A priori time regularity estimates and a simplified proof of existence in perfect plasticity. Issue 14 (18th May 2015)

• Record Type: Journal Article
• Authors: Solombrino, Francesco
• Is Part Of: Mathematische Nachrichten. Volume 288:Issue 14/15(2015)
• Page Start: 1786
• Page End: 1800
• Publication Date: 2015-05-18
• Subjects: Quasistatic evolution -- rate‐independent processes -- perfect plasticity -- Prandtl‐Reuss plasticity -- shear bands -- incremental problems -- variational problems in BD -- 74C05 -- 74G65 -- 49J45 -- 47J20 -- 35Q72; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201300110
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : 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.