Second-order elastic solutions for spherical gels subjected to spherically symmetric dilatation

► The problem of a spherical gel subjected to a dilatation is investigated. ► Analytical solutions are found within the framework of second-order elasticity. ► Stresses, displacements and energy are computed from five elastic constants. ► It is found that the physical quantities may be dominated by nonlinear components. ► The closed-form solutions permit a detailed study of the physical behaviors.