  A new mathematical formulation for the constitutive laws governing elastic
perfectly plastic materials is proposed here. In particular, it is shown that
the elastic strain rate and the plastic strain rate form an orthogonal
decomposition with respect to the tangent cone and the normal cone of the yield
domain. It is also shown that the stress rate can be seen as the projection on
the tangent cone of the elastic stress tensor. This approach leads to a
coherent mathematical formulation of the elasto-plastic laws and simplifies the
resulting system for the associated flow evolution equations. The cases of one
or two yields functions are treated in detail. The practical examples of the
von Mises and Tresca yield criteria are worked out in detail to demonstrate the
usefulness of the new formalism in applications.
