Calculus of Variations and Geometric Measure Theory

F. Solombrino

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

created by solombrin on 30 Apr 2013
modified on 17 May 2015


Published Paper

Inserted: 30 apr 2013
Last Updated: 17 may 2015

Journal: Mathematische Nachrichten
Year: 2015
Doi: 10.1002/mana.201300110


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.