Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 13
42
Views
0
CrossRef citations to date
0
Altmetric
Articles

Short-time regularity for dynamic evolution problems in perfect plasticity

Pages 4553-4573 | Received 28 Nov 2020, Accepted 29 Nov 2020, Published online: 25 Dec 2020

References

  • Matthies H, Strang G, Christiansen E. The saddle point of a differential program. Energy methods in finite element analysis. Chichester: Wiley; 1979. p. 309–318.
  • Suquet P. Un espace fonctionnel pour les équations de la plasticité. Ann Fac Sci Toulouse Math (5). 1979;1(1):77–87.
  • Duvaut G, Lions J-L. Les inéquations en mécanique et en physique. Paris: Dunod; 1972. (Travaux et Recherches Mathématiques; 21).
  • Anzellotti G, Luckhaus S. Dynamical evolution of elasto-perfectly plastic bodies. Appl Math Optim. 1987;15(2):121–140.
  • Suquet P. Evolution problems for a class of dissipative materials. Quart Appl Math. 1980/81;38(4):391–414.
  • Suquet P. Sur les équations de la plasticité: existence et régularité des solutions. J Mécanique. 1981;20(1):3–39.
  • Babadjian J-F, Mora MG. Approximation of dynamic and quasi-static evolution problems in elasto-plasticity by cap models. Quart Appl Math. 2015;73(2):265–316.
  • Babadjian J-F, Mifsud C. Hyperbolic structure for a simplified model of dynamical perfect plasticity. Arch Ration Mech Anal. 2017;223(2):761–815.
  • Hughes TJR, Marsden JE. Classical elastodynamics as a linear symmetric hyperbolic system. J Elasticity. 1978;8(1):97–110.
  • Després B, Lagoutière F, Seguin N. Weak solutions to Friedrichs systems with convex constraints. Nonlinearity. 2011;24(11):3055–3081.
  • Mifsud C, Després B, Seguin N. Dissipative formulation of initial boundary value problems for Friedrichs' systems. Comm Partial Differ Equ. 2016;41(1):51–78.
  • Bensoussan A, Frehse J. Asymptotic behaviour of the time dependent Norton–Hoff law in plasticity theory and H1 regularity. Comment Math Univ Carolin. 1996;37(2):285–304.
  • Demyanov A. Regularity of stresses in Prandtl–Reuss perfect plasticity. Calc Var Partial Differ Equ. 2009;34(1):23–72.
  • Frehse J, Málek J. Boundary regularity results for models of elasto-perfect plasticity. Math Models Meth Appl Sci. 1999;9(9):1307–1321.
  • Knees D. Global regularity of the elastic fields of a power-law model on Lipschitz domains. Math Meth Appl Sci. 2006;29(12):1363–1391.
  • Dal Maso G, DeSimone A, Mora MG. Quasistatic evolution problems for linearly elastic-perfectly plastic materials. Arch Ration Mech Anal. 2006;180(2):237–291.
  • Temam R. Mathematical problems in plasticity. Gauthier-Villars; Montrouge:1985.
  • Dautray R, Lions J-L. Mathematical analysis and numerical methods for science and technology. Vol. 3, Berlin: Springer-Verlag; 1990. Spectral theory and applications, With the collaboration of Michel Artola and Michel Cessenat, Translated from the French by John C. Amson.
  • Goffman C, Serrin J. Sublinear functions of measures and variational integrals. Duke Math J. 1964;31:159–178.
  • Demengel F, Temam R. Convex functions of a measure and applications. Indiana Univ Math J. 1984;33(5):673–709.
  • Demengel F, Temam R. Convex function of a measure: the unbounded case. FERMAT days 85: mathematics for optimization (Toulouse, 1985. Vol. 129, Amsterdam: North-Holland; 1986. p. 103–134. (North-Holland Math. Stud).
  • Brézis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Universitext. Springer; 2011.
  • Babadjian J-F. Traces of functions of bounded deformation. Indiana Univ Math J. 2015;64(4):1271–1290.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.