COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 152

during loading) n is between 0.0 ~ 0.5, E is between 0.01 ~ 600GPa, σ y
is between 1MPa ~ 2GPa, and E / σ y is between 1 ~ 5000. 44 Note that the

material deformation is not uniaxial during indentation, therefore, the
influence of the Poisson's ratio, ν , must be taken into account.

σ

σ R

σ y

E E

1 2

2 R ε

εε −

ε

2 R ε εε − 2 R

R

Figure 6-2. A schematic of the uniaxial true stress-strain curve ( σ − ε ) of a representative

power-law material, and the definitions of the representative strain ( ε R ) and representative

stress ( σ R ) used in this study.

σ y , n ) are needed to completely
characterize the constitutive properties of a power law stress-free
material. Probing these material parameters by indentation has in recent
years become a focal point of interest in the indentation literature and
various techniques were proposed, see the review by Cheng and Cheng. 1
In most cases, the relationship between characteristic shape factors of the
P - h curve and ( E , ν , σ y , n ) needs to be established from extensive
numerical analyses. Although indentation is a very broad and versatile
technique, in this review we only focus on the measurement of
constitutive properties.

Four independent parameters ( E , ν ,

2. Computational Method

The finite element method (FEM) is the primary tool of computational
indentation analysis. Commercial software such as ANSYS 45 or
ABAQUS 46 could effectively account for the nonlinear finite
deformation due to contact, and to establish relationships between