### A comparative study of models for incompressible granular materials

Alexandrov, S; Harris, D *(Ins for Problems in Mechanics/Manchester)*

Tuesday 06 January 2009, 12:15-12:30

Seminar Room 1, Newton Institute

#### Abstract

Models of pressure-dependent plasticity are used for describing deformation of granular materials, among other materials. In contrast to classical metal plasticity, there is no commonly accepted model of pressure-dependent plasticity, though most of such models reduce to classical plasticity at a specific set of parameters. Nevertheless, the solution behaviour can essentially depend on the pressure-dependent model chosen, independently of how close the input parameters are to these specific values. Therefore, it is of interest to carry out a systematic study for understanding the difference in solution behaviour. First, several analytic solutions based on different models of pressure-dependent plasticity (the coaxial model, the double-shearing model, and the double-slip and rotation model) are compared to each other and to the corresponding solutions based on the classical metal plasticity. It is concluded that the qualitative difference in solution behaviour can occur in the vicinity of maximum friction surfaces. One typical difference occurs in flows where the classical rigid plastic solutions are singular (some strain rate components approach infinity in the vicinity of maximum friction surfaces). The same qualitative behaviour demonstrates solutions based on the double-shearing model and the double-slip and rotation model as well, but not on the coaxial model. The other difference is related to the transition between the regimes of sliding and sticking at the friction surface. In this case, the same qualitative behaviour is revealed in solutions based on the double-slip and rotation model only. Using these mathematical arguments, it is concluded that the double-slip and rotation model leads to a more adequate description of material behaviour. It is a matter of special importance for materials with a large value of internal friction. In this case the pressure-dependency of material is very low and it is necessary that in applications both the classical rigid plastic model and the model of pressure-dependent plasticity give acceptable results for the same material. Obviously, the area of applicability of this or that model is rather conditional on the specific area of application. Therefore, it is advantageous that the solutions based on both models show the same qualitative behaviour everywhere.

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