Inserted: 16 jan 2017
Last Updated: 16 jan 2017
This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic - perfectly plastic materials obeying a Drucker-Prager or Mohr-Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress.
Keywords: regularity, quasi-static evolution, Functions of Bounded Deformation, capacity, Elasto-Plasticity