On the shape of a plastic layer compressed by parallel planes

The problem of the shape of the contour which bounds a thin layer made of an ideally plastic material is investigated. The layer is compressed by parallel planes which approach one another along a common normal (a spreading problem). New formulations of the problems are presented together with the traditional formulation. In all cases, they reduce to a Cauchy problem for non-linear evolutionary equations and the study is carried out in the class of self-similar solutions. Using the method proposed in this paper, new solutions are obtained in both the traditional and new formulations.