Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion

Jean-François Babadjian (1) , Maria Giovanna Mora (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 Dipartimento di Matematica

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.

Mots clés: regularity; Functions of Bounded Deformation; quasi-static evolution; capacity; Elasto-Plasticity

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Babadjian, Maria Giovanna Mora. Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion. Journal of Differential Equations, 2018, 264 (8), pp.5109-5151. ⟨hal-01445466⟩