Analytical solutions for bilayered spherical hydrogel subjected to constant dilatation

The application of multilayered hydrogel capsules in biomedical engineering has stimulated much interest in the mechanics of soft matter. Based on second-order elasticity theory, this paper presents analytical solutions for a spherically symmetric bilayered hydrogel subjected to a constant dilatation. The results show that: (1) elastic nonlinearity and inhomogeneity play a crucial role in the mechanical state, (2) a wide range of mechanical states can be designed for specific applications by manipulating the layer elasticity and interface position, and (3) the displacement and stresses can be characterized by a reduced set of eight geometric–elastic constants.

► Analytical solutions are obtained for the problem of a spherical composite with dilatation.
► A bilayered sphere is considered with dissimilar elastic constants for the layers.
► The theory emphasizes material nonlinearity.
► The solutions may be used to design the mechanical properties of a bioenvironment.
► Results may be relevant to tissue engineering, drug delivery and stem cell technology.