Abstract
It is shown that the Cosserat continuum and the theory of elasticity with micro-structure can be interpreted as analytical models describing the dynamic behavior of a composite material. The nonclassical material constants are simply functions of the geometry and the classical constants of the two materials constituting the composite. The study of wave propagation in a laminated composite reveals that a more complex micro-structure needs to be introduced in a continuum in order to describe adequately the dispersive character of (essentially) longitudinal waves.
This work was supported by the Office of Naval Research under Contract ONR Nonr. 1228(34) with Northwestern university.
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References
Mindlin, R. D., and H. F. Tiersten : Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal. 11, 415 (1962).
Toupin, R. A.; Elastic materials with couple-stresses. Arch. Rational Mech., Anal. 11, 385 (1962).
Touin, R. A.: Theories of elasticity with couple-stress. Arch. Rational Mech. Anal. 17, 85 (1964).
Koiter, W. T.: Couple-stresses in the theory of elasticity. Proc. Koninkl. Nederi. Akad. Wet., Ser. B. 67, 17 (1964).
Schaefer, H.: Das Cosserat-Kontinuum. ZAMM (in press).
Mindlin, R. D., and N.N. Eshel: On first strain-gradient theories in linear elasticity. Int. J. of Solids and Structures 4, 109 (1968).
Mindlin, R. D.: Micro-structure in linear elasticity. Arch. Rational Mech. Anal. 16, 51 (1964).
Kunin, I. A.: Theory of elasticity with spatial dispersion. One-dimensional complex structure. PMM 30, 866 (1966).
Herrmann, G., and J. D. Achenbach: On dynamic theories of fiber-reinforced composites. Northwestern Univ. Str. Mech. Lab. Techn. Rep. 67–2 (1967); also Proc. AIAA/ASME Eighth Structures, Structural Dynamics, and Materials Conf., New York: AIAA 1967, pp. 112–118.
Herrmann, G., and J. D. Achenbach: Wave propagation in laminated and fiber-reinforced composites. To be pub. in Proc. of the Int. Conf. on the mechanics of composite materials, Pergamon Press 1968.
Sun, C. T., J. D. Achenbach and G. Herrmann: Time-harmonic waves in a stratified medium propagating in the direction of the layering. J. Appl. Mech., forthcoming.
Sun, C. T., J. D. Achenbach and G. Herrmann: Effective stiffness theory for laminated media. Northwestern Univ. Str. Mech. Lab. Techn. Rep. 67–4 (1967).
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Herrmann, G., Achenbach, J.D. (1968). Applications of Theories of Generalized Cosserat Continua to the Dynamics of Composite Materials. In: Kröner, E. (eds) Mechanics of Generalized Continua. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-30257-6_7
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DOI: https://doi.org/10.1007/978-3-662-30257-6_7
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