A Simple Model for a Fluid-Filled Open-Cell Foam

A simple microstructure model is used to describe a fluid-filled open-cell foam. In the simplest case it consists of parallel elastic plates with gaps between them, which are filled with a Newtonian fluid. We assume that the load applied to this model material is uniaxial. The constitutive equation is formulated with the pressure of the fluid as an inner variable. The model yields an evolutional equation for the fluid pressure which itself is a field equation, that is a partial differential equation in time and space coordinates. This differential equation is solved for an instantaneously applied constant load and for a harmonically oscillating load. The solution of the differential equation, in combination with the constitutive equation leads to a relation between mean applied load and global strain of the test specimen. Finally, we obtain the creep compliance and the complex modulus of the foam material, respectively. The influence of different geometries of the foam and of different material behaviour of the matrix and fluid on the creep compliance and the complex modulus is discussed.