Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
FILIPPOV, A.F., Differential Equations with Discontinuous Right-Hand Side (in Russian), Mat. Sbornik 51, 1960. AMS Translations 42, 199–231, 1964.
TRUESDELL, C., and W. NOLL, The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol III/3, Springer 1965.
PIPKIN, A.C., and R.S. RIVLIN, Mechanics of Rate-Independent Materials, Z.A.M.P., 16, 313–327, 1965.
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.
OWEN, D.R., A Mechanical Theory of Materials with Elastic Range, Arch. Rational Mech. Anal. 37, 85–110, 1970.
NOLL, W., A New Mathematical Theory of Simple Materials, Arch. Rational Mech. Anal, 48, 1–50, 1972.
PERZYNA, P., On material isomorphism in description of dynamic plasticity, Arch. Mech. Stosow. 27, 473–484, 1975.
DEL PIERO, G., On the Elastic-Plastic Material Element, Arch. Rational Mech. Anal. 59, 111–129, 1975.
BUHITE, J.L., Ph. D. Thesis - Dept. of Mathematics, Carnegie-Mellon University, 1978.
BUHITE, J.L., and D.R. OWEN, An Ordinary Differential Equation from the Theory of Plasticity, Arch. Rational Mech. Anal. 71, 357–383, 1979.
NEMATNASSER, S., Decomposition of Strain Measures and their Rates in Finite Deformation Elastoplasticity, Int. J. Solids Structures 15, 155–166, 1979.
MATSUMOTO, E., A Mathematical Theory of Elastic-Plastic Materials with Memory with General Work-Hardening, Q. Jl. Mech. Appl. Math. 35, 197–218, 1982.
DEL PIERO, G., Materials with Elastic Range and the New Theory of Simple Materials (in preparation).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Wien
About this chapter
Cite this chapter
Del Piero, G. (1984). Well Posedness of Constitutive Equations of the Kinematical Hardening Type. In: Lehmann, T. (eds) The Constitutive Law in Thermoplasticity. CISM International Centre for Mechanical Sciences, vol 281. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2636-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2636-3_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81796-4
Online ISBN: 978-3-7091-2636-3
eBook Packages: Springer Book Archive