A geometrically-exact Finite Element Method for micropolar continua with finite deformations

Micropolar theory is a weakly non-local higher-order continuum theory based on the inclusion of independent (micro-)rotational degrees of freedom. Subsequent introduction of couple-stresses and an internal length scale mean the micropolar continuum is therefore capable of modelling size effects. This paper proposes a non-linear Finite Element Method based on the spatial micropolar equilibrium equations, but using the classical linear micropolar constitutive laws defined in the reference configuration. The method is verified rigorously with the Method of Manufactured Solutions, and quadratic Newton-Raphson convergence of the minimised residuals is demonstrated

Simulation of strain localisation with an elastoplastic micropolar material point method

The thickness of shear bands, which form along slip surfaces during certain modes of geotechnical failure, depends directly on the size of the soil particles. Classical continuum models, however, are invariant to length scale, so the strain localisation zone cannot converge to a finite size when employing numerical techniques such as the finite element method. Instead, the present approach adopts the micropolar (Cosserat) continuum, a weakly non-local higher-order theory which incorporates a characteristic length and allows independent rotations of the material micro-structure as well as transmission of couple stresses. As a result, strain can localise naturally in micropolar continua to form realistic finitesized shear bands. By extending an elastic finite-strain micropolar implementation of the material point method (a numerical method well-suited to modelling large deformation problems) with an elasto-plastic constitutive model suitable for geomaterials, this novel combined approach will provide a powerful tool to analyse numerically challenging localisation problems in geotechnics