Cosserat approach to localization in geomaterials

Accepted for publication in "Handbook of Nonlocal Continuum Mechanics for Materials and Structures", SpringerA renewed interest towards Cosserat or micropolar continuum has driven researchers to the development of specific constitutive models for upscaling discrete media such as masonry, granular assemblies, fault gouges, porous media and biomaterials. Cosserat continuum is a special case of what is called micro-morphic, generalized or higher order continua. Due to the presence of internal lengths in its formulation, Cosserat continuum is quite attractive for addressing problems involving strain localization. It enables modeling the shear band thickness evolution, tracking the post localization regime and correctly dissipating the energy when using numerical schemes. In this chapter we summarize the fundamental governing equations of a Cosserat continuum under multiphysical couplings. Several examples of the numerical advantages of Cosserat continuum are also presented regarding softening behavior, strain localization, finite element formulation, reduced integration and hourglass control. The classically used constitutive models in Cosserat elastoplasticity are presented and some common approaches for upscaling and homogenization in Cosserat continuum are discussed. Finally, a simple illustrative example of the adiabatic shearing of a rock layer under constant shear stress is presented in order to juxtapose a rate-independent Cosserat with a rate-dependent Cauchy formulation as far as it concerns strain localization