Well Posedness of Constitutive Equations of the Kinematical Hardening Type

  • G. Del Piero
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 281)


The purpose of the first part of these Lectures is to characterize the class of elastic-plastic materials starting from the more general class of the materials with elastic range and introducing a small number of ad hoc assumptions. This is done in the general framework of NOLL’s new theory of simple materials [6] After some preliminary work intended to re-define in this new context the class of materials with elastic range, a supplementary assumption on the nature of the inelastic behaviour defines a subclass of materials with elastic range of the rate type, which exhibits a number of mate rial properties considered as typical of elastic-plastic materials.


Constitutive Equation Elastic Response Plastic Response Elastic Region Stress Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    FILIPPOV, A.F., Differential Equations with Discontinuous Right-Hand Side (in Russian), Mat. Sbornik 51, 1960. AMS Translations 42, 199–231, 1964.MATHGoogle Scholar
  2. [2]
    TRUESDELL, C., and W. NOLL, The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol III/3, Springer 1965.Google Scholar
  3. [3]
    PIPKIN, A.C., and R.S. RIVLIN, Mechanics of Rate-Independent Materials, Z.A.M.P., 16, 313–327, 1965.MathSciNetCrossRefGoogle Scholar
  4. [4]
    LEE, E.H., and D.T. LIU, Finite-Strain Elastic-Plastic Theory with Application to Plane-Wave Analysis, Jl. of Appl. Physics, 38, 19–27, 1967.Google Scholar
  5. [5]
    OWEN, D.R., A Mechanical Theory of Materials with Elastic Range, Arch. Rational Mech. Anal. 37, 85–110, 1970.MathSciNetMATHGoogle Scholar
  6. [6]
    NOLL, W., A New Mathematical Theory of Simple Materials, Arch. Rational Mech. Anal, 48, 1–50, 1972.MathSciNetMATHGoogle Scholar
  7. [7]
    PERZYNA, P., On material isomorphism in description of dynamic plasticity, Arch. Mech. Stosow. 27, 473–484, 1975.MathSciNetMATHGoogle Scholar
  8. [8]
    DEL PIERO, G., On the Elastic-Plastic Material Element, Arch. Rational Mech. Anal. 59, 111–129, 1975.MATHGoogle Scholar
  9. [9]
    BUHITE, J.L., Ph. D. Thesis - Dept. of Mathematics, Carnegie-Mellon University, 1978.Google Scholar
  10. [10]
    BUHITE, J.L., and D.R. OWEN, An Ordinary Differential Equation from the Theory of Plasticity, Arch. Rational Mech. Anal. 71, 357–383, 1979.MathSciNetMATHGoogle Scholar
  11. [11]
    NEMATNASSER, S., Decomposition of Strain Measures and their Rates in Finite Deformation Elastoplasticity, Int. J. Solids Structures 15, 155–166, 1979.CrossRefGoogle Scholar
  12. [12]
    MATSUMOTO, E., A Mathematical Theory of Elastic-Plastic Materials with Memory with General Work-Hardening, Q. Jl. Mech. Appl. Math. 35, 197–218, 1982.CrossRefMATHGoogle Scholar
  13. [13]
    DEL PIERO, G., Materials with Elastic Range and the New Theory of Simple Materials (in preparation).Google Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • G. Del Piero
    • 1
  1. 1.Istituto di Meccanica Teorica e ApplicataUniversità degli Studi di UdineItaly

Personalised recommendations