On Nonlocality and Locality: Differential and Discrete Formulations

Nonlocal approaches are discussed with regard to the differential and discrete formulations. Nonlocality was found to be a concept non attaining to the description of the material, but of the physical phenomenon. When using the differential formulation for modeling heterogeneous materials, a length scale must be introduced into the material description. This need has been here justified on the basis of the geometrical information which has been lost in performing the limit process. It was shown how, avoiding the limit process, a length scale is intrinsically taken into account into a discrete formulation. This made it possible to discuss the opportunity of using nonlocality in order to give respectability to strain-softening damage models.