SUMMARYIn this paper a micro-polar continuum approach is proposed to model the essential properties of cohesionless granular materials like sand. The model takes into account the influence of particle rotations, the mean grain size, the void ratio, the stresses and couple stresses. The constitutive equations for the stresses and couple stresses are incrementally non-linear and based on the concept of hypoplasticity. For plane strain problems the implementation of the model in a finite element program is described. Numerical studies of the evolution of micro-polar effects within a granular strip under plane shearing are presented. It is shown that the location and evolution of shear localization is strongly influenced by the initial state and the micro-polar boundary conditions. For large shearing the state quantities tend towards a stationary state for which a certain coupling between the norm of the stress deviator and the norm of the couple stress tensor can be derived.

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The paper presents a simple constitutive model for normally consolidated clay. A mathematical formulation, using a single tensor-valued function to define the incrementally nonlinear stress-strain relation, is proposed based on the basic concept of hypoplasticity. The structure of the tensor-valued function is determined in the light of the response envelope. Particular attention is paid towards incorporating the critical state and to the capability for capturing undrained behaviour of clayey soils. With five material parameters that can be determined easily from isotropic consolidation and triaxial compression tests, the model is shown to provide good predictions for the response of normally consolidated clay along various stress paths, including drained true triaxial tests and undrained shear tests.