A simplified second gradient model for dilatant materials: Theory and numerical implementation

This paper deals with the development of a new second gradient model, its numerical implementation and its validation. In order to remedy to the spurious mesh dependency of the post localized computation enhanced models incorporating some internal length are necessary. These models are very time consuming. In this paper we present a simplified theory within the framework of constrained micromorphic models involving only the micro volumetric strain. Provided the use of an additional penalty term in the numerical treatment, this model is quite efficient to regularize problems modelling behaviors exhibiting plastic volumetric strain such as the ones of geomaterials. More over this model is notably less time consuming than the more general ones.