Discrete mechanical models and upscaling techniques for discrete materials

Numerous natural and man-made materials are essentially discrete
structures at the mesoscale or microscale (see Fig. 1). Discrete
mechanical models can be formulated to capture typical mechanical
phenomena arising from this discreteness. Failure in these materials,
which often starts with the fracture of an individual bond, can be predicted
based on the small-scale mechanics with these models. For failure, but
also for non-local mechanics, no phenomenological descriptions are
required in these models. This makes them more predictive than
constitutive material models for this type of materials.