Micromechanical studies of shear bands

Micromechanically the solid consists of grains of different shapes which mutually hinder their diplacements and force the formation of a plane in which the grains essentially rotate. The appearing holes produce the dilatancy.

The figure to the left shows an originally completely dense system after being sheared horizontally under a vertical pressure as produced by Hans Jürgen Tillemanns. On large scales this gives shear bands. For more details see our paper published in Physica A 217, 261-288 (1995).

In a (2d) Couette experiment where only the inner wheel rotates the shear band is fixed next to the inner wall as seen in experiments . A simulation with Steffen Schollmann and Stefan Luding allowed for the measurement of the force lines and displacements . For more details see our paper .

In a uniaxial compression simulation in two dimensions and semiflexible sidewalls we obtained with Fernando Alonso-Marroquin shear bands as shown below. This allowed for a detailed description of the plastic constitutive relation of a polygonal packing as can be seen in our recent paper published in Phys.Rev.E Vol.66, p.021301 (2002). In the next paper published in the proceedings of the Int.Mech.Eng.Conf. 2002 p.32498 (Orleans) we studied the incremental response in a representative volume element and found that already for very small shear stress the system is plastic which means that strictly speaking there exists no elastic regime as opposed to the predictions of the Drucker-Prager theory. In a recent preprint with Andres Pena and Arcesio Lizcano we also studied the fluctuations in biaxial tests.

Another interesting discovery we made for shear bands under uniaxial load is the spontaneous appearance of regions of particles rolling on each other like a bearing. These appear in particular if the particles are circular, i.e. discs in two-dimensions, as published with Jan Astrom and Jussi Timonen in Physcal Review Letter, Vol. 84, 638-641 (2000). Very interesting is also the question what happens when the particles can fragment. Then as shown in our paper published in Europ. Phys. J. E, Vol.4, p.273-279 (2001) the shear bands densify and become stiffer.

In a recent paper published in Phys.Rev.Lett. Vol.92, p.054301 (2004) we show that under cyclic loading one obtains a very slow plastic deformation as seen in the figure which is due to configurations in the packing that act as a ratchet. The motions of such a configuration after one cycle can be seen in this image .

This ratcheting is also observed in systems of spheres and using a different numerical technique, namely Contact Dynamics as shown with Ramón García Rojo in the proceedings to ECCOMAS 2004 and in the proceedings for Bochum 2004. Particularly interesting is also the existence of a transition between ratcheting and shakedown, i.e. the definite setting of a granular packing under vibration as discussed in a preprint for Granular Matter .

You can also download a talk that I gave in several occasions on the subject.

Much of the work done in the last years was within a so called "Forschergruppe" of the DFG (German Science Foundation) with the name: "Continuous and Discontinuous Modelling of Cohesive-Frictional Materials". which gave me the chance to collaborate with my colleagues Wolfgang Ehlers, Ekkehard Ramm and Pieter Vermeer and their students. Within this group we published a paper by Ellen Kuhl on the microplane model. We also organized two meetings, CDM2000 and CDM2004. On the photo you see Stefan Luding, Ramón García Rojo and myself at the CDM2004.

With Ramón we try to get some heavenly inspiration.