Chemo-electro-mechanical formulation

Huyghe, J.M. and Janssen, J.D. (1999) Thermo-chemo-electro-mechanical formulation of saturated charged porous solids, Transport in Porous Media 34, 129-141... 

To gain a more precise insight into the phenomena occurring in gels, the Theory of Porous Media (TPM), or the coupled chemo-electro-mechanical formulation is a good choice. Normally, the TPM is applied for the gel only, while the coupled multi-field formulation incorporates the gel and the surrounding solution. 

In this test case, the chemical stimulation of the gel film placed in the solution bath is investigated by the fuUy coupled chemo-electro-mechanical formulation. That is additionally, the mechanical deformation of the gel domain is considered and the chemo-electro-mechanical field is directly solved on the deformed domain. 

The coupled chemo-electro-mechanical formulation is a quite powerful tool for capturing the behaviour of the chemical, electrical and mechanical unknowns. In order to compare numerical results with experimental results, the numerically obtained relative swelling ratio q versus the prescribed concentration in the solution is depicted in Fig. 17. The initial state of the test cases discussed in Sect 2 has been taken as reference value. 

WaUmersperger, T., KropUn, B. Gulch, R.W. 2004, Coupled chemo-electro-mechanical formulation for ionic polymer gels - numerical and experimental investigations . Mechanics of Materials, vol. 36, no. 5-6, pp. 411-420. 

For modeling the transport within both the gel and the surrounding solution, in this section, a continuum chemo-electro-mechanical formulation is presented. For this formulation, (i) the balance laws of the different constituents, i.e., polymer, solution, mobile, and bound charges (ii) flie kinematics as well as (iii) the materials laws have to be considered. 

The resulting initial-boundary value problem is a fully coupled chemo-electro-mechanical formulation. This problem may be solved by a numerical method, e.g., by the Finite Element Method, the Finite Difference Method, or a combined method. For more details, see, e.g., Wallmersperger and Ballhause (2008). 

The coupled chemo-electro-mechanical multi-field formulation is a model on the micro-mesoscopic scale. It has been developed to gain a more precise insight into... 

In this chapter numerical simulations by applying the coupled chemo-electro-mechanical multi-field formulation on a deforming mesh have been performed. It has been shown that this formulation is an excellent method for describing the coupled behaviour of polymer gels in a solution. This method is capable to explain the mechanisms of the behaviour of polyelectrolyte gels under chemical and electrical stimulation, the ion distributions as well as the swelling and bending behaviour. 

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