Non-linear deformations of porous elastic solids

This paper is concerned with the non-linear theory of porous elastic bodies. First, we present the basic equations in general curvilinear coordinates. The constitutive equations for porous elastic bodies with incompressible matrix material are derived. Then, the equilibrium theory is investigated. An existence result within the one-dimensional theory is presented. The theory is applied in order to study the torsion of an isotropic circular cylinder and the flexure of a cuboid made of an anisotropic material. It is shown that the equations of equilibrium reduce to a single ordinary differential equation governing an unknown function which characterizes the aforementioned deformations.

► We present the basic equations of the non-linear theory of elastic materials with voids in curvilinear coordinates.
► We study the torsion of an isotropic circular cylinder and the flexure of a cuboid made of an anisotropic material.
► We present an existence result within the one-dimensional theory.