A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels

Bouklas, Nikolaos; Landis, Chad M.; Huang, Rui

doi:10.1016/j.jmps.2015.03.004

Cited by 123 publications

(84 citation statements)

References 45 publications

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“…Thereby, with our use of the heat transfer and gel swelling analogy, oscillations in the chemical potential during transient swelling is avoided. See [41,62] and the references therein for a further discussion on oscillations in the chemical potential during finite element simulations of transient gel swelling.…”

Section: Element Type and Sizementioning

confidence: 99%

“…Figure 15 shows the time to the onset of instability on a log-log plot for the simulations where wrinkling was obtained as the mode of instability (see Section 6.5 for a discussion on buckling profiles). Simulations predicting creasing were excluded from the plot as the time to onset of creasing is known to show a strong mesh dependence [41].…”

Section: Swelling Ratio At Buckling Initiationmentioning

confidence: 99%

“…Transient effects related to swelling induced buckling are less described. Bouklas et al [41] briefly discussed simulations of transient swelling, however, they did not demonstrate the difference between equilibrium and transient swelling for the initiation of buckling. Toh et al [48] only considered plates with homogeneous material properties, in addition, they used a multi-point constraint routine to force a sinusoidal buckling pattern and hence neglected creasing as a possible mode of instability.…”

Section: Introductionmentioning

confidence: 99%

“…The most available approach is to utilize the analogy between gel diffusion and heat transfer and implement the swelling process using the thermal modeling capabilities already available in commercial finite element codes [37,38]. The other and more general approach is to formulate diffusion-deformation specific elements [39,40,41], however, the implementation of such elements can be considered challenging and time-consuming.…”

Section: Introductionmentioning

confidence: 99%

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Buckling initiation in layered hydrogels during transient swelling

Ilseng

Prot

Skallerud

et al. 2019

Journal of the Mechanics and Physics of Solids

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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.

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Section: Element Type and Sizementioning

confidence: 99%

Section: Swelling Ratio At Buckling Initiationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Buckling initiation in layered hydrogels during transient swelling

Ilseng

Prot

Skallerud

et al. 2019

Journal of the Mechanics and Physics of Solids

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“…Surface patterns due to instability have been experimentally observed in both flat and non flat bodies [9,13,[20][21][22]. On the other side, the theoretical and/or numerical characterization of the process is still lacking, even if a number of accurate studies have been proposed [13,16].…”

mentioning

confidence: 99%

Transient instabilities in the swelling dynamics of a hydrogel sphere

Curatolo

Nardinocchi

Puntel

et al. 2017

Journal of Applied Physics

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We investigate the swelling dynamics driven by solvent absorption in a hydrogel sphere immersed in a solvent bath, through a computational model and a numerical study. We extensively describe the transient process from dry to wet and discuss the onset of surface instabilities through a measure of the lack of smoothness of the outer surface and a morphological pattern of that surface with respect to the two material paremeters driving the swelling dynamics

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