Re-examination of the equations of poroelasticity
To study the mechanical behavior of poroelastic media, we apply the method of homogenization to derive effective equations on the macroscale, for a matrix with a periodic structure on the microscale. We allow the matrix displacement corresponding to the global strain to be comparable to the granular size, and show that the resulting effective equations are nonlinear in general. The constitutive coefficients of the nonlinear terms nevertheless vanish under two conditions: (i) when the global-scale deformation is also much smaller than the granular size, and (ii) when the global-scale deformation is comparable to the granular or pore size, but the microcell geometry is symmetric with respect to three orthogonal planes.
scientific article; zbMATH DE number 1162174