An irregular lattice model to simulate crack paths in bonded granular assemblies

• This paper presents a simple lattice model for bonded granular materials.
• The bonding laws mimic the interaction of the grains.
• Simulations of some standard tests and deforming masonry elements are presented.
• Realistic crack patterns and load–displacement behaviour is predicted.

A 2D model of a bonded granular material is presented and its properties confirmed to be that of a brittle, isotropic elastic solid. The bond stiffnesses (axial tension/compression, shear and bending) are taken from the classical solutions to the external crack problem with two half-spaces bonded by a disc of intact material. An assembly of granules is simulated using a random array of points (representing the granule locations) with a prescribed minimum separation. The bonds are then generated by a Delaunay triangulation. This produces an isotropic array of bonds giving rise to a model material with isotropic properties. Crack growth is simulated by sequentially removing the most highly stressed bond in turn. Crack paths are then produced which are shown to agree with the predictions of linear elastic fracture mechanics, in respect of both the direction of propagation and the influence of specimen size. Some well-known problems are then simulated including: the interaction of two parallel cracks; diametrical compression of a disc; the four point bending of a beam; the influence of mortar strength on the behaviour of masonry; and a flat arch.