| Abstract: | A major problem in the mathematical modelling of the deformation of granular materials has been the lack of an easily usable variational principle. This is because the frictional dissipation of energy in these materials does not allow the use of the classical extremum principles. In this paper, a variational principle is constructed which is valid even when frictional dissipation occurs. Its derivation uses results from the mathematical theory of envelopes. Both the stresses and the strains can be varied, and for the case of non-frictional plasticity it reduces to the maximum work principle of Hill. An example is presented to show how this new principle can be used to obtain approximate solutions to boundary-value problems with granular materials. The only requirements in advance are a displacement field that obeys the kinematic boundary conditions, and a stress field that obeys equilibrium and the static boundary conditions. The principle is therefore quite straightforward to apply. |
