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Challenges in the multiphysics modeling of polymer gels

Banff International Research Station for Mathematical Innovation and Discovery

Among soft active materials, i.e. systems that respond to a non-mechanical stimulus (electric field, exposure to a solvent, pH change, temperature field) with a mechanical deformation, polymer gels play a major role in the current research on innovative materi- als. Applications where gels are employed in the form of thin structures have stimulated the interest in developing dimensionally reduced theories. Hence, a number of plate and shell models have been proposed in the recent years, mainly based on the framework of incompatible elasticity. Despite their success in reproducing experimental results, these models are restricted to equilibrium problems. In general, while dimensionally reduced theories are well established in the study of equilibrium problems in elasticity and struc- tural mechanics, the development of the same theories in a multiphysics, non-equilibrium context such that of swelling thin gels poses challenging theoretical questions. In this talk, we present a survey of our contribution to the derivation of reduced theories for swelling gels. Specifically, we present a theory of swelling material surfaces to model poly- mer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. Furthermore, we introduce a transient large-strain plate theory for polymer gels obtained by a thermo- dynamically consistent dimensional reduction of a coupled three-dimensional model. We apply the model to the shape programming of composite gel plates, where the spatial modulation of the gel stiffness can be designed so that the composite realizes a target, three-dimensional shape upon swelling. Fracture is another challenging aspect of the mechanics of polymer gels that provides, in the context of these materials, a new angle of a classical, well-studied issue. Indeed, fracture in hydrogels is often accompanied by vari- ous instabilities and dissipation mechanisms that may significantly affect the macroscopic toughness of the system. In synthetic chemical gels, fracture is typically brittle. However, here we show that the unstable character that is characteristic of brittle fracture may be radically altered when a brittle, impermeable hydrogel is hydraulically coupled with a tougher, poroelastic solid. Moreover we revisit the classical problem of Mode I fracture in the context of gels. Specifically, we show the existence of a velocity-independent toughen- ing, which is innate in the poroelastic nature of polymer gels. These fundamental studies on the flaw-tolerance of hydrogels may both shed light on the fracture of soft biological tissues and suggest toughening strategies to improve their mechanical performance.

Mathematics; Mechanics of deformable solids; Statistical mechanics, structure of matter; Mathematical physics

video/mp4

Author affiliation: Sissa

2017-03-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60816

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/