A note on the existence and global stability of deformations of compressible nonlinearly elastic solids

• Autorzy: Aron M. , Christopher C.
• Języki publikacji: EN

Abstrakty

EN

The existence and global stability of certain deformations of isotropic compressible hyperelastic solids is investigated for the case when the body forces are zero and boundary conditions of place are satisfied. Certain global stability results are obtained and, using a phase-plane analysis, the existence of deformations describing the bending of rectangular blocks into annular cylindrical sectors is established.

Słowa kluczowe

EN

deformation; global stability; hyperelastic solid; nonlinearly elastic solid

PL

nieliniowe ciało stałe

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2001
• Tom: Vol. 53, nr 3
• Strony: 195--204
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Aron M.

• School of Mathematics and Statistics, University of Plymouth, Drake Circus Plymouth, PL4 8AA, United Kingdom

autor

Christopher C.

• School of Mathematics and Statistics, University of Plymouth, Drake Circus Plymouth, PL4 8AA, United Kingdom

Bibliografia

• 1. S. S. ANTMAN, Nonlinear problems of elasticity, Springer-Verlag, New York 1995.
• 2. M. ARON, C. CHRISTOPHER and Y. WANG, On the straightening of compressible, nonlinearly elastic, annular cylindrical sectors, Mathematics and Mechanics of Solids, 3, 131, 1998.
• 3. D. J. STEIGMANN and A. C. PIPKIN, Stability of harmonic materials in plane strain, Quarterly of Applied Mathematics, 46, 559, 1988.
• 4. J. SIVALOGANATHAN, The generalized Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity, Archive for Rational Mechanics and Analysis, 107, 347, 1989.
• 5. M. ARON, A note on the stability of certain deformations of compressible nonlinearly elastic media, Zeitschrift für Angewandte Mathematik und Physik, 49, 558, 1998.
• 6. M. ARON and S. AIZICOVICI, On a class of deformations of compressible, isotropic, nonlinearly elastic solids, J. of Elasticity, 49, 175, 1997.
• 7. P. ROSAKIS, Characterization of convex isotropic functions, J. of Elasticity, 49, 257, 1998.
• 8. C. TRUESDELL and W. NOLL, The non-linear field theory of mechanics [In.] Handbuch der Physik, Volume III/3, Springer-Verlag, New York 1965.
• 9. P. G. CIARLET, Mathematical Elasticity Volume 1: Three-Dimensional Elasticity, North-Rolland, Amsterdam 1988.
• 10. R. M. BOWEN, Introduction to continuum mechanics for engineers, Plenum Press, New York 1989.
• 11. F. JOHN, Plane strain problems for a perfectly elastic material of harmonic type, Communications in Pure and Applied Mathematics, 13, 239, 1960.
• 12. R. W. OGDEN, Non-linear elastic deformations, Ellis Horwood, Chichester 1984.
• 13. H. K. WILSON, Ordinary differential equations, Addison-Wesley, London 1971.
• 14. M. ARON and Y. WANG, Remarks concerning the flexure of a compressible nonlinearly elastic rectangular block, J. of Elasticity, 40, 99, 1995.