A priori time regularity estimates and a simplified proof of existence in perfect plasticity

We revisit the time-incremental method for proving existence of a quasistatic evolution in perfect plasticity. We show how, as a consequence of a priori time regularity estimates on the stress and the plastic strain, the piecewise affine interpolants of the solutions of the incremental minimum problems satisfy the conditions defining a quasistatic evolution up to some vanishing error. This allows for a quicker proof of existence: furthermore, this proof bypasses the usual variational reformulation of the problem and directly tackles its original mechanical formulation in terms of an equilibrium condition, a stress constraint, and the principle of maximum plastic work.