Finite strain elastoplastic bulging of circular diaphragms

The inflation of planar thin films represents a phenomenon widely employed by engineering and biological systems, with applications ranging from pressure sensors and material characterization to growing skins in the human body. In this paper, the bulging of plane circular membranes composed of isotropic elastoplastic materials is analytically, computationally and experimentally studied. An analytical finite strain formulation is developed and implemented to model the deformation response of inflated thin films. The solution accurately predicts the elastic and plastic phases of bilinear and nonlinear elastoplastic materials, for both small and large plastic strains. It shows that a sudden change in the full-field strain distribution during diaphragm inflation is associated with the plastic strain localization that first develops at the membrane apex. The results are compared with finite element simulations for a wide range of material parameters, showing an excellent agreement. The mathematical formulation is also validated by bulge tests performed on ETFE membranes, representative of a bilinear elastoplastic response, and aluminium foils that show a nonlinear plastic behaviour. The comparison between theoretical predictions and experimental measures proves the validity of the proposed model at small and large plastic strains, which promises to find applications in the modelling of the finite strain inflation of thin films, especially for the determination of elastoplastic material parameters through bulge testing.