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Effects of Poisson's ratio on the deformation of thin membrane structures under indentation

Deformation/deflection of thin shells/membranes with clamped boundaries is a common material behaviour relevant to many engineering and medical conditions. A detailed understanding of the deformation mechanisms of different materials/structures with different Poisson's ratios under such a loading condition is of great significance to materials testing and product development. In this work, the deformation of circular elastic membranes with a clamped edge under point loading and finite contact conditions is systematically studied incorporating auxeticity behaviours. The effect of Poisson's ratio on the deformation of the material is investigated and the influence of parameters including sample thickness, indentation depth and indenter size is analysed. The feasibility and limitation of an analytical solution is evaluated. The work shows that the P/δ3 relationship is applicable to describe the force–displacement data over the membrane domain for both point loading and finite contact conditions. It is shown that negative Poisson's ratios have direct influence on the membrane deformation domain, including the force–displacement curve, the deflection profile and the contact area. Critical factors affecting the P–h curves and the deformation mechanisms are discussed with reference to potential use of the Poisson's ratio effects.