A comparison of multilaminate and micro-plane models for soils and rocks

The project consists in developing and study the links and differences between two families of constitutive models that come from a same principle of angular discretization of space. These techniques consist in simplified micromechanics approaches where the macroscopic stress strain law is obtained by superposition of the constitutive response on planes of arbitrary orientation, covering all directions in space. On each plane, the constitutive law is expressed in terms of stress-strain relations for the projection of the overall stress or strain tensors, which makes for a simpler formulation than utilising the classical tensorial constitutive relations. These models are called Multilaminate models and Microplane models. The project will be focused in continuing to define the main theoretical aspects of both frameworks and some practical features of their implementation that are still not overcome, as well as working on a precise understanding of some basic definitions that have been lacking. The Multilaminate types of constitutive models simulate the deformation behaviour of the soil by considering the response on several so-called contact planes, whereon the yield surface and plastic potential are defined individually. On the other hand, Microplane models are developed through a strain driven formulation, based on a micro-macro kinematic constraint. This concept is derived from the hypothesis that the strain vector acting on a plane of arbitrary orientation, is equal to the projection of the strain tensor over the same plane.