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.