Group Analysis of a System of Anisotropic Plane Plasticity

Abstract:
The system of plane plasticity with a general yield criterion [1] describes a plastic plane deformation of anisotropic materials, in particular, is applying in the static of soil medias [2].

In the report we'll present a group classification of this system using well-known methods of group analysis [3]. There were found some specifications, for which we have the extension of a basic group of symmetries. For the algebras of Lie, corresponding to this specifications the optimal systems of subalgebras were constructed and some invariant solutions were obtained.

This research was supported by PROMEP (Mexico).

1. Hill R., The Mathematical Theory of Plasticity, Oxford, Clarendon Press, 1960.
2. Sokolovsky V.V., Statics of Soil Media, London, Butterworth's Scientific Publications, 1960.
3. Ovsyannikov L.V., Group Analysis of Differential Equations, New York, Academic Press, 1982.