Distal and non-symmetrical crack nucleation in delamination of plates via dimensionally-reduced peridynamics

TL;DR

This paper develops a dimensionally-reduced peridynamics model for plates that captures through-thickness crack nucleation and growth, including non-symmetrical and distal crack behaviors, bridging nonlocal and local fracture theories.

Contribution

It introduces a novel reduced-order peridynamics formulation for plates that explicitly models delamination and crack propagation with complex behaviors.

Findings

Captures distal and curved crack paths in plates.

Shows convergence to local elastic fracture models as nonlocal lengthscale vanishes.

Provides semi-analytical solutions for simplified fracture scenarios.

Abstract

Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional model. Delamination fracture nucleation and propagation are treated by choosing the kinematics to be composed of an absolutely continuous part and a zone where jumps in the displacements are allowed. This assumption allows the explicit derivation of the dimensionally-reduced elastic energy, which shows a hierarchy of terms characterising the stored energy in the plane element. An interpretation of the various terms of the reduced energy is shown by means of the most straightforward paradigm of bond-based peridynamics. A striking feature of the reduced energy is that, despite the small-displacement assumption, there is a coupling between the membrane and bending terms. Semi-analytical solutions for simplified settings are obtained through a minimization procedure, and a range of nonstandard behaviours such as \textit{distal} crack nucleation and curved crack path are captured by the model. Finally, convergence of the proposed peridynamic reduced model to a local elastic theory for vanishing nonlocal lengthscale is determined, giving a local cohesive model for fracture.