TABLE OF CONTENTS In the previous chapters we have considered the solution of solid mechanics problems from the view of a continuum. A computational framework which allows for some level of displacement field discontinuity to be represented a priori might be better suited to model particular phenomena, for example the behaviour of jointed rock or the granular material flow in silos. The treatment of these classes of problems is more naturally related to discrete element methods, in which distinctly separate material regions interacting with other discrete elements in some way are considered. A number of more complex models for both solid materials as well as for contact interactions have been formulated in the context of a discrete element methodology, with successful applications in many fields of science and engineering.
Moreover, most media are discontinuous at some level of observation ( nano, micro, meso, macro), where the continuum assumptions cease to apply. This happens when the scale of the problem becomes similar to the characteristic length scale of the associated material structure and surface interaction laws between bodies or particles are invoked instead of a homogenized continuum constitutive law. The computational modelling of inherently discontinuous media requires the discrete nature of discontinuities to be taken into account. Discontinuities can be either pre-existing (e.g. joints, bedding planes, interfaces, planes of weakness, construction joints) or they evolve (e.g. in the case of cohesive frictional materials, where the growth and coalescence of micro cracks eventually appear in a form...
