An Eulerian Deformable Cosserat Model for Large Deformations of Porous Geomaterials

The deformable Cosserat theory discussed in this paper models a continuum with interacting macro- and micro-continua. The macro-continuum describes elastic-plastic response, whereas the micro-continuum is represented by a triad of deformable director vectors determined by director momentum equations that include director-gradient effects. One objective of the paper is to modify the elastic measures of the micro-continuum to be independent of the plastic rate characterizing the macro-continuum. To this end, an additional triad of vectors is introduced through Eulerian evolution equations for material line elements. Elastic deformation measures are then defined to model the deformation of the director vectors relative to this triad of material line elements. The nonlinear purely mechanical theory of the resulting deformable Cosserat model is developed for both anisotropic and isotropic response. Limiting attention to elastically isotropic elastic-plastic response of the macro-continuum, specific equations are developed for a generalized yield criterion for geological materials with evacuated pores and dependence on the Lode angle, porosity, pressure, and hardening/softening of the yield strength. Finally, a small-deformation notched-plate example is used to emphasize the importance of the modified measures: the earlier measures lead to mesh-dependent softening responses, whereas the modified measures predict mesh-independent load-displacement curves, dissipated energy, and shear-band width for the single set of parameters considered.