On the viscoelastic behaviour of fluid-saturated porous materials

It is well known that fluid-saturated porous materials undergo time-depending deformation processes under external loads, as occur, e.g., during the so-called consolidation process. The reason for this behaviour lies in the flow-dependent viscous properties of the pore-fluid, which, in case of viscoelastic skeleton materials is overlayed by flow-independent dissipative effects. In the present contribution, we intend to describe the flow-dependent as well as the flow-independent viscoelastic behaviour. Therefore, a linear viscoelastic two-phase model based on the macroscopic Theory of Porous Media is developed. The applied linear viscoelasticity law to describe the intrinsic energy absorbing behaviour of the solid skeleton is given in differential form deduced from rheological considerations. The governing model equations are treated within the finite element method for spatial discretization. This leads to a system of differential-algebraic equations in the time domain. To show the capability of this approach, the model is applied to cartilage tissues, where some representative initial boundary value problems are computed. On this occasion, the influence of the viscoelasticity of the solid skeleton alone is studied. In addition, the problem of separating the flow-independent dissipative behaviour from the flow-dependent consolidation process is discussed.