Reliably modelling the emergence of shear bands in geotechnical failure events has long posed problems to conventional numerical modelling techniques, for two key reasons. Firstly, as such events generally involve very large deformations and complex boundary dynamics, mesh-based techniques like the finite element method can suffer a loss of accuracy and even breakdown of the numerics as elements become increasingly distorted. The chosen numerical technique for this work, the material point method (MPM), avoids this issue by instead discretising the domain into Lagrangian particles which deform through a background mesh. The mesh is used to complete a standard finite element calculation but is reset to its initial position after each load step, minimising any inaccuracy arising from mesh distortion.

Secondly, the localisation of strain into shear bands introduces a discontinuity into an otherwise smooth displacement field; when using a classical continuum theory, this forces the governing system of equations to become ill-posed. This manifests as an unacceptable mesh-dependent solution, which does not converge towards a steady shear band thickness or failure load with refinement. To regularise this, the micropolar (Cosserat) continuum introduces a field of independent micro-rotations to the configuration space. The rotations and their spatial gradient (curvature) smoothen the solution field around the shear band with respect to a length scale taken to be indicative of the size of the microstructure. Simulations based on the micropolar continuum can therefore reliably predict shear bands with a finite thickness depending on the scale of the constituent microstructure, without resorting to artificial smoothing techniques.

This presentation will outline an approach based on an extension of geometrically-exact micropolar theory into the paradigm of classical plasticity, incorporating frictional effects, and implemented within an implicit MPM. Application of the method to several quasi-static examples, including plane-strain tests and slope stability problems, will also be demonstrated.

In terms of classical continuum constitutive models, the loss of ellipticity of the governing rate equilibrium equations entails localizing deformations and mesh sensitivity in finite element simulations. Extensions of such models rooted in the micromorphic continuum aim at remedying mesh sensitivity by introducing length scales to the constitutive formulation. The micropolar continuum, which goes back to the Cosserat brothers, constitutes a special case of the micromorphic continuum and is commonly employed for remedying mesh sensitivity accompanying shear band failure. Despite this fact, localizing deformations in the micropolar continuum remain a largely unexplored phenomenon. The aim of the present study is to thoroughly investigate the conditions for localizing deformations in the context of the micropolar continuum and to highlight their implications for structural simulations. To this end, we propose an infinitesimal elastoplastic micropolar constitutive model rooted in critical state soil mechanics and establish its localization characteristics. Investigations at the constitutive level highlight the stabilizing effect of the micropolar extension, which is increased both by the presence of couple stresses as well as by increasing the Cosserat shear modulus. Structural simulations exhibit good agreement with the results obtained at the constitutive level. Nevertheless, cases where shear band failure is not adequately regularized by means of the micropolar model are also identified. Moreover, the destabilizing effect of structural inhomogeneity is highlighted.

Mixed control problems represent the material problems for solving the part of stress and strain response if the counterparts of stress and strain are given/controlled. Most strain-controlled experiments belong to the mixed control problems such as the strain controlled uniaxial tests, the strain-controlled axial-torsional test, and strain-controlled biaxial tests. To deal with the mixed control problems, the plastic integration based on the pure stress representation or the pure strain representation are not workable hence additional treatment is needed in general. In this study, we explored the internal symmetry of an elastoplastic model for anisotropic materials under mixed control and developed its return-free integration for mixed control problems based on the theory of Lie algebra and Lie group. We conducted an error analysis of the return-free integration to demonstrate the its accuracy under different initial conditions. Using the accurate return-free integration, we investigated the contraction ratio and the r-value of differential materials.

In granular soils, shear loading often results in a failure that is distinctively characterised by the formation of shear bands in which the deformations localise. In order to predict the mechanical behaviour of geotechnical structures, it is essential to accurately capture this behaviour in numerical simulations.

The objective of this contribution is to critically assess the capability of a micropolar hypoplastic material model in predicting the shear failure of sand with finite element analysis. Specifically, the micropolar hypoplastic model introduced by Maier (2002) is evaluated, which enhances the well-established hypoplastic material model for sand developed by Wolffersdorff (1996). By employing both 2D and 3D finite element simulations, this study aims to predict the mechanical behaviour of sand specimens in standard laboratory tests, such as the biaxial and triaxial compression tests. It is shown that the micropolar hypoplastic model accurately represents the nonlinear, inelastic behaviour of sand, accounting for its density and pressure dependencies. A mesh sensitivity study confirms that the model is capable of predicting stress and deformation states during shear-dominated failure without encountering mesh sensitivity issues. This capability is superior compared to classical hypoplastic models that neglect the inherent granular microstructure. Additionally, the influence of the micropolar material parameters --the mean grain diameter and the grain roughness-- on material behaviour as well as shear band characteristics is studied. Finally, the numerical results of this study are compared with experimental laboratory test data to confirm the validity of the model.