  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.

Soft Condensed Matter