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

Abstract

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.

Towards understanding the influence of porosity on mechanical and fracture behaviour of quasi-brittle materials: experiments and modelling

“…Lattice models have been used in the past to simulate deformation and fracture in quasi-brittle materials such as concrete (Bolander et al 2000;Schlangen and Garboczi 1997;Schlangen and Qian 2009), nuclear graphite (Šavija et al 2016;Smith et al 2013), and rock (Asahina et al 2014;Sands 2016). Unlike conventional approaches based on continuum mechanics, the material is discretized as a set of two-node (spring, truss, or beam) elements which can transfer forces in lattice models.…”

Use of phase change materials (PCMs) to mitigate early age thermal cracking in concrete: Theoretical considerations

“…Lattice models have long been used to simulate fracture processes in concrete [33][34][35] and other quasibrittle materials [36,37]. Unlike the continuum mechanics approaches, in this type of models the continuum is discretized as a set of two-node (truss or beam) elements which can transfer forces.…”

On adaptive refinements in discrete probabilistic fracture models

“…There is a complex damage-mechanics based constitutive law used at the facets. Its deterministic version has been adapted from [9], where it is also described in detail. The main material parameters for fracture behavior are tensile strength, ft, and tensile fracture energy, GF.…”

“…There are several versions of discrete models developed and used for many purposes. In case of simulating fracture in concrete, the lattice models are often employed [6][7][8]. These models represent the concrete meso-structure by projecting it onto the independently generated lattice.…”

“…They are excellent in describing fracture phenomena, but applicable only for small laboratory specimens due to their extreme computational demands. Another group of discrete meso-level modelling approaches, sometimes called particle models, generates the network geometry directly according to the meso-structure of concrete [9,10]; typically one node for each mineral aggregate. We focus here on the latter group with geometry generated via Voronoi tessellation [11][12][13][14].…”