Magneto-diffusion-viscohyperelasticity for magneto-active hydrogels: Rate dependences across time scales

Abstract

Soft materials have experienced an increasing interest from both scientific and industrial communities during the last years. This interest has become even stronger with the potential of such materials to mechanically respond to external stimuli. Among these materials, magneto-active hydrogels (MAHs) offer great opportunities for novel applications, especially within the biomedical field. However, the design of these stimuli-responsive materials is rather complex as they combine nonlinear mechanical behaviour, rate dependences, magneto-active responses and solvent diffusion processes. To help the understanding of the magneto-mechanical behaviour of these materials, their design and optimization, this work proposes a general continuum framework to couple magnetics, solvent diffusion and nonlinear mechanics. This framework is specialised to and implemented within the finite element method for 3D problems. Different rate-dependent responses of a free-standing MAH are analysed: (i) the strain rate dependency of the instantaneous response to magnetic fields applied at different rates; (ii) the viscous relaxation mechanisms occurring after the complete application of the magnetic field; and (iii) the long-time responses due to solvent diffusion. In addition, an evaluation of the interplay between magnetic fringing effects and solvent diffusion processes is performed. This work provides a flexible computational framework to model the coupled effects of different physical processes occurring within MAHs and highlights the importance of considering rate dependences. The computational framework has the potential to guide the future design of bioactive scaffolds and drug delivery systems based on MAHs.