Buckling initiation in layered hydrogels during transient swelling

Abstract

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.

Controlled Cooperative Wetting Enabled Heterogeneous Structured 3D Morphing Transducers

“…We believe, the buckling conformation is achieved due to the influence of high transient swelling forces with swelling mismatch occurring in one of the functional blocks. [ 40 ] When more than two patterns were involved, complex surface convex and concave buckling can be observed that transients over time with changing diffusion coefficients and ionic equilibrium, as detailed in the Supporting Information and Figure S2, Supporting Information.…”

A Perturbation Analysis Approach for Studying the Effect of Swelling Kinetics on Instabilities in Hydrogel Plates

“…The successful design of hydrogel systems relies on predictive methods for the stability of swelling gels providing sound stability diagrams. Previous computational studies on the instability of gels have made use of two main methods, finite element (FE) simulations [16][17][18][19][20][21] or perturbation analysis (PA) [22][23][24][25][26][27].…”

“…FE simulations have successfully been applied to study geometrical instability of transiently swelling gels in a few recent studies [19][20][21]. This method excels in its applicability to general geometries and loading conditions, and use of the method has demonstrated that the swelling kinetics can alter both the level of swelling and the wavelength of the surface pattern at the onset of instability.…”

“…In particular, soft bilayered gels with a low stiffness ratio (i.e. the stiffness of the upper layer relative to the lower layer) have been shown to change their instability mode from a global long-wavelength wrinkling pattern to localized creasing as the speed of the swelling process is reduced [20,21]. Nevertheless, the application of FE simulations of swelling gels in the design of new hydrogel systems can be limited by its requirements of advanced software, highly skilled analysts, and computational resources.…”

Donnan Contribution and Specific Ion Effects in Swelling of Cationic Hydrogels are Additive: Combined High-Resolution Experiments and Finite Element Modeling

“…These provide improved hyperelastic models that describe the equilibrium swelling behavior of hydrogels [ 16 , 17 , 18 , 19 ]. More complex time-dependent models can also describe the transient nature of swelling [ 20 , 21 , 22 , 23 , 24 , 25 ]. Nevertheless, most of the work dealing with the modeling of hydrogel swelling are qualitative evaluations of the model’s capability of capturing important features of the swelling process.…”