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

Bjorn Skjetne·Torbjorn Helle·Alex Hansen
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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.

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Bjorn Skjetne, Torbjorn Helle, Alex Hansen. 2005-05-27. Stochastic Model for the Interaction of Buckling and Fracture in Thin Tension-Loaded Sheets. https://arxiv.org/abs/cond-mat/0505667

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