Simpson, H. C.; Spector, S. J. On copositive matrices and strong ellipticity for isotropic elastic materials. (English) Zbl 0526.73026 Arch. Ration. Mech. Anal. 84, 55-68 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 43 Documents MSC: 74B20 Nonlinear elasticity 74A20 Theory of constitutive functions in solid mechanics 35J60 Nonlinear elliptic equations Keywords:copositive matrices; representation theorem; necessary and sufficient conditions for strong ellipticity; isotropic; compressible; nonlinearly elastic material at equilibrium Citations:Zbl 0196.056; Zbl 0351.73061 PDF BibTeX XML Cite \textit{H. C. Simpson} and \textit{S. J. Spector}, Arch. Ration. Mech. Anal. 84, 55--68 (1983; Zbl 0526.73026) Full Text: DOI OpenURL References: [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 (1954), 33–35. Reprinted in Foundations of Elasticity Theory. Intl. Sci. Rev. Serv. New York: Gordon and Breach 1965. [2] Cottle, R. W., G. J. Habetler & C. E. Lemke, On classes of copositive matrices, Lin. Alg. Appl. 3 (1970), 295–310. · Zbl 0196.05602 [3] Gantmacher, F. R., The Theory of Matrices, New York: Chelsea 1960. · Zbl 0088.25103 [4] Gurtin, M. E., An Introduction to Continuum Mechanics. New York: Academic Press 1981. · Zbl 0559.73001 [5] Knowles, J. K., & E. Sternberg, On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch. Rational Mech. Anal. 63 (1977), 321–336. · Zbl 0351.73061 [6] Zee, L., & E. Sternberg, Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Rational Mech. Anal. 83 (1983), 53–90. · Zbl 0553.73011 [7] Truesdell, C., & W. Noll, The non-linear field theories of mechanics, Handbuch der Physik Vol. III/3. Berlin Heidelberg New York: Springer 1965. · Zbl 0779.73004 [8] Dunn, J. E., Elastic materials of coaxial type and inequalities sufficient to insure strong ellipticity. To appear: Int. J. Solids Structures. · Zbl 0571.73042 [9] Hadeler, K. P., On copositive matrices. Lin. Alg. Appl. 49 (1983), 79–89. · Zbl 0506.15016 [10] Sawyers, K. N., & R. S. Rivlin, On the speed of propagation of waves in a deformed compressible elastic material. Z. Angew. Math. Phys. 29 (1978), 245–251. · Zbl 0399.73035 [11] Simpson, H. C., & S. J. Spector, On barrelling instabilities in elasticity. To appear: J. Elasticity. · Zbl 0542.73048 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.