Tissue-growth model for the swelling analysis of core-shell hydrogels

Water-imbibing of core-shell hydrogel particles may result in large deformation and inhomogeneous stress distributions. In this paper, we use a growth model, which was originally established for simulating the growth of biological tissues, to investigate the swelling behavior of gel particles. As two representative and practically important configurations, spherical and cylindrical core-shell particles consisting of compressible hyperelastic gel materials are studied by using this nonlinear finite volumetric growth theory and the results are compared with the analytical solutions based on the linear elastic theory. Our analysis shows that the mismatch between the properties of the core and the shell significantly affects the deformation of gel particles and the stress at their core-shell interfaces. Furthermore, we find that a limit point instability phenomenon, which is different from conventional surface buckling or folding, may occur in the swelling of spherical particles when the swelling factor exceeds a critical value.