Newcastle Chapter

Evolution of strain localisation in granular materials

Prof Erich Bauer, Institute of Mechanics, Technical University Graz, Austria

It is experimentally evident that large monotonic shearing of a granular material causes a concentra-tion of the shear deformation into narrow zones along walls or inside of the granular body. Location, orientation and the evolution of strain localisation is determined by the mechanical properties of the granular material and the boundary conditions of the described problem. The evolution of the shear zone is characterised by dilatancy, strain softening and polar effects, i.e. grain rotations and couple stresses can be observed.

In this presentation numerical studies of polar effects within a planar shear layer of a cohesionless granular material are presented. The investigations are carried out for finite and infinite shear layers and differ-ent boundary conditions. In order to simulate the evolution of polar effects a micro-polar approach is formulated within the framework of hypo-plasticity. The model takes into account the current void ratio, Cosserat rotations, couple stresses and the mean grain diameter as an internal length. From the presents of an internal length the thickness of the localised zone obtained from the finite element cal-culation is not sensitive to the element size provided that the element size is small enough. The model captures the influence of the pressure level and the current void ratio on the incremental stiffness for both contractant or dilatant deformations using one set of constitutive constants. The interaction be-tween the grain boundary and the roughness of the surfaces adjoining the boundaries of the granular body is simulated by a certain rotation resistance of the Cosserat rotation. For instance very rough surfaces can capture grains in the boundary layer and no sliding and rotation may occur while for a medium rough surface a kinematic relation between the boundary displacement and the corresponding Cosserat rotation is assumed.

The results of the numerical investigations show that Cosserat rotations are significant in the shear zone and substantial for the thickness of this zone. But the thickness of this zone is not a material con-stant. The thickness strongly depends on the initial void ratio, the mean grain diameter and the mean pressure. As a result of dilatancy the void ratio within the localised zone is higher than outside of this zone. Thus, an initial isotropic material becomes anisotropic and in a stationary state a so-called criti-cal void ratio cannot be determined as an average value, which is important for the interpretation of experimental results and the calibration of the constitutive constants. A variation of the assumed roughness of the boundaries has a strong influence on the location of the localised zone. For a finite or an infinite shear layer the location of strain localisation is different and mainly depends on the lateral boundary conditions. Comparison between numerical calculations and experimental results presented in scientific literature shows acceptable agreement.

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