×

A new mathematical theory of simple materials. (English) Zbl 0271.73006


MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bernstein, B., Hypo-elasticity and elasticity. Arch. Rational Mech. Anal. 6, 89–104 (1960). · Zbl 0094.36702
[2] Bernstein, B., Remarks on materials of the rate type and the principle of determinism. Trans. Soc. Rheol. 5, 35–40 (1961).
[3] Bourbaki, N., Topologie Générale, Chapitres 1 et 2, quatrième édition. Paris: Hermann 1965.
[4] Coleman, B. D., Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids. Arch. Rational Mech. Anal. 9, 273–300 (1962). · Zbl 0109.18001
[5] Coleman, B. D., & V. J. Mizel, On the general theory of fading memory. Arch. Rational Mech. Anal. 29, 18–31 (1968). · Zbl 0167.24704
[6] Coleman, B. D., H. Markovitz, & W. Noll, Viscometric Flows of Non-Newtonian Fluids. New York: Springer 1966. · Zbl 0137.21903
[7] Coleman, B. D., & W. Noll, On the thermostatics of continuous media. Arch. Rational Mech. Anal. 4, 97–128 (1959). · Zbl 0231.73003
[8] Coleman, B. D., & W. Noll, Material symmetry and thermostatic inequalities in finite elastic deformations. Arch. Rational Mech. Anal. 15, 87–111 (1964). · Zbl 0123.40703
[9] Day, W. A., Thermodynamics based on a work axiom. Arch. Rational Mech. Anal. 31, 1–34 (1968). · Zbl 0188.58901
[10] Fairchild, W. W., & C. Ionescu-Tulcea, Topology. Philadelphia-London-Toronto: W. B. Saunders 1971.
[11] Kelley, J. L., General Topology. Princeton: Van Nostrand 1955.
[12] Noll, W., On the continuity of the solid and fluid states. J. Rational Mech. Anal. 4, 3–81 (1955). · Zbl 0064.42001
[13] Noll, W., A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2, 197–226 (1958). · Zbl 0083.39303
[14] Noll, W., The foundations of classical mechanics in the light of recent advances in continuum mechanics. Proc. of the Berkeley Symposium on the Axiomatic Method, p. 266–281, Amsterdam 1959. · Zbl 0087.39401
[15] Noll, W., Motions with constant stretch history. Arch. Rational Mech. Anal. 11, 97–105 (1962). · Zbl 0112.18301
[16] Noll, W., Proof of the maximality of the orthogonal group in the unimodular group. Arch. Rational Mech. Anal. 18, 100–102 (1965). · Zbl 0161.02501
[17] Noll, W., Space-time structures in classical mechanics. Delaware Seminar in the Foundations of Physics, p. 28–34. Berlin-Heidelberg-New York: Springer 1967.
[18] Noll, W., Materially uniform simple bodies with inhomogeneities. Arch. Rational Mech. Anal. 27, 1–32 (1967). · Zbl 0168.45701
[19] Noll, W., The representation of monotonous processes by exponentials. To appear. · Zbl 0338.15014
[20] Owen, D. R., Thermodynamics of materials with elastic range. Arch. Rational Mech. Anal. 32, 91–112 (1968). · Zbl 0169.28003
[21] Owen, D. R., A mechanical theory of materials with elastic range. Arch. Rational Mech. Anal. 37, 85–110 (1970). · Zbl 0197.23403
[22] Truesdell, C., Hypo-elasticity. J. Rational Mech. Anal. 4, 83–133 (1955). · Zbl 0064.42002
[23] Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Encyclopedia of Physics, Vol. III/3. Berlin-Heidelberg-New York: Sringer 1965. · Zbl 0779.73004
[24] Sternberg, S., Lectures on Differential Geometry. Englewood Cliffs: Prentice Hall 1964. · Zbl 0129.13102
[25] Wang, C. C., A general theory of subfluids. Arch. Rational Mech. Anal. 20, 1–40 (1965). · Zbl 0139.43801
[26] Wang, C. C., On the geometric structures 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
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.