Effect of Nonlinear Elasticity on the Swelling Behaviors of Highly Swollen Polyelectrolyte Gels

Polyelectrolyte gels exhibit swelling behaviors that are dependent on the external environment. The swelling behaviors of highly charged polyelectrolyte gels can be well explained using the Flory–Rehner model combined with the Gibbs–Donnan effect and Manning’s counterion condensation effect (the FRGDM model). This study investigated the swelling properties of a series of model polyelectrolyte gels, namely tetra-polyacrylic acid-polyethylene glycol gels (Tetra-PAA-PEG gels), and determined the applicability of the FRGDM model. The swelling ratio (Vs/V0) was well reproduced by the FRGDM model in the moderate swelling regime (Vs/V0 < 10). However, in the high swelling regime (Vs/V0 > 10), the FRGDM model is approx. 1.6 times larger than the experimental results. When we introduced the finite extensibility to the elastic free energy in the FRGDM model, the swelling behavior was successfully reproduced even in the high swelling regime. Our results reveal that finite extensibility is one of the factors determining the swelling equilibrium of highly charged polyelectrolyte gels. The modified FRGDM model reproduces well the swelling behavior of a wide range of polyelectrolyte gels.

A CONSTITUTIVE MODEL FOR BOTH LOW AND HIGH STRAIN NONLINEARITIES IN HIGHLY FILLED ELASTOMERS AND IMPLEMENTATION WITH USER-DEFINED MATERIAL SUBROUTINES IN ABAQUS

ABSTRACT Strain energy functions (SEFs) are used to model the hyperelastic behavior of rubberlike materials. In tension, the stress–strain response of these materials often exhibits three characteristics: (i) a decreasing modulus at low strains (&lt;20%), (ii) a constant modulus at intermediate strains, and (iii) an increasing modulus at high strains (&gt;200%). Fitting an SEF that works in each regime is challenging when multiple or nonhomogeneous deformation modes are considered. The difficulty increases with highly filled elastomers because the small strain nonlinearity increases and finite-extensibility occurs at lower strains. One can compromise by fitting an SEF to a limited range of strain, but this is not always appropriate. For example, rubber seals in oilfield packers can exhibit low global strains but high localized strains. The Davies–De–Thomas (DDT) SEF is a good candidate for modeling such materials. Additional improvements will be shown by combining concepts from the DDT and Yeoh SEFs to construct a more versatile SEF. The SEF is implemented with user-defined material subroutines in Abaqus/Standard (UHYPER) and Abaqus/Explicit (VUMAT) for a three-dimensional general strain problem, and an approach to overcome a mathematically indeterminate stress condition in the unstrained state is derived. The complete UHYPER and VUMAT subroutines are also presented.

Electroelasticity of dielectric elastomers based on molecular chain statistics

The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.