Determination of Poisson's ratio by spherical indentation using neural networks - Part I: Theory

When studying analytically the penetration of an indenter of revolution int o 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, whil e the value of v is usually assumed. However as shown in the paper if plast ic deformation is involved during lending, the depth-load trajectory depend s 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 mod el exhibiting linear isotropic hardening, that the Poisson ratio can be det ermined uniquely from spherical indentation if the onset of plastic yield i s known. To this end a loading and at least two unloadings in the plastic r egime have to be considered. Using finite element simulations, the relation between the material parameters and the quantities characterizing the dept h-load response is calculated pointwise. An approximate inverse function re presented by a neural network is derived on the basis of these data.