2D mixed hybrid FEM of lanir model

Osmoelastic media have large negatively charged groups attached to the solid matrix. Due to the fixed charges, the total ion concentration inside the medium is higher than in the surrounding fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the medium. Lanir's osmoelastic model assumes that small ions are always in equilibrium with the external salt concentration. This means that ion contribution is neglected and the medium is described by two constituents only: the solid and the fluid. In this paper, we implemented Lanir model using MHFEM (Mixed Hybrid Finite Element Method) for consolidation experiment in both 1D and 2D cases, with result verification with analytical solution in 1D. The constituents are assumed to be incompressible. Infinitesimal deformations are assumed. The material is linear elastic, isothermal, isotropic, homogeneous and fully saturated.</p

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Master Class (Scientific Computing) of the Mathematical Researc

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

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%

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

\u3cp\u3eIonized 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%.\u3c/p\u3

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

\u3cp\u3eA 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.\u3c/p\u3

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

A hydrogel is a cross-linked polymer network with water as solvent. Industrially widely used superabsorbent polymers (SAP) are partially neutralized sodium polyacrylate hydrogel. 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 the physiological solution. The large deformation resulting from the swelling demands a careful numerical treatment. In this work, we present a biphasic continuum-level swelling model using mixed hybrid finite element method (MHFEM) in three dimensions. The hydraulic permeability is highly dependent on swelling ratio, resulting in values that are orders of magnitude apart from each other. The property of 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 squeezing of fluid out of a swollen gel. At last, we make use of the proposed numerical model to study the onset of surface instability in transient swelling