  A Finite Element procedure based on a full implicit backward Euler
predictor/corrector scheme for the Cosserat continuum is here presented. Since
this is based on invariants of the stress and couple stress tensors and on the
spectral decomposition of the former, considerable benefits are achieved. The
integration requires the solution of a single equation in a single unknown,
which is a considerable improvement as compared to the system of seven or four
equations required by other approaches available in the literature for the
Cauchy medium. The scheme also allows for a very efficient treatment of the
singularity which affects the apex of most of the existing yield and plastic
potential surfaces. Moreover, no complications arise when some of the principal
stresses coincide. The algorithm has been implemented in a proprietary Finite
Element program, and used for the constitutive model proposed in part I of this
paper. Numerical analyses have been conducted to simulate a biaxial compression
test and a shallow strip footing resting on a Tresca, Mohr-Coulomb,
Matsuoka-Nakai and Lade-Duncan soil. The benefits of the Cosserat continuum
over the Cauchy/Maxwell medium are discussed considering mesh refinement,
non-associated flow and softening behaviour.
