Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

Most of engineering and biological thin shell structures are characterized by non-axisymmetric and statically indeterminate configurations, which often require the knowledge of the constitutive material model to determine the stress state. In this work, a forward elastostatic method is introduced for the direct stress measurements in elastic homogeneous thin shells of arbitrary shape. The stress distribution is proven to be independent of the material properties for incompressible solids, while in compressible materials it depends only on the Poisson’s ratio, which is shown to have a negligible influence on the stress state. Hence, the proposed technique enables the direct assessment of the stress field in statically indeterminate thin shells without a known material model. The shell formulation is implemented using the finite difference method to independently measure the stresses during finite inflation of planar elliptical membranes and from the deformed shapes obtained through digital image correlation during bulge tests on a hyperelastic material, showing very good agreement with finite-element predictions and the applicability of the method to nonlinear elastic materials. Therefore, the procedure can be coupled with imaging techniques for the direct assessment of stresses in thin shell structures and in the identification of material parameters through non-axisymmetric bulge tests.