Advertisement

Four Linear Continuum Theories

Absract

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.”

Keywords

Stress Equation Couette Flow Relaxation Function Surface Traction Pore Fluid Pressure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Relevant Literature

Theory of Rigid Porous Media

  1. Bear J. 1972. Dynamics of fluids in porous media. New York: Elsevier.Google Scholar
  2. Carman PC. 1956. Flow of gases through porous media. London: Butterworths.MATHGoogle Scholar
  3. Scheidegger AE. 1960. The physics of flow through porous media, 2nd ed. Toronto: U Toronto P.MATHGoogle Scholar

Elasticity Theory (Classical)

  1. Gurtin ME. 1972. The linear theory of elasticity. In Handbuch derphysik, ed. S Flugge, pp. 1–296. Berlin: Springer-Verlag.Google Scholar
  2. Love AEH. 1927. Elasticity. New York: Dover.MATHGoogle Scholar
  3. Saada AS. 1974. Elasticity theory and applications. Oxford: Pergamon.MATHGoogle Scholar
  4. Sokolnikoff IS. 1956. Mathematical theory of elasticity. New York: McGraw-Hill.MATHGoogle Scholar
  5. Timoshenko SP, Goodier JN. 1951. Theory of elasticity. New York: McGraw-Hill.MATHGoogle Scholar

Elasticity Theory (Anisotropic)

  1. Fedorov FI. 1968. Theory of elastic waves in crystals. New York: Plenum Press.Google Scholar
  2. Hearmon RFS. 1961. An introduction to applied anisotropic elasticity. Oxford: Oxford UP.Google Scholar
  3. Lekhnitskii SG. 1963. Theory of elasticity of an anisotropic elastic body. San Francisco: Holden Day.Google Scholar
  4. Ting TCT. 1996. Anisotropic elasticity — theory and applications. New York: Oxford UP.MATHGoogle Scholar

Classical Fluid Theory

  1. Batchelor GK. 2000. An introduction to fluid mechanics. Cambridge: Cambridge.Google Scholar
  2. Lamb H. 1932. Hydrodynamics. New York: Dover.MATHGoogle Scholar
  3. Langois WE. 1964. Slow viscous flow. New York: Macmillan.Google Scholar
  4. Prandtl L, Tietjens OG. 1934a. Fundamentals of hydro-and aeromechanics. New York: McGraw-Hill.Google Scholar
  5. Prandtl L, Tietjens OG. 1934b. Applied hydro-and aeromechanics. New York: McGraw-Hill.Google Scholar
  6. Schlichting H. 1960. Boundary layer theory. New York: McGraw-Hill.MATHGoogle Scholar

Viscoelasticity Theory

  1. Christensen RM. 1971. Theory of viscoelasticity. New York: Academic Press.Google Scholar
  2. Lakes RS. 1999. Viscoelastic solids. Boca Raton, FL: CRC Press.Google Scholar
  3. Lockett FJ. 1972. Nonlinear viscoelastic solids. New York: Academic Press.MATHGoogle Scholar
  4. Pipkin AC. 1972. Lectures on viscoelasticity theory. New York: Springer.MATHGoogle Scholar
  5. Wineman AS, Rajagopal KR. 2000. Mechanical response of polymers. Cambridge: Cambridge UP.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Personalised recommendations