Book Review

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Book Information:

Author: T. Valent

Title: Boundary value problems of finite elasticity

Additional book information: Springer-Verlag, Heidelberg, 1988, xii+192 pp., $64.00. ISBN 0-387-96550-5.

**1.**Stuart Antman,*Existence of solutions of the equilibrium equations for non-linearly elastic rings and arches*, Indiana Univ. Math. J.**20**(1970/1971), 281–302. MR**0266478****2.**S. S. Antman,*Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders*, Arch. Rational Mech. Anal.**83**(1983), no. 1, 1–52. MR**695361**, 10.1007/BF00281086**3.**John M. Ball,*Convexity conditions and existence theorems in nonlinear elasticity*, Arch. Rational Mech. Anal.**63**(1976/77), no. 4, 337–403. MR**0475169****4.**J. M. Ball,*Global invertibility of Sobolev functions and the interpenetration of matter*, Proc. Roy. Soc. Edinburgh Sect. A**88**(1981), no. 3-4, 315–328. MR**616782**, 10.1017/S030821050002014X**5.**M. van Buren,*On the existence and uniqueness of solutions to boundary value problems in finite elasticity*, Thesis, Carnegie-Mellon University, Pittsburgh, 1968.**6.**D. R. J. Chillingworth, J. E. Marsden, and Y. H. Wan,*Symmetry and bifurcation in three-dimensional elasticity. I*, Arch. Rational Mech. Anal.**80**(1982), no. 4, 295–331. MR**677564**, 10.1007/BF00253119**7.**D. R. J. Chillingworth, J. E. Marsden, and Y. H. Wan,*Symmetry and bifurcation in three-dimensional elasticity. II*, Arch. Rational Mech. Anal.**83**(1983), no. 4, 363–395. MR**714980**, 10.1007/BF00963840**8.**Philippe G. Ciarlet,*Mathematical elasticity. Vol. I*, Studies in Mathematics and its Applications, vol. 20, North-Holland Publishing Co., Amsterdam, 1988. Three-dimensional elasticity. MR**936420****9.**P. G. Ciarlet and P. Destuynder,*A justification of the two-dimensional linear plate model*, J. Mécanique**18**(1979), no. 2, 315–344 (English, with French summary). MR**533827****10.**Philippe G. Ciarlet and Jindřich Nečas,*Unilateral problems in nonlinear, three-dimensional elasticity*, Arch. Rational Mech. Anal.**87**(1985), no. 4, 319–338 (English, with French summary). MR**767504**, 10.1007/BF00250917**11.**Philippe G. Ciarlet and Jindřich Nečas,*Injectivity and self-contact in nonlinear elasticity*, Arch. Rational Mech. Anal.**97**(1987), no. 3, 171–188. MR**862546**, 10.1007/BF00250807**12.**Bernard D. Coleman and Walter Noll,*On the thermostatics of continuous media*, Arch. Rational Mech. Anal.**4**(1959), 97–128 (1959). MR**0109527****13.**R. L. Fosdick and J. Serrin,*On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids*, J. Elasticity**9**(1979), no. 1, 83–89. MR**528599**, 10.1007/BF00040982**14.**Morton E. Gurtin,*An introduction to continuum mechanics*, Mathematics in Science and Engineering, vol. 158, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR**636255****15.**Hervé Le Dret,*Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence*, J. Elasticity**17**(1987), no. 2, 123–141 (English, with French summary). MR**885602**, 10.1007/BF00043020**16.**J. E. Marsden and T. J. R. Hughes,*Topics in the mathematical foundations of elasticity*, Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. II, Res. Notes in Math., vol. 27, Pitman, Boston, Mass.-London, 1978, pp. 30–285. MR**576233****17.**J. E. Marsden and T. J. R. Hughes,*Mathematical foundations of elasticity*, Prentice-Hall, Englewood Cliffs, 1983.**18.**Francesco Stoppelli,*Un teorema di esistenza ed unicità relativo alle equazioni dell’elastostatica isoterma per deformazioni finite*, Ricerche Mat.**3**(1954), 247–267 (Italian). MR**0074237****19.**C. Truesdell and W. Noll,*The non-linear field theories of mechanics*, Handbuch der Physik, Band III/3, Springer-Verlag, Berlin, 1965, pp. 1–602. MR**0193816****20.**Tullio Valent,*Local theorems of existence and uniqueness in finite elastostatics*, Proceedings of the IUTAM Symposium on Finite Elasticity (Bethlehem, Pa., 1980) Nijhoff, The Hague, 1982, pp. 401–421. MR**676677****21.**T. Valent,*Pressure boundary problems infinite elasticity. Results on local existence, uniqueness and analyticity*, in Proceedings, meeting on finite thermoelasticity (G. Grioli, Editor), Accademia Nazionale dei Lincei, Roma, 1986, pp. 241-264.**22.**Tullio Valent and Giuseppe Zampieri,*The differentiability of an operator connected with a class of quasilinear differential systems*, Rend. Sem. Mat. Univ. Padova**57**(1977), 311–322 (1978) (Italian, with English summary). MR**526198****23.**C. C. Wang and C. Truesdell,*Introduction to rational elasticity*, Noordhoff International Publishing, Leyden, 1973. Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics of Continua. MR**0468442**

Review Information:

Reviewer: Philippe G. Ciarlet

Journal: Bull. Amer. Math. Soc.

**23**(1990), 209-222

DOI: http://dx.doi.org/10.1090/S0273-0979-1990-15934-8