Incremental methods in nonlinear, three-dimensional, incompressible elasticity

 Access to full text

 Full (PDF)

1. [1] R. ABRAHAM and J. ROBBIN, Transversal Mappings and Flows, New York (1967). Zbl0171.44404MR240836
2. [2] R. A. ADAMS, Sobolev Spaces, Academic Press, New York (1975). Zbl0314.46030MR450957
3. [3] S. AGMON, A. DOUGLIS and L. NIRENBERG; Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math XII (1959), 623-727. Zbl0093.10401MR125307
4. [4] S. AGMON, A. DOUGLIS and L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math XVII (1964), 35-92. Zbl0123.28706MR162050
5. [5] M. BERNADOU, P. G. CIARLET and J. HU, On the convergence of the semi-discrete incremental method in nonlinear, three-dimensional, elasticity, Journal of Elasticity 14 (1984), 425-440. Zbl0551.73019MR770299
6. [6] D. R. J. CHILLINGWORTH, J. E. MARSDEN and Y. H. WAN, Symmetry and Bifurcation in three-dimensional elasticity, part I, Arch. Rat. Mech. An. 80 pp. 296-322 (1982). Zbl0509.73018MR677564
7. [7] P. G. CIARLET, Élasticité Tridimensionnelle, Masson, Paris (1986). Zbl0572.73027MR819990
8. [8] P. G. CIARLET, Topics in Mathematical Elasticity, Vol. 1 : Three-Dimensional Elasticity, North-Holland, Amsterdam (1987). Zbl0648.73014MR936420
9. [9] M. CROUZEIX and A. MIGNOT, Analyse Numérique des Équations Différentielles, Masson, Paris (1984). Zbl0635.65079MR762089
10. [10] G. GEYMONAT, Sui problemi ai limiti per i systemi lineari ellitici, Ann. Mat. Pura Appl. LXIX (1965), 207-284. Zbl0152.11102MR196262
11. [11] M. E. GURTIN, Introduction to Continuum Mechanics, Academic Press, New York (1981). Zbl0559.73001MR636255
12. [12] S. LANG, Introduction to differential manifolds, John Wiley and Sons, Inc. New York (1962). Zbl0103.15101MR155257
13. [13] H. LE DRET, Quelques Problèmes d'Existence en Élasticité Non Linéaire, Thesis, Université Pierre et Marie Curie Paris (1982). 
14. [14] H. LE DRET, Constitutive laws and Existence Questions in Incompressible Nonlinear Elasticity, to appear in Journal of Elasticity (1983). Zbl0648.73013MR817376
15. [15] P. LE TALLEC and J. T. ODEN, Existence and Characterization of Hydrostatic Pressure in finite deformations of Incompressible Elastic Bodies, Journal of Elasticity, 11, 341-358 (1981). Zbl0483.73035MR637620
16. [16] P. LE TALLEC, Existence and approximation results for nonlinear mixed problems : application to incompressible finite elasticity, Numer. Math. 38, 365-382 (1982). Zbl0487.76008MR654103
17. [17] J. E. MARSDEN and T. J. R. HUGHES, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs (1983). Zbl0545.73031
18. [18] J L THOMPSON, Some existence theorems for the traction boundary-value problem of linearized elastostatics, Arch Rat Mech An 32, 369-399 (1969) Zbl0175.22108MR237130
19. [19] C TRUESDELL and W NOLL, The Nonlinear Field theories of Mechanics, Handbuch der Physik, Vol III/3, 1-602 (1965) Zbl1068.74002MR193816
20. [20] T VALENT, Sulla differenziabilita dell' operatore di Nemystky, Mend Acc Naz Lincei 65, 15-26 (1978) Zbl0424.35084
21. [21] Y H WAN, The traction problem for incompressible materials, To appear in Arch Rat Mech An Zbl0574.73013MR797048
22. [22] C C WANG and C TRUESDELL, Introduction to Rational Elasticity, Noordhoff Groningen (1973) Zbl0308.73001MR468442

1. R. Nzengwa, Resolution of a fixed point problem by an incremental method and application in nonlinear elasticity