Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load

Abstract

a b s t r a c tA network of polymers can imbibe a large quantity of a solvent and swell, resulting in a gel. The swelling process can be markedly influenced by a mechanical load and geometric constraint. When the network, solvent, and mechanical load equilibrate, inside the gel the chemical potential of the solvent is homogeneous, but the concentration of the solvent and the deformation of the network can be inhomogeneous. We use the chemical potential of the solvent and the deformation gradient of the network as the independent variables of the free-energy function, and show that the boundary value problem of the swollen gel is equivalent to that of a hyperelastic solid. We implement this approach in the finite-element package, ABAQUS, and analyze examples of swelling-induced deformation, contact, and bifurcation. Because commercial software like ABAQUS is widely available, this work may provide a powerful tool to study complex phenomena in gels.

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

“…11). Moreover, while in most of the cases mechanical loading is used to deform the structures and trigger the instabilities, it has also been shown that other stimuli including swelling [160,[165][166][167][168]183] (see Fig. 12(a)), capillary pressure [172] (see Fig.…”

A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

“…Complex material behaviors of hydrogels with large, reversible deformation and various instability patterns have been observed in experiments [8][9][10][11][12][13][14][15][16][17], which have motivated a large body of theoretical and numerical studies [18][19][20][21][22][23][24][25][26][27][28][29][30]. Recently, following the classical works by Gibbs [31] and Biot [32,33], Hong et al [27] formulated a nonlinear field theory coupling diffusion of solvent molecules and large deformation of polymeric gels.…”

Study of swelling behavior of temperature sensitive hydrogels considering inextensibility of network

“…To define the free energy functionality, an additive decomposition of the free energy density is assumed in the form of (See e.g., [7,25,26,[30][31][32] among others): (6) where  and J are volume of a fluid molecule and the determinant of F , respectively. This constraint is considered by using Lagrange multiplier method and modifying the free energy function as [9,30]:…”