19. Cosserat Approach to Localization in Geomaterials

A renewed interest toward Cosserat or micropolar continuum has driven researchers to the development of specific 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 micromorphic, 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 postlocalization 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.