Ayhan Acartürk

A Coupled FE Analysis of the Intervertebral Disc Based on a Multiphasic TPM Formulation

The results presented above show that the model under consideration is capable of describing the complex inhomogeneous and coupled behaviour of the IVD. Herein, the different characterizing moduli, namely inhomogeneous fibers, permeability, FCD or intrinsic viscoelasticity, are easily activated or deactivated, which yields an efficient tool to aid the study of their influence on a variety of effects, such as the interstitial fluid flow or the disc bulge. As a next step, the theoretically introduced material parameters must be determined by independent experiments involving more complex deformation modes, such as superimposed flexion, lateral bending and torsion. Finally, together with an appropriate damage model, it is then possible to describe further degeneration effects and explore mechanisms leading to disc herniation.

A Continuum Approach for the Swelling of Charged Hydrated Media

Swelling of charged hydrated tissues is an important topic both in biomechanics and in biomedical surgery. From the mathematical point of view, the problem is based on an electro-chemomechanical multiphase formulation, consisting of a porous solid skeleton saturated by an interstitial fluid which itself is an ideal mixture of a liquid solvent (water) and dissolved electrolytes (ions).

Large Strain Analysis of 3-D Viscoelastic Swelling of Charged Tissues and Gels

Materials like soft biological tissues undergo large viscoelastic deformations during the swelling process. Following this, it is the goal of this contribution to merge the advances of finite viscoelasticity laws and the state of the art in electrochemical swelling theories within a well-founded multiphasic concept. The numerical treatment is carried out fully 3-d in the framework of the FEM.

Swelling Phenomena in Electro-Chemically Active Hydrated Porous Media

Charged hydrated materials exhibit internal coupling mechanisms stemming from the intrinsic characteristics of the constituents. In this context, the model under consideration consists of a fluid-saturated solid matrix carrying volume-free fixed negative charges, while the pore fluid is given by a mixture of a liquid solvent and the cations and anions of a dissolved salt. Based on the well-founded Theory of Porous Media (TPM), use is made of the assumption of quasi-static processes. The governing equations are given by the volume balance of the fluid mixture governed by the hydraulic pressure, the concentration balance governed by the cation concentration, the overall momentum balance governed by the solid displacement and the electrical continuity equation governed by the electrostatic force. Furthermore, the mechanical solid extra stress is described by an extended neo-Hookean material law, while the viscous fluid flow follows an extended Darcy’s law, which includes the gradients of the ion concentrations and the electrical potential. Furthermore, the ion diffusion is described by an extended Nernst-Planck equation. Finally, the model is implemented into the FE tool PANDAS by use of a mixed finite element scheme. The presented examples proceed from boundary conditions depending on internal variables such that certain stabilisation techniques are needed.