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By Patrizio G., Tomassini A.
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Hashin, Z. , 1963. A variational approach to the theory of the elastic behavior of multiphase materials, J. Mech. Phys. Solids, 11, 127-140. D. dissertation, University of Alberta. , Spanos, T. J. T. , 1995. Deformation parameters of permeable media, Geophysical Journal International, 121, 359-370. , 1963. Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, 11, 357-372. , 1971. Effective thermal conductivity of porous rocks, J. Geophys. , 76(26), 6420-6427.
In the remainder of this chapter thermomechanical coupling will be neglected in order to concentrate on poromechanics. v Megascopic Potential Energy In order to establish a relation between the stress and strain components of the solid-fluid medium Biot assumes the existence of energy potential. Because of the existence of a potential energy the matrix of coefficients relating the stress and strain tensor must be symmetric, thereby reducing the number of independent parameters. Therefore, the consequences of a single energy potential will be explored here in the context of this work.
102) where c, c' are constants. 103) When the porosity is not uniform a translational displacement of the porous medium as a whole results in a change in porosity from φo to φ = φo - us⋅∇ φo. Thus φ - φo is replaced by φ - φo + us⋅∇ φo as a measure of true deformation. 104) It is reasonable to assume that τsik is now a function of usij '' only. 108) A further symmetry follows from assuming that τsik can be obtained from an energy density (cf. , 1993). 113) is the megascopic shear tensor generalizing µM.