Subjected to compressive stresses, soft polymers with stiffness gradients can display various buckling patterns. These compressive stresses can have different origins, like mechanical forces, temperature changes, or, for hydrogel materials, osmotic swelling. Here, we focus on the influence of the transient nature of osmotic swelling on the initiation of buckling in confined layered hydrogel structures. A constitutive model for transient hydrogel swelling is outlined and implemented as a user-subroutine for the commercial finite element software Abaqus. The finite element procedure is benchmarked against linear perturbation analysis results for equilibrium swelling showing excellent correspondence. Based on the finite element results we conclude that the initiation of buckling in a two-layered hydrogel structure is highly affected by transient swelling effects, with instability emerging at lower swelling ratios and later in time with a lower diffusion coefficient. In addition, for hard-on-soft systems the wavelength of the buckling pattern is found to decrease as the diffusivity of the material is reduced for gels with a relatively low stiffness gradient between the substrate and the upper film. This study highlights the difference between equilibrium and transient swelling when it comes to the onset of instability in hydrogels, which is believed to be of importance as a fundamental aspect of swelling as well as providing input to guiding principles in the design of specific hydrogel systems.while the flux of the solvent molecules in a gel was given in Equation (6). By comparing Equation (A.1) to Equation (A.3) and Equation (A.2) to Equation (6), we find that the equivalents of temperature, specific heat capacity, mass density, and conductivity can be identified asμ, ∂C ∂μ , 1 J , and CD J = J−1 vJ D respectively. These values are calculated as internal variables in the Fortran code using the USDFLD subroutine in Abaqus. The internal heat source in Abaqus, r, is set to zero.

This article presents uniaxial tension tests of three different elastomer compounds commonly applied as seal materials in the oil and gas industry. The tests were performed at five different temperatures, ranging from −20 to 150 • C. Optical measurements were used to ensure high quality stress-strain data. The material samples were exposed to a cyclic deformation history, enabling the viscoelastic behaviour to be explored. A considerable effect of temperature changes was found, with a pronounced increase of stiffness and viscosity for the lowest temperatures. A dip in the stress-strain curve was seen for one of the hydrogenated nitrile butadiene rubbers tested at low temperatures. Matrix-particle debonding simulations qualitatively described this stress dip. For the tests performed at the highest temperatures, a considerable number encountered material failure.

Laboratory tests show that there is a pronounced dierence in the volumetric response between uniaxial tension and conned axial compression loading for commercial particle-lled hydrogenated nitrile butadiene rubber (HNBR) and uoroelastomer (FKM) compounds. In uniaxial tension (UT), a volume increase of 5 and 20 % for the HNBR and FKM respectively was present for a hydrostatic stress of less than 6 MPa, in addition, both compounds showed a clear hysteresis loop in the hydrostatic stress -volume ratio space. For conned axial compression (CAC) tests, on the other hand, the materials reached a 6-7 % volume change for a hydrostatic stress of 140 MPa, and an elastic behaviour was seen. This loading mode dependence of the volumetric response has severe implications for the constitutive representation of the materials. It is demonstrated that existing elastomer models, whereof many assume incompressible volumetric response, are unable to capture the behaviour in both loading modes. To gain an increased understanding of the macroscopically obtained results, a tension in situ scanning electron microscopy study was performed.Matrix-particle debonding was observed to occur at the external surface of the materials, rendering a possible explanation for the loading mode dependent volumetric behaviour. Finite element simulations of a single-particle model, incorporating a cylinder of matrix material with a spherical particle in its centre, showed that the observed debonding can explain the experimental response of the materials in a qualitative manner.

Finite element modeling applied to analyze experimentally determined hydrogel swelling data provides quantitative description of the hydrogel in the aqueous solutions with well-defined ionic content and environmental parameters. In the present study, we expand this strategy to analysis of swelling of hydrogels over an extended concentration of salt where the Donnan contribution and specific ion effects are dominating at different regimes. Dynamics and equilibrium swelling were determined for acrylamide and cationic acrylamide-based hydrogels by high-resolution interferometry technique for step-wise increase in NaCl and NaBr concentration up to 2 M. Although increased hydrogel swelling volume with increasing salt concentration was the dominant trend for the uncharged hydrogel, the weakly charged cationic hydrogel was observed to shrink for increasing salt concentration up to 0.1 M, followed by swelling at higher salt concentrations. The initial shrinking is due to the ionic equilibration accounted for by a Donnan term. Comparison of the swelling responses at high NaCl and NaBr concentrations between the uncharged and the cationic hydrogel showed similar specific ion effects. This indicates that the ion non-specific Donnan contribution and specific ion effects are additive in the case where they are occurring in well separated ranges of salt concentration. We develop a novel finite element model including both these mechanisms to account for the observed swelling in aqueous salt solution. In particular, a salt-specific, concentration-dependent Flory–Huggins parameter was introduced for the specific ion effects. This is the first report on finite element modeling of hydrogels including specific ionic effects and underpins improvement of the mechanistic insight of hydrogel swelling that can be used to predict its response to environmental change.

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Aortic dissection is a life-threatening pathology that mainly affects the medial layer, which consists of multiple lamellar units. Glycosaminoglycans/proteoglycans (GAGs/PGs) can accumulate in the interlamellar space within the media and under certain circumstances swell considerably. Such behavior of GAGs/PGs induces high stresses in the elements connecting the elastic laminae and, in the event of tissue failure, leads to medial delamination and thus to the initiation of aortic dissection. The present study takes up the swelling polymer theory and couples the swelling behavior of GAGs/PGs with the anisotropic response of aortic tissues in order to investigate the initiation mechanism of aortic dissection. The computational simulation uses an advanced weighted constitutive model, which is combined with the global and submodel technique in the finite element software Abaqus. The numerical results show that the proposed method is able to generate failure stresses of the same order of magnitude as the failure stresses indicated in tensile tests. Stress concentrations are observed at the connection between interlamellar struts made of elastic fibers and elastic laminae. Such connections are hotspots at which dissections are expected to initiate. Therefore, this study presents the prediction of the onset of aortic dissection due to the accumulation and swelling of GAGs/PGs and provides a solid foundation for future modeling work.

The onset of surface instability during diffusion-driven swelling of hydrogels depends on the kinetics of the swelling process. Here, we outline a perturbation analysis framework using a finite difference approach for calculating the stability limit of swelling hydrogel plates with graded material properties accounting for kinetic effects. The framework is implemented as a Python routine which is made freely available. Results obtained for bilayered hydrogel plates illustrate that the onset of instability occurs earlier in time and at a lower global swelling ratio when kinetics is accounted for compared to the homogeneous swelling case. This work presents an accessible calculation tool for stability analysis of swelling gels, providing input for the design of novel hydrogel systems.