Abstract
In linear elasticity theory, one usually assumes that the strain energy function is non-negative. Our purpose is to show that this assumption is necessary. This is an old question that has already been discussed by Kirchhoff and Gibbs during the last century. Recently, the problem was raised again by Truesdell [7] and Ericksen [4].
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.
References
Brun L., Potier-Ferry M.: submitted to J. Thermal Stresses.
Brun L., Potier-Ferry M.: submitted to C. Rend. Acad. Sci. Paris, serie B.
Dafermos C.: 1976, in Lecture Notes in Math. 503, pp. 295–306, Springer-Verlag.
Ericksen J.L.: 1978, J. Elasticity 8, pp. 439–446.
Hale J.K.: 1969, J. Math. Anal. Appl. 26, pp. 39–59.
Slemrod M., Infante E.F.: 1971, in Instability of continuous systems, pp. 215–221, Springer-Verlag.
Truesdell C.: 1978, in Contemporary developments in continuum mechanics, North-Holland.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 D. Reidel Publishing Company
About this chapter
Cite this chapter
Brun, L., Potier-Ferry, M. (1983). Constitutive Inequalities and Dynamic Stability in the Linear Theories of Elasticity, Thermoelasticity and Viscoelasticity. In: Ball, J.M. (eds) Systems of Nonlinear Partial Differential Equations. NATO Science Series C: (closed), vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7189-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-009-7189-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7191-2
Online ISBN: 978-94-009-7189-9
eBook Packages: Springer Book Archive