Numerical stability of non-local viscoplastic FEM analyses for the study of localisation processes

As is well known, numerically handling, by means of finite element codes, localisation problems involving softening materials is still quite delicate. As soon as strain localisation occurs, mesh dependence and serious problems of convergence take place. This paper deals with this type of problem in the case where localisation occurs in an ideal naturally cemented granular specimen tested under plane strain conditions. Different versions (a local elasto-plastic, a local viscoplastic and a non-local viscoplastic) of the same strain softening model are taken into consideration and the relative numerical results are critically discussed and compared. The snap-back problem is numerically taken into account and it has been demonstrated to be affected not only by the softening parameters but also by the viscous nucleus definition. To highlight the relationship between viscosity and non-locality, the results of a numerical parametric analysis are finally discussed.