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Four Linear Continuum Theories

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Tissue Mechanics
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Four linear theories are considered in this chapter. Each has a distinctive and interesting history. Each one of the theories was originally formulated between 1820 and 1860. Representative of the theme of this chapter are the opening lines of the Historical Introduction in A.E.H. Love’s Theory of Elasticity (original edition, 1892): “The Mathematical Theory of Elasticity is occupied with an attempt to reduce to calculation] the state of strain, or relative displacement, within a solid... object... which is subject to the action of an equilibrating system of forces, or is in a state of slight internal relative motion, and with endeavours to obtain results which shall be practically important in applications to architecture, engineering, and all other useful arts in which the material of construction is solid.”

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Relevant Literature

Theory of Rigid Porous Media

  • Bear J. 1972. Dynamics of fluids in porous media. New York: Elsevier.

    Google Scholar 

  • Carman PC. 1956. Flow of gases through porous media. London: Butterworths.

    MATH  Google Scholar 

  • Scheidegger AE. 1960. The physics of flow through porous media, 2nd ed. Toronto: U Toronto P.

    MATH  Google Scholar 

Elasticity Theory (Classical)

  • Gurtin ME. 1972. The linear theory of elasticity. In Handbuch derphysik, ed. S Flugge, pp. 1–296. Berlin: Springer-Verlag.

    Google Scholar 

  • Love AEH. 1927. Elasticity. New York: Dover.

    MATH  Google Scholar 

  • Saada AS. 1974. Elasticity theory and applications. Oxford: Pergamon.

    MATH  Google Scholar 

  • Sokolnikoff IS. 1956. Mathematical theory of elasticity. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Timoshenko SP, Goodier JN. 1951. Theory of elasticity. New York: McGraw-Hill.

    MATH  Google Scholar 

Elasticity Theory (Anisotropic)

  • Fedorov FI. 1968. Theory of elastic waves in crystals. New York: Plenum Press.

    Google Scholar 

  • Hearmon RFS. 1961. An introduction to applied anisotropic elasticity. Oxford: Oxford UP.

    Google Scholar 

  • Lekhnitskii SG. 1963. Theory of elasticity of an anisotropic elastic body. San Francisco: Holden Day.

    Google Scholar 

  • Ting TCT. 1996. Anisotropic elasticity — theory and applications. New York: Oxford UP.

    MATH  Google Scholar 

Classical Fluid Theory

  • Batchelor GK. 2000. An introduction to fluid mechanics. Cambridge: Cambridge.

    Google Scholar 

  • Lamb H. 1932. Hydrodynamics. New York: Dover.

    MATH  Google Scholar 

  • Langois WE. 1964. Slow viscous flow. New York: Macmillan.

    Google Scholar 

  • Prandtl L, Tietjens OG. 1934a. Fundamentals of hydro-and aeromechanics. New York: McGraw-Hill.

    Google Scholar 

  • Prandtl L, Tietjens OG. 1934b. Applied hydro-and aeromechanics. New York: McGraw-Hill.

    Google Scholar 

  • Schlichting H. 1960. Boundary layer theory. New York: McGraw-Hill.

    MATH  Google Scholar 

Viscoelasticity Theory

  • Christensen RM. 1971. Theory of viscoelasticity. New York: Academic Press.

    Google Scholar 

  • Lakes RS. 1999. Viscoelastic solids. Boca Raton, FL: CRC Press.

    Google Scholar 

  • Lockett FJ. 1972. Nonlinear viscoelastic solids. New York: Academic Press.

    MATH  Google Scholar 

  • Pipkin AC. 1972. Lectures on viscoelasticity theory. New York: Springer.

    MATH  Google Scholar 

  • Wineman AS, Rajagopal KR. 2000. Mechanical response of polymers. Cambridge: Cambridge UP.

    Google Scholar 

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(2007). Four Linear Continuum Theories. In: Cowin, S.C., Doty, S.B. (eds) Tissue Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49985-7_7

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  • DOI: https://doi.org/10.1007/978-0-387-49985-7_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-36825-2

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