Some nonlinear diffusion problems within the context of the theory of interacting continua (Q1095697)

The authors had earlier discussed the appropriate boundary conditions to be used in the general nonlinear theory of interacting two phase continua [ibid. 24, 1453-1463 (1986; Zbl 0594.73007)]. By assuming that the solid- fluid wall is in a saturated state for surface tractions, the authors had earlier formulated the boundary conditions which enable unique solutions to the partial differential equations. Two problems are solved for the radial diffusion through (i) a nonlinearly elastic isotropic hollow cylinder and (ii) a uniformly stretched or sheared nonlinear porous elastic layer. Shearing and stretching have qualitatively opposing effects on the diffusion process. The inadequacy of the linear solutions are indicated. The applications of these studies to several biomechanical problems are also pointed out.