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G V Levina Institute for Continuous Media Mechanics

Abstract

The application of Hamilton's principle to a continuous medium is described, beginning with ideal fluids and elastic solids. The general case of a continuum that does not exhibit microstructural effects is presented. Then two particular theories of materials with microstructure are presented to illustrate the use of Hamilton's principle to generalize the ordinary theories of fluid and solid mechanics.

Notes

  1. 1.

    Theories in which this restriction is relaxed will be described in the next section.

  2. 2.

    Notice that, because S and DIV S must be continuous, the form of the constitutive equation for S or T may impose a more stringent smoothness requirement on the motion of the material.

  3. 3.

    See Drumheller and Bedford [22]. Similar procedures have been suggested by Ericksen [26] and Serrin ( [65], p. 148).

  4. 4.

    See the related discussion in Sect. 4.4.

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Authors and Affiliations

  1. The University of Texas at Austin, Austin, TX, USA

    Anthony Bedford

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Bedford, A. (2021). Mechanics of Continuous Media. In: Hamilton's Principle in Continuum Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-90306-0_3

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