In this study we show that the nonlinear von Kármán theory may serve as an appropriate tool to calculate the stress distributions as functions of the external load, while the Kirchhoff theory has turned out to be completely inappropriate. Our main focus is devoted to (i) calculation of the contact area between the load sphere and the wafer, (ii) study of the influence of the anisotropic character of the material, (iii) study of the important geometric nonlinearity. Finally we compare the calculated and theoretical load–flexure relations in order to demonstrate the high accuracy of the von Kármán theory and its finite element implementation.
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