Suppose that a cylindrical bar
is twisted by terminal couples beyond its elastic range. What will happen if the
applied load is (gradually) removed? This question will be formulated, according to
the deformation theory of plasticity, as a problem of variational inequalities over a
convex set in a Hilbert space and the existence, uniqueness and the regularity of the
solution will be established. In addition, physically relevant results will be
derived.