-dependent energy based failure criterion has been developed based on the work of Foster et. al. The criterion has been implemented in the peridynamic code Peridigm.

In the scope of this publication, the fundamental theory of the failure criterion as well as the implementation in a massively parallel peridynamics code are explained. Based on these implementations, studies regarding the effect of probabilistic material properties to the crack initiation position are shown.