Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution

Malakpoor, K.; Kaasschieter, E.F.; Huyghe, Jmrj Jacques

doi:10.1051/m2an:2007037

Cited by 14 publications

(13 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Motived by the success of MHFEM in solving Darcy's type equations and Biot consolidation problems, we apply MHFEM in swelling simulations in order to achieve more reliable and satisfactory results. Malakpoor et al [29] applied MHFEM in the simulation of the swelling of cartilaginous tissues. However, his simulations were limited to small deformations.…”

Section: Introductionmentioning

confidence: 99%

A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels

Malakpoor

Huyghe

2018

Comput Mech

Self Cite

View full text Add to dashboard Cite

Ionized hydrogels, as osmoelastic media, swell enormously (1000 times its original volume in unionized water) due to the osmotic pressure difference caused by the presence of the negatively charged ion groups attached to the solid matrix (polymer chains). The coupling between the extremely large deformations (induced by swelling) and fluid permeation is a field of application that regular poroelasticity formulations cannot handle. In this work, we present a mixed hybrid finite element (MHFE) computational framework featuring a three-field (deformation-chemical potential-flux) formulation. This formulation guarantees that mass conservation is preserved both locally and globally. The impact of such a property on the swelling simulations is demonstrated by four numerical examples in 2D. This paper focuses on the implementation aspects of the MHFE model and shows that it stays robust and accurate for a volume increase of more than 3000%.

show abstract

Section: Introductionmentioning

confidence: 99%

A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels

Malakpoor

Huyghe

2018

Comput Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the amount of net flux across one element has a direct influence on the volumetric change of the element in hydrogel swelling simulation, an accurate calculation of flux is also of great importance. Malakpoor et al 24 applied MHFEM in the simulation of the swelling of cartilaginous tissues and achieved good agreement with the analytical solutions in small deformation regime. To our knowledge, there is no work available yet that enables a full 3D simulation of a swelling hydrogel using MHFEM.…”

Section: Introductionmentioning

confidence: 83%

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability

Malakpoor

Huyghe

2018

Soft Matter

Self Cite

View full text Add to dashboard Cite

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogels. The extremely large degree of swelling is one of the most distinctive characteristics of such hydrogels, as the volume increase can be about 30 times its original volume when exposed to physiological solution. The large deformation resulting from the swelling demands careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using the mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on the swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of the local mass conservation of MHFEM contributes to a more accurate calculation of the deformation as the permeability across the swelling gel in a transient state is highly non-uniform. We show that the proposed model is able to simulate the free swelling of a random-shaped gel and the squeezing of fluid out of a swollen gel. Finally, we make use of the proposed numerical model to study the onset of surface instability in transient swelling.

show abstract

“…In order to handle the strong non-linearities of the quadriphasic model in large deformations, it is advisable to replace the present formulation by a Raviart–Thomas formulation that respects local mass balance at all times. 16 …”

Section: Discussionmentioning

confidence: 99%

1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump

et al. 2015

View full text Add to dashboard Cite

NMR is used to measure sodium flow driven by a 1D concentration gradient inside poly-acrylamid (pAA) hydrogel. A sodium concentration jump from 0.5 M NaCl to 0 M NaCl is applied at the bottom of a cylindrical pAA sample. The sodium level and hydrogen level are measured as a function of time and position inside the sample for 5 days. Then a reversed step is applied, and ion flow is measured for another 5 days. During the measurement, the cylindrical sample is radially confined and allowed to swell in the axial direction. At the same time, sodium and moisture in the sample are measured on a 1D spatial grid in the axial direction. A quadriphasic mixture model (Huyghe and Janssen in Int J Eng Sci 35:793, 1997) is used to simulate the results and estimate the diffusion coefficient of sodium and chloride. The best fit results were obtained for D cm2/s and D cm2/s, at 25 degrees centigrade. Different time constants were observed for swelling and deswelling.

show abstract

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution

Cited by 14 publications

References 13 publications

A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels

A mixed hybrid finite element framework for the simulation of swelling ionized hydrogels

A three-dimensional transient mixed hybrid finite element model for superabsorbent polymers with strain-dependent permeability

1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump

Contact Info

Product

Resources

About