This paper deals with a nonlinear problem modelling the contact between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled by the well-known Signorini conditions. Two weak formulations of the model are presented and existence and uniqueness results are established using classical arguments of elliptic variational inequalities. Some equivalence results are presented and a strong convergence result involving a penalized problem is also proved.
@article{bwmeta1.element.bwnjournal-article-apmv69z1p75bwm, author = {S. Drabla and M. Sofonea and B. Teniou}, title = {Analysis of a frictionless contact problem for elastic bodies}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {75-88}, zbl = {0928.74069}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p75bwm} }
S. Drabla; M. Sofonea; B. Teniou. Analysis of a frictionless contact problem for elastic bodies. Annales Polonici Mathematici, Tome 69 (1998) pp. 75-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p75bwm/
[000] [1] H. Brezis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier (Grenoble) 18 (1968), 115-175. | Zbl 0169.18602
[001] [2] M. Burguera and J. M. Via no, Numerical solving of frictionless contact problems in perfectly plastic bodies, Comput. Methods Appl. Mech. Engrg. 121 (1995), 303-322. | Zbl 0851.73055
[002] [3] S. Drabla, M. Rochdi and M. Sofonea, On a frictionless contact problem for elastic-viscoplastic materials with internal state variables, Math. Comput. Modelling 26 (1997), no. 12, 31-47. | Zbl 1185.35278
[003] [4] G. Duvaut et J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972. | Zbl 0298.73001
[004] [5] G. Fichera, Boundary value problem of elasticity with unilateral constraints, Encyclopedia of Physics, S. Flugge (ed.), Vol. VI a/2, Springer, Berlin, 1972.
[005] [6] J. Haslinger and I. Hlaváček, Contact between elastic bodies. I. Continuous problem, Appl. Math. 25 (1980), 324-347.
[006] [7] J. Haslinger and I. Hlaváček, Contact between elastic perfectly plastic bodies, Appl. Math. 27 (1982), 27-45.
[007] [8] I. Hlaváček and J. Nečas, Mathematical Theory of Elastic and Elastoplastic Bodies: an Introduction, Elsevier, Amsterdam, 1981. | Zbl 0448.73009
[008] [9] I. Hlaváček and J. Nečas, Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method, Appl. Math. 28 (1983), 199-214. | Zbl 0512.73097
[009] [10] I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford Univ. Press, Oxford, 1993. | Zbl 0787.73005
[010] [11] N. Kikuchi and J. T. Oden, Theory of variational inequalities with application to problems of flow through porous media, Internat. J. Engrg. Sci. 18 (1980), 1173-1284. | Zbl 0444.76069
[011] [12] N. Kikuchi and J. T. Oden, Contact Problems in Elasticity, SIAM, Philadelphia, 1988. | Zbl 0685.73002
[012] [13] P. D. Panagiotopoulos, Inequality Problems in Mechanics and Applications, Birkhäuser, Basel, 1985.
[013] [14] M. Rochdi and M. Sofonea, On frictionless contact between two elastic-viscoplastic bodies, Quart. J. Mech. Appl. Math. 50 (1997), 481-496. | Zbl 0886.73059
[014] [15] M. Sofonea, On a contact problem for elastic-viscoplastic bodies, Nonlinear Anal. 29 (1997), 1037-1050. | Zbl 0918.73098