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/(1 - 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 lending, the depth-load trajectory depends on the reduced modulus and, additionally on the Poisson ratio explicitly. The aim of the paper is to show, 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.