A course in continuum mechanics, vol. 1: Basic equations and by L. I. Sedov, J. R. M. Radok

By L. I. Sedov, J. R. M. Radok

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Additional info for A course in continuum mechanics, vol. 1: Basic equations and analytical techniques

Example text

Axisymmetric two- and three-dimensional systems may be treated similarly. In one dimension we obtain the equation (Philip, 196ge) (29) with in close analogy to (15). 3 Discussion The maj or burden of this section 5 has been that, reinterpretation of various quantities, with appropriate the macroscopic analysis of flow and volume change in porous media carries over to the same processes in tissues. One facet is the comparable use of Lagrangian coordinates in the two systems, an aspect recognized by Raats (1987).

4 Two remarks. First we recall that the results presented are based on the linear Debye-HUckel form of the Poisson-Boltzmann equation. here a striking example of a linear process on the We have microscopic scale leading to a strongly nonlinear process on the macroscopic scale. Second, we observe that, in the unloaded state the water is generally in tension and the particle in compression. behaves essentially as a prestressed analogy is with prestressed concrete, the particles like the concrete.

Substitution for Fw from (4) in (1), and also -68 s for 8w yields (5) Differentiation by parts followed by the elimination of two terms using (2), and division by 8 s then yield the equation a-6) (at = z _ (1/8 s ) (au) az _ (F s 18 s ) (a-6) az t (6) t which satisfies both continuity equations (1) and (2), but which focusses on the water component of the system. Material Coordinates Philip (1968) and Wakeman (1986) implicitly develop an Eulerian analysis of unsteady flow problems expressed in terms of the space coordinate z consistent with (6).

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