Finite inflation analysis of a hyperelastic toroidal membrane of initially circular cross-section

In this work, we have studied the finite inflation of a hyperelastic toroidal membrane with an initially circular cross-section under internal pressure. The membrane material is assumed to be a Mooney–Rivlin solid. The inflation problem is formulated as a variational problem for the total potential energy comprising the membrane strain energy and internal energy of the gas. The problem is then discretized and solved up to a high degree of accuracy through a sequence of approximations based on the Ritz expansion of the field variables combined with a potential energy density perturbation and Newton–Raphson method. The effects of the inflation pressure and material properties on the state of stretch and geometry of the inflated torus have been studied, and some interesting results have been obtained. The stability of the inflated configurations in terms of impending wrinkling of the membrane has been investigated on the principal stretch parameter plane for both isotropic and anisotropic (transversely isotropic) material cases. Certain shape factors quantifying the geometry of the membrane have been defined and calculated which characterize the cross-sectional shape and size of the torus during inflation.

► Finite inflation of a hyperelastic toroidal membrane is formulated as a variational problem. ► A Ritz method based numerical scheme for computing the inflated shapes is proposed. ► Effect of anisotropy on structural instability (impending wrinkling) is studied. ► Meridional/circumferential stretch is found to depend on curvature and leads to impending wrinkling. ► Localized anisotropy near the inner equator can help in delaying impending wrinkling.