Direct and inverse problems for the eversion of a spherical shell

Motivated by an interest in material parameter determination for a structure with residual stresses, we revisit the classical eversion problem of a spherical shell, as studied by Ericksen, 1955 and more recently Johnson and Hoger, 1993. The spherical shell is made of an isotropic, incompressible, hyperelastic, Mooney-Rivlin material. In the direct problem, we examine the dependence of the elasticity tensor coefficients on residual and initial stresses and represent it for three numerical cases. In the inverse problem, we analyse the effect of measurement uncertainties on the determined values of material parameters and we suggest an experimental protocol that allows for a robust recovery of these parameters.