Acta Mechanica

, Volume 111, Issue 3, pp 181–192

On the well-posedness of the initial value problem in elasto-plastodynamics for a linear comparison solid

  • H. Örs
  • J. H. Prévost
Original Papers

DOI: 10.1007/BF01376929

Cite this article as:
Örs, H. & Prévost, J.H. Acta Mechanica (1995) 111: 181. doi:10.1007/BF01376929


This work deals with the well-posedness of the linearized initial value problem in solid elastoplastodynamics. By well-posedness we understand existence, uniqueness and continuous dependence of the solution with respect to initial and boundary data. The initial value problem is studied in its most general form using a technique from Kreiss [1]. The cases of elastic and elastic-plastic materials with associated and non-associated plastic flow rules are considered. The analysis is carried under the assumption that the material response remains within the same constitutive cone everywhere (i.e.; exclude loading/unloading subregions). A complete answer to the well-posedness question is given without the requirement of major symmetry of the constitutive tensor. First it is shown that in 2-D the necessary and sufficient condition for well-posedness is the strong ellipticity condition. Up to now this condition had been known only to be a sufficient condition.

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • H. Örs
    • 1
  • J. H. Prévost
    • 2
  1. 1.Boğazići University Dept. of Mech. Ing.İstanbulTurkey
  2. 2.Dept. of Civil Engineering and Ops. Res.PrincetonUSA