Non-associated Cosserat plasticity

Frictional plasticity models with a non-associated flow rule, ubiquitous for describing failure in geomaterials, can lead to a local loss of ellipticity for low hardening rates, i.e. before entering a strain-softening regime. This leads to an excessive dependence on the spatial discretisation and to an inability of Newton-Raphson methods to converge. Higher-order continuum models can remedy this. The Cosserat continuum is particularly suitable for granular media because the rotational degrees of freedom of this model can represent the rotation of (assemblies of) grains or blocks which form the microstructure of such materials. We illustrate this analytically by the example of an infinitely long shear layer and through a three-dimensional bifurcation analysis. Numerical simulations show the consequences, i.e. the anomalies of standard continuum models and the correct behaviour of non-associated plasticity models embedded in a Cosserat continuum. The motivation for using a Cosserat continuum for granular and blocky materials is further strengthened through shear band simulations of biaxial tests, where the inclination angle shows the same dependence on the internal length scale as that on the grain size in tests. This result is the first proper explanation for this dependence.