Poroelasticity pp 189-228 | Cite as

Governing Equation

  • Alexander H.-D. Cheng
Part of the Theory and Applications of Transport in Porous Media book series (TATP, volume 27)


In Chaps.  2 through 5 we have constructed the constitutive laws that relate the forces (stresses) applied to a porous body to its deformation (strains). In addition to these constitutive laws, there are other physical laws that are relevant to the deformation and motion of porous materials. These are presented in this chapter.

For the purpose of modeling, these laws are formulated in the form of mathematical equations. To reduce the size of the solution system, variables can be eliminated among the physical laws to produce governing equations that contain fewer variables. Given a complete set of governing equations, together with a set of well-posed boundary conditions, the mathematical system can be solved either analytically or numerically. There are times, however, that the mathematical system can be further reduced by the introduction of non-physical variables, known as potentials, to replace the physical ones. The physical variables are typically associated with the potentials as their spatial derivatives. We shall refer the mathematical system involving potentials as field equations. In this chapter we shall discuss these equations, as well as the initial and boundary conditions, leading to a complete mathematical solution system.


Porous Medium Pore Pressure Diffusion Equation Displacement Function Rank Tensor 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Alexander H.-D. Cheng
    • 1
  1. 1.University of MississippiOxfordUSA

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