Elẓanowski, Marek; Epstein, Marcelo Geometric characterization of hyperelastic uniformity. (English) Zbl 0574.73010 Arch. Ration. Mech. Anal. 88, 347-357 (1985). 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 Cited in 4 Documents MSC: 74E05 Inhomogeneity in solid mechanics 74B20 Nonlinear elasticity 57R22 Topology of vector bundles and fiber bundles 55R10 Fiber bundles in algebraic topology Keywords:torsion operator of constitutive connection; split into two main parts; vanishing of one guarantees uniformity; other essentially identifiable with material connection; parallelism structures in manifolds; geometrical characterization of hyperelastic bodies; uniform and nonuniform bodies PDF BibTeX XML Cite \textit{M. Elẓanowski} and \textit{M. Epstein}, Arch. Ration. Mech. Anal. 88, 347--357 (1985; Zbl 0574.73010) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.