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Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks—Part I: Theory

When studying analytically the penetration of an indenter of revolution into an elastic half-space use is commonly made of the fraction E r =E/(I - v 2 ). Because of this, only E r is determined from the indentation test, while the value of v is usually assumed. However, as shown in the paper, if plastic deformation is involved during Ioading, the depth-load trajectory depends on the reduced modulus and, additionally, on the Poisson ratio explicitly. The aim of the paper is to shown, with reference to a simple plasticity model exhibiting linear isotropic hardening, that the Poisson ratio can be determined uniquely from spherical indentation if the onset of plastic yield is known. To this end, a loading and at least two unloadings in the plastic regime have to be considered. Using finite element simulations, the relation between the material parameters and the quantities characterizing the depth-load response is calculated pointwise. An approximate inverse function represented by a neural network is derived on the basis of these data.