A Viscoelastic Two-Phase Model for Cartilage Tissues

摘要

Hydrated soft tissues such as cartilage can be considered as porous materials consisting of an organic solid matrix (collagen and proteoglycans) ventilated by a pore-fluid (water and elektrolytes). These types of biological tissues significantly demonstrate viscoelastic phenomena under various configurations of deformation. Two distinct mechanisms exist for this dissipative behaviour, the frictional drag associated with the interstitial fluid flow through the porous solid matrix and the flow-independent viscoelastic properties of the organic solid matrix itself. The goal of this paper is to describe this complex behaviour by a biphasic viscoelastic model accounting for both the flow-dependent fluid-solid interaction and the intrinsic skeleton viscoelasticity. Therefore, the macroscopic Theory of Porous Media (TPM) is applied, where the effective skeleton stress is determined by an appropriate viscoelasticity law. The fundamental approach of the viscoelasticity law is based on the thermodynamics with internal state variables, where a hyperelastic material formulation is used. Since cartilage tissues exhibit deformation dependent permeability effects, it is assumed that the permeability is a function of the actual porosity of the solid skeleton. Futhermore, both constituents are modelled materially incompressible; thermal effects and mass exchanges are excluded. The viscoelastic two-phase model is implemented into PANDAS, an adaptive finite element code for multi-phase problems. To show the capability, the model is applied to articular cartilage, where some representative problems are computed. On this occasion, the influence of the intrinsic viscoelasticity of the solid skeleton is studied. In addition, the problem of separating the flow-independent dissipative behaviour from the flow-dependent consolidation process is discussed.