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Geometric characterization of hyperelastic uniformity. (English) Zbl 0574.73010
The authors present a geometrical characterization of hyperelastic bodies. The characterization is an extension of previously developed concepts of W. Noll [Arch. Rotation. Mech. Anal. 27, 1-32 (1967; Zbl 0168.457)] and C. C. Wang [ibid. 27, 33-94 (1967; Zbl 0187.488)]. The characterization is applicable with both uniform and nonuniform bodies.
The paper is theoretical. As such it will probably be of greatest interest to theoreticians working in elastic theory.
Reviewer: R.L.Huston

MSC:
74E05 Inhomogeneity in solid mechanics
74B20 Nonlinear elasticity
57R22 Topology of vector bundles and fiber bundles
55R10 Fiber bundles in algebraic topology
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[1] Noll, W., ”Materially Uniform Simple Bodies with Inhomogeneities”, Arch. Rational Mech. Anal., 27, 1–32, 1967. · Zbl 0168.45701 · doi:10.1007/BF00276433
[2] Wang, C.-C., ”On the Geometric Structure of Simple Bodies, a Mathematical Foundation for the Theory of Continuous Distributions of Dislocations”, Arch. Rational Mech. Anal., 27, 33–94, 1967. · Zbl 0187.48802 · doi:10.1007/BF00276434
[3] Toupin, R. A., ”Dislocated and Oriented Media”, reprinted from IUTAM-Symposium (1968) in Continuum Theory of Inhomogeneities in Simple Bodies, Springer-Verlag, New York Inc., 1968. · Zbl 0216.25703
[4] Poor, W. A., ”Differential Geometric Structures”, McGraw-Hill Book Company, 1981. · Zbl 0493.53027
[5] Epstein, M. & Segev, R., ”Differentiable Manifolds and the Principle of Virtual Work in Continuum Mechanics”, J. Math. Phys., 21 (5), 1243–1245, 1980. · Zbl 0448.73003 · doi:10.1063/1.524516
[6] Cohen, H. & Epstein, M., ”Remarks on Uniformity in Hyperelastic Materials”, Int. J. Solids and Structures, 20 (3), 233–243, 1984. · Zbl 0555.73024 · doi:10.1016/0020-7683(84)90035-0
[7] Truesdell, C. & Noll, W., ”The Nonlinear Field Theories of Mechanics”, Encyclopedia of Physics, Vol. III/3, Springer-Verlag, Berlin Heidelberg New York 1965. · Zbl 0779.73004
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