Stochastic Model for the Interaction of Buckling and Fracture in Thin Tension-Loaded Sheets

TL;DR

This paper presents a new stochastic lattice model for thin sheets that captures the interaction between buckling and fracture, allowing for the study of complex crack behaviors and buckling phenomena in tension-loaded materials.

Contribution

The paper introduces a novel elastic beam lattice model incorporating out-of-plane buckling degrees of freedom for fracture analysis in thin sheets.

Findings

Model successfully simulates buckling and fracture interactions.

Results include force and displacement fields and buckling response ratios.

Framework adaptable to disorder and complex crack geometries.

Abstract

We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to preserve rotational invariance. Fracture is initiated by displacement control, applying a uniaxial force couple at the top and bottom rows of the lattice in mode-I type loading. The approach lends itself naturally to the inclusion of disorder and enables a wide variety of fracture behaviours to be studied, ranging from systems with a simple geometrical discontinuity to more complex crack geometries and random cracking. Breakdown can be initiated from a pre-cracked sheet or from an intact sheet where the first damage appears at random, and buckling sets in when a displacement vector containing out-of-place components becomes energetically favourable over one which does not. In this paper we only consider center-cracked sheets with no disorder and include some results relevant to the force- and displacement-fields, and the buckling response ratio. Rather than carry out a comprehensive study of such systems, the emphasis presently is on the development of the model itself.