References
[1888] Thomson, W.: On the reflection and refraction of light. Phil. Mag. (5) 26, 414–425. Reprinted in part as §§ 107–111 of Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. London: Clay and Sons 1904.
[1903] Hadamard, J.: Leçons sur la Propagation des Ondes. Paris: Hermann.
[1905] Duhem, P.: Recherches sur l'élasticité, Troisième partie. La stabilité des milieux élastiques. Ann. Ecole Norm. (3) 22, 143–217.
[1907] Boggio, T.: Nuova risoluzione di un problema fondamentale della teoria dell'elasticità. Rend. accad. Lincei (5) 162, 248–255.
[1949] Signorini, A.: Trasformazioni termoelastiche finite. Memoria 2a. Annali di Mat. Pur. Appl. (4) 30, 1–72.
[1950] Fichera, G.: Sull'esistenza e sul calcolo delle soluzioni dei problemi al contorno relativi all'equilibrio di un corpo elastico. Ann. Sc. Norm. Pisa (3) 4, 35–99.
[1952] Truesdell, C.: The mechanical foundations of elasticity and fluid dynamics. J. Rational Mech. Anal. 1, 125–300. To be reprinted shortly, in corrected form, in the International Science Review Series, Gordon and Breach, New York.
[1953, 1] Ericksen, J. L.: On the propagation of waves in isotropic incompressible elastic materials. J. Rational Mech. Anal. 2, 329–337.
[1953, 2] Mişicu, M.: Echilibrul mediilor continue cu deformâri mari. Studii şi cerc. mec. metal. 4, 31–53.
[1954, 1] Baker, M., & J. L. Ericksen: Inequalities restricting the form of the stress deformation relations for isotropic elastic solids and Reiner-Rivlin fluids. J. Wash. Acad. Sci. 44, 33–35.
[1954, 2] Browder, F. E.: Strongly elliptic systems of differential equations. Contrib. Theory Partial Diff. Eqns., Annals Math. Studies No. 33, 15–51.
[1954, 3] Morrey, C. B.: Second order elliptic systems of differential equations. Contrib. Theory Partial Diff. Eqns., Annals Math. Studies No. 33, 101–159.
[1954, 4] Stoppelli, F.: Un teorema di esistenza e di unicità relativo alle equazioni dell'elastostatica isoterma per deformazioni finite. Ricerche mat. 3, 247–267.
[1955] Noll, W.: On the continuity of the solid and fluid states. J. Rational Mech. Anal. 4, 3–81.
[1956, 1] Ericksen, J. L., & R. A. Toupin: Implication of Hadamard's condition for elastic stability with respect to uniqueness theorems. Canad. J. Math. 8, 432–436.
[1956, 2] Truesdell, C.: Das ungelöste Hauptproblem der endlichen Elastizitätstheorie. Z. angew. Math. Mech. 36, 97–103.
[1957, 1] Barta, J.: On the non-linear elasticity law. Acta Tech. Acad. Sci. Hungaricae 8, 55–65.
[1957, 2] Ericksen, J. L.: On the Dirichlet problem for linear differential equations. Proc. Amer. Math. Soc. 8, 521–522.
[1957, 3] Hill, R.: On uniqueness and stability in the theory of finite elastic strain. J. Mech. Phys. Solids 5, 229–241.
[1959] Coleman, B. D., & W. Noll: On the thermostatics of continuous media. Arch. Rational Mech. Anal. 4, 97–128.
[1960, 1] Green, A. E., & J. E. Adkins: Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford: Clarendon Press.
[1960, 2] Gurtin, M. E., & E. Sternberg: On the first boundary-value problem of linear elastostatics. Arch. Rational Mech. Anal. 6, 177–187.
[1960, 3] Truesdell, C., & R. Toupin: The Classical Field Theories. Flügge's Encyclopedia of Physics 3 1 226–793. Berlin-Göttingen-Heidelberg: Springer.
[1961, 1] Bramble, J. H., & L. E. Payne: An analogue of the spherical harmonics for the equations of elasticity. J. Math. Phys. 15, 163–171.
[1961, 2] Gurtin, M. E., & E. Sternberg: A note on uniqueness in classical elastodynamics. Q. Appl. Math. 19, 169–171 (1961/2).
[1961, 3] Hayes, M., & R. S. Rivlin: Propagation of plane waves in an isotropic elastic material subject to pure homogeneous deformation. Arch. Rational Mech. Anal. 8, 15–22.
[1961, 4] Hill, R.: Uniqueness in general boundary-value problems for elastic or inelastic solïds. J. Mech. Phys. Solids 9, 114–130.
[1961, 5] Toupin, R. A., & B. Bernstein: Sound waves in perfectly elastic materials. Acoustoelastic effect. J. Acoust. Soc. Amer. 33, 216–225.
[1961, 6] Truesdell, C.: General and exact theory of waves in finite elastic strain. Arch. Rational Mech. Anal. 8, 263–296.
[1962, 1] Bernstein, B., & R. A. Toupin: Some properties of the Hessian matrix of a strictly convex function. J. Reine Angew. Math. 210, 65–72.
[1962, 2] Bramble, J. H., & L. E. Payne: Some uniqueness theorems in the theory of elasticity. Arch. Rational Mech. Anal. 9, 319–328.
Bramble, J. H., & L. E. Payne: Proc. 4th U.S. Congr. Applied Mech. forthcoming.
[1962, 4] Coleman, B. D.: Mechanical and thermodynamical admissibility of stressstrain functions. Arch. Rational Mech. Anal. 9, 172–186.
[1962, 5] Hill, R.: Acceleration waves in solids. J. Mech. Phys. Solids 10, 1–16.
[1962, 6] Zorski, H.: On the equations describing small deformations superimposed on finite deformations. Proc. Int. Sympos. Second-order Effects Haifa, forthcoming.
[1963] Bragg, L. E., & B. D. Coleman: On strain energy functions for isotropic elastic materials. In preparation.
Author information
Authors and Affiliations
Additional information
We are grateful to Messrs. Noll and Bragg for detecting errors in an earlier version of this paper and for informing us of various complementary results. The work of Truesdell was supported by a grant from the U. S. National Science Foundation.
Rights and permissions
About this article
Cite this article
Truesdell, C., Toupin, R. Static grounds for inequalities in finite strain of elastic materials. Arch. Rational Mech. Anal. 12, 1–33 (1963). https://doi.org/10.1007/BF00281217
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281217