Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies.

*(English)*Zbl 1047.74522Summary: Many plastic second gradient models have been developed in the last 10 years. However some plastic second gradient models are nonlocal ones. This paper is an attempt to give a general framework to deal with local second gradient theories within theories with microstructure, keeping in mind future applications for geomaterials. It is advocated that particular elasto-plastic local models with microstructure, namely local second gradient and Cosserat second gradient models, which are the least developed in the literature have some advantages which are somewhat promising. One main objective of this paper is to present these two families of models. The first one (Cosserat second gradient model) is shown to be well adapted to granular materials. The second model family is likely to be a good model for cohesive geomaterials. Another aim of this work is to give a method to obtain basic solutions, which can be seen as localization analysis, in one and two dimensions cases. The key point of this method is the use of patch conditions between loading and unloading parts.