When studying analytically the penetration of an indenter of revolution into an elastic half-space use is commonly made of the fraction $Er=E/1−ν2.$ Because of this, only $Er$ is determined from the indentation test, while the value of ν is usually assumed. However, as shown in the paper, if plastic deformation is involved during loading, 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.

1.
Rossi
,
R. E.
, and
Laura
,
P. A. A.
,
1996
, “
On the Effect of Poisson Ratio and Certain Approximation Schemes on Transverse Vibration of Thin Rectangular Plates With a Free Edge
,”
J. Sound Vib.
,
194
, pp.
439
444
.
2.
Rossi
,
R. E.
, and
Laura
,
P. A. A.
,
1996
, “
Symmetric and Antisymmetric Normal Modes of a Cantilever Rectangular Plate: Effect of Poisson’s Ratio and a Concentrated Mass
,”
J. Sound Vib.
,
195
, pp.
142
148
.
3.
Laura
,
P. A. A.
,
Sonzogni
,
V.
, and
Romanelli
,
E.
,
1996
, “
Effect of Poisson’s Ratio on the Fundamental Frequency of Transverse Vibration and Buckling Load of Circular Plates With Variable Profile
,”
Appl. Acoust., Oxford
,
74
, pp.
263
274
.
4.
Evans
,
A. G.
, and
Hutchinson
,
J. W.
,
1984
, “
On the Mechanics of Delamination and Spalling in Compressed Films
,”
Int. J. Solids Struct.
,
20
, pp.
455
466
.
5.
Hardwick
,
D. A.
,
1987
, “
The Mechanical Properties of Thin Films: A Review
,”
Thin Solid Films
,
154
, pp.
109
124
.
6.
Hertz
,
H.
,
1882
, “
U¨ber die Beru¨hrung fester elastischer Ko¨rper
,”
J. Reine Angew. Math.
,
92
, pp.
156
171
.
7.
Love
,
A. E. H.
,
1939
, “
Boussinesq’s Problem for a Rigid Cone
,”
Quart. J. Math.
,
10
, pp.
161
175
.
8.
Harding
,
J. W.
, and
Sneddon
,
I. N.
,
1945
, “
The Elastic Stresses Produced by the Indentation of the Plane Surface of a Semi-Infinite Elastic Solid by a Rigid Punch
,”
Proc. Cambridge Philos. Soc.
,
43
, pp.
16
26
.
9.
Doerner
,
M. F.
, and
Nix
,
W. D.
,
1986
, “
A Method for Interpreting the Data From Depth-Sensing Indentation
,”
J. Mater. Res.
,
1
, pp.
601
609
.
10.
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
1992
, “
An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,”
J. Mater. Res.
,
7
, pp.
1564
1583
.
11.
Field
,
J. S.
, and
Swain
,
M. V.
,
1993
, “
A Simple Predictive Model for Spherical Indentation
,”
J. Mater. Res.
,
8
, pp.
297
306
.
12.
Taljat
,
B.
,
Haggag
,
F. M.
, and
Zacharia
,
T.
,
1997
, “
Analysis of Ball-Indentation Load-Depth Data: Part I. Determining Elastic Modulus
,”
J. Mater. Res.
,
12
, pp.
965
974
.
13.
Huber
,
N.
,
Munz
,
D.
, and
Tsakmakis
,
Ch.
,
1997
, “
Determination of Young’s Modulus by Spherical Indentation
,”
J. Mater. Res.
,
12
, pp.
2459
2469
.
14.
Olaf, 1992, “Ein Verfahren zui Bersertung des Mechanischen Verholtens von Ramischichten,” Ph.D. thesis, Albert-Ludwigs-Universita¨t Freiburg im Breisgau, Germany.
15.
Huber
,
N.
, and
Tsakmakis
,
Ch.
,
1999
, “
Determination of Constitutive Properties From Spherical Indentation Data Using Neural Networks, Part I: The Case of Pure Kinematic Hardening in Plasticity Laws
,”
J. Mech. Phys. Solids
,
47
, pp.
1569
1588
.
16.
Huber
,
N.
, and
Tsakmakis
,
Ch.
,
1999
, “
Determination of Constitutive Properties From Spherical Indentation Data Using Neural Networks, Part II: Plasticity With Nonlinear Isotropic and Kinematic Hardening
,”
J. Mech. Phys. Solids
,
47
, pp.
1589
1607
.
17.
Johnson, K. L., 1985, Contact Mechanics, Oxford University Press, Oxford, UK.
18.
Huber
,
N.
, and
Tsakmakis
,
Ch.
,
1998
, “
A Finite Element Analysis of the Effect of Hardening Rules on the Indentation Test
,”
J. Eng. Mater. Technol.
,
120
, pp.
143
148
.
19.
Hibbit, Karlsson, & Sorensen, 1996, ABAQUS theory, Version 5.6.
20.
Aifantis
,
E. C.
,
1987
, “
The physics of plastic deformation
,”
Int. J. Plasticity
,
3
, pp.
211
247
.
21.
Aifantis
,
E. C.
,
1995
, “
From Micro- to Macro-Plasticity: The Scale Invariance Approach
,”
J. Eng. Mater. Technol.
,
117
, pp.
352
355
.
22.
Yagawa
,
G.
, and
Okuda
,
H.
,
1996
, “
Neural Networks in Computational Mechanics
,”
Arch. Comput. Meth. Eng.
,
3
, pp.
435
512
.
23.
Sumpter
,
B. G.
, and
Noid
,
D. W.
,
1996
, “
On the Design, Analysis and Characterization of Materials Using Computational Neural Networks
,”
Annu. Rev. Mater. Sci.
,
26
, pp.
223
278
.
24.
SNNS, 1995, “SNNS Stuttgart Neural Network Simulator,” User Manual, Version 4.1. University of Stuttgart, Institute for Parallel and Distributed High Performance Systems (IPVR).
25.
Huber
,
N.
, and
Tsakmakis
,
Ch.
,
2001
, “
Determination of Poisson’s Ratio by Spherical Indentation Using Neural Networks. Part II: Identification method
,”
ASME J. Appl. Mech.
,
68
, pp.
224
229
.