Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Stuart S. Antman
Title: Nonlinear problems of elasticity
Additional book information: Appl. Math. Sci., vol. 107, Springer-Verlag, Berlin and New York, 1995, xviii + 750 pp., ISBN 0-377-94199-1, $59.95$

References [Enhancements On Off] (What's this?)

  • Stuart S. Antman and John E. Osborn, The principle of virtual work and integral laws of motion, Arch. Rational Mech. Anal. 69 (1979), no. 3, 231–262. MR 522525, DOI 10.1007/BF00248135
  • John M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), no. 4, 337–403. MR 475169, DOI 10.1007/BF00279992
  • Kaushik Bhattacharya, Nikan B. Firoozye, Richard D. James, and Robert V. Kohn, Restrictions on microstructure, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 5, 843–878. MR 1303758, DOI 10.1017/S0308210500022381
  • 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
  • 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, DOI 10.1007/BF00250917
  • P. J. Davies, Buckling and barrelling instabilities in finite elasticity, J. Elasticity 21 (1989), no. 2, 147–192. MR 1002449, DOI 10.1007/BF00040894
  • Penny J. Davies, Buckling and barrelling instabilities on non-linearly elastic columns, Quart. Appl. Math. 49 (1991), no. 3, 407–426. MR 1121674, DOI 10.1090/qam/1121674
  • 8.
    L Euler. Additamentum I de curvis elasticis, methodus inveniendi lineas curvas maximi minimivi proprietate gaudentes. Bousquent, Lausanne, 1744. In Opera Omnia I, Vol. 24, 231-297.
  • Lawrence C. Evans, Quasiconvexity and partial regularity in the calculus of variations, Arch. Rational Mech. Anal. 95 (1986), no. 3, 227–252. MR 853966, DOI 10.1007/BF00251360
  • R. L. Fosdick and R. T. Shield, Small bending of a circular bar superposed on finite extension or compression, Arch. Rational Mech. Anal. 12 (1963), 223–248. MR 145737, DOI 10.1007/BF00281227
  • Jerrold E. Marsden and Thomas J. R. Hughes, Mathematical foundations of elasticity, Dover Publications, Inc., New York, 1994. Corrected reprint of the 1983 original. MR 1262126
  • Alexander Mielke, Saint-Venant’s problem and semi-inverse solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 102 (1988), no. 3, 205–229. MR 944546, DOI 10.1007/BF00281347
  • P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
  • Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. MR 0202511
  • S. Müller, Tang Qi, and B. S. Yan, On a new class of elastic deformations not allowing for cavitation, Ann. Inst. H. Poincaré C Anal. Non Linéaire 11 (1994), no. 2, 217–243 (English, with English and French summaries). MR 1267368, DOI 10.1016/S0294-1449(16)30193-7
  • Vladimír Šverák, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 1-2, 185–189. MR 1149994, DOI 10.1017/S0308210500015080
  • Tullio Valent, Boundary value problems of finite elasticity, Springer Tracts in Natural Philosophy, vol. 31, Springer-Verlag, New York, 1988. Local theorems on existence, uniqueness, and analytic dependence on data. MR 917733, DOI 10.1007/978-1-4612-3736-5
  • L. M. Zubov and A. N. Rudev, On the peculiarities of the loss of stability of a non-linearly elastic rectangular beam, Prikl. Mat. Mekh. 57 (1993), no. 3, 65–83 (Russian, with Russian summary); English transl., J. Appl. Math. Mech. 57 (1993), no. 3, 469–485. MR 1249429, DOI 10.1016/0021-8928(93)90126-7

  • Review Information:

    Reviewer: J. M. Ball
    Affiliation: Heriot-Watt University
    Email: J.M.Ball@ma.hw.ac.uk
    Journal: Bull. Amer. Math. Soc. 33 (1996), 269-276
    DOI: https://doi.org/10.1090/S0273-0979-96-00648-9
    Review copyright: © Copyright 1996 American Mathematical Society