Large Plastic Deformations of Circular Membranes

An investigation is presented for the plastic behavior of clamped circular membranes subjected to hydrostatic pressure, based on the Hencky-Mises theory. New strain-displacement relations, valid for finite deformations in the plastic domain, are introduced. The solution is presented in terms of two simultaneous implicit integral equations, which can be solved by numerical methods. The solution also permits the formulation of the instability condition. Experimental work consisted of bulge tests carried out on annealed copper plates of two thicknesses, whose τ-γ curve was previously determined from uniaxial tests. A good correlation is obtained between theoretical predictions and experimental results.