To date, a number of different numerical modelling tools have been used successfully to investigate aspects of deformation in geological materials at all scales from microscopic to lithospheric. Different methodologies are best suited to different applications, and the choice of numerical approach is principally governed by the rheology of interest. Viscoelastic and plastic behaviour has been most successfully simulated using finite element of lagrangian finite difference codes. These codes have the advantage of an accurate representation of the deformation mechanisms, but are restricted in that strain localisation is strongly grid dependent, and the initiation and propagation of dislocations (faults or fractures) must either be approximated by localised plastic behaviour, or require computationally intensive iterative re-gridding as the geometry evolves. The simulation of fault and fracture growth is handled well by boundary element schemes, but the modeller is restricted to considering only linear elastic materials to represent rocks. Some of the problems associated with the development of discontinuities are solved by discrete particle schemes. These represent the rock as an assembly of elastic particles which may be bonded together to produce a material with the desired macroscopic properties. Elastic and plastic rheologies are reproduced in discrete particle schemes, but visco-elastic behaviour is restricted to the low-strain relaxation of stress.

A new numerical scheme is presented that allows high-strain viscoelastic rheology within the same system as elastic, brittle and plastic rheologies. Based on the discrete particle methodology, the code differs from previous codes in that individual particles can deform in response to local stresses. Most significantly, any number of contrasting rheologies can be included in the same model without compromising numerical accuracy. Simulated lab tests are presented to illustrate the range of rheological behaviours available. Simple example models are developed to illustrate the potential application of this scheme to geological deformation processes such as diapirism, igneous intrusion, whole-lithosphere deformation, deformation at the brittle-ductile transition and folding.