Formulation of a 3‐D numerical model of brittle behaviour

SUMMARY A 3‐D numerical model of brittle behaviour is proposed where matter is discretized in individual elements. These particles are linked by tensile interaction forces generating cohesive media. These spring‐like forces are linear and elastic when a small stretching effect is applied and decrease linearly to zero if the stretching exceeds a rupture threshold. Hence, for infinitesimal strains, the medium has an elastic response and elastic waves can propagate. For finite deformations, links can break, thus simulating microcracks, and eventually evolve into a macroscopic fracturing process. If the particles are stacked according to a face‐centred cubic lattice structure and interact with the first and second nearest neighbours, then the medium is isotropic and elastic. To determine the strength properties of this model, uniaxial compressional tests are run. On the basis of Mohr circle analysis, the fracture criterion of a reference model agrees with the Mohr‐Coulomb criterion. However, the evolution of the macroscopic fractures do not follow the direction predicted by this criterion. The evolution of the volumetric strains is comparable to laboratory observations on rock samples under uniaxial compression. Dilatancy begins at about half the failure stress and microcracking propagates pervasively throughout the sample prior to the failure. For small angles of dilatancy, the fractures are vertical. With an increase in the dilatancy angle the vertical fractures disappear and shear fractures appear at 45° from the main axis of strain. Ultimately, with increasing angles these shear fracture zones migrate to the centre of the sample. Fractures in the medium are aligned preferentially along the axes of symmetry of the FCC lattice structure. This is emphasized by the use of central interaction forces and a low residual friction.