Advances in modelling saturated soft biological tissues and chemically active gels

Abstract

Swelling-active materials are numerous and can be found in many applications regarding geotechnical, biological or chemical problems. In general, these materials consist of a charged solid skeleton which is saturated by a fluid mixture containing a solvent and one or more dissolved electrolytes. Following this, the swelling mechanism can either be triggered via changes of the solute concentration in the surrounding solution or by the application of an electric field. Due to the complex micro structure and the numerous coupled effects which result from the electro-mechanical coupling, this class of materials is very effectively described using the Theory of Porous Media. In this regard, the present paper will provide a brief overview of the involved mixture kinematics, the balance equations, as well as the necessary constitutive theory. The presented model is then brought into a weak formulation which is suitable for a numerical treatment using the Finite Element Method. The chosen degrees of freedom are the solid displacement, the ion concentrations, the pressure and the electrical potential, which are discontinuous over the domain boundary. These discontinuities lead to stability problems which can be solved by a penalty method. Finally, two representative examples are presented addressing a free swelling experiment of a cylindrical nucleus pulposus specimen, as well as an electrically initiated bending of a cantilever made of an electro-active polymer like hydrogel, for instance.

Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

“…In the numerical range, both problems have been embedded in the Finite Element Analysis, thus yielding sound numerical results. In particular, the numerical results of the unsaturated soil example have been taken from Ehlers, Graf and Ammann [27], whereas the results of the swelling media example have been taken from Ehlers and Acartürk [31] and those of the electro-active polymer from Ehlers and Karajan [33]. Material parameters which have not been included in this article, can also be found in these articles.…”

“…Given (42), it is immediately seen that the sum relations defined by (33) are also valid for the entropy flux and the entropy supply term. In comparison to the relations (35) and (42), it is furthermore seen that the entropy principles for single-phase and multiphasic materials only leads to the same inequalities if the diffusion process vanishes (d α = 0) and if all constituents ϕ α additionally have the same Kelvin's temperature (θ α ≡ θ ).…”

Multisensitive Swelling of Hydrogels for Sensor and Actuator Design

“…The swelling of hydrogels can be modeled in various ways, e.g., on the continuum level by using the multifield theory [7][8][9] or the Theory of Porous Media. [10][11][12][13][14] The behavior of the polymer on the molecular level can be captured, e.g., by stochastic modeling. [15] In many cases, monosensitive hydrogels show cross-sensitivities toward other influences different from the targeted one.…”

Modeling and simulation of hydrogels for the application as finger grippers

“…These models were suggested for both free swelling (e.g. Ateshian et al, 2011; Ehlers and Acartürk, 2009; Ehlers et al, 2010; Loret and Simões, 2004, 2005; Mauck et al, 2003; Sun et al, 1999) and stimulus-driven deformation (e.g. Chen and Ma, 2006; Ehlers et al, 2005; Lai and Mow, 1999) of hydrogels.…”