COMPUTATIONAL MODELING OF INDENTATION - Nanoindentation with Biological Applications - page 168

S E

and , (6-17) = g , n

(2)

hE σ

R

2

14

1000 1000 1000 1000

12

800 800 800 800

10

600 600

600 600

8

Line: input data
Symbol: result from
reverse analysis of
improved spherical
indent a tion

Line: input data
Symbol: result from
reverse analysis of
improved spherical
indentation

Line: input data Line: input data

400 400 400 400

6

200 200

4

200 200

Indenter radius: 1.6mm
max / R = 0.3

In denter radius: 1. 6mm
δ max /R = 0.3

2

0 0 0 0

0.00 0.00 0.05 0.05 0.10 0.10 0.15 0.15

0.00 0.00 0.05 0.05 0.10 0.10 0.15 0.15

0

Uniaxial strain, ε Uniaxial strain, ε

Uniaxial strain, ε Uniaxial strain, ε

0.0 0.1 0.2 0.3 0.4 0.5

Indentation depth (mm)

Figure 6-8. The P h curves of spherical indentation on the mystical materials found in

Fig. 6-7a (solid curve for material #1 and dash curve for material #2). The deep spherical
indentation method 70 can distinguish the mystical materials - in the figure on the left, the
uniaxial

−

curves obtained from reverse analysis (symbols) is compared with the
input (true) data, and show excellent agreement.

σ − ε

where P is measured at 1 /

hR = 0.13

during loading,

P is measured at

maximum penetration of the experiment, 2 /

= = , and S is the
contact stiffness, measured from unloading at h 2 . The representative
stresses

hRh r / .3

m

and are related with the representative strains, and σ

(1)
R

σ

(2)
R

ε

(1)
R

, respectively, whose functional form and values can be determined
from numerical analyses in a way that is similar for sharp indentation
test. 70 The functions 6-15 to 6-17 are calibrated from extensive numerical
forward analysis; next, during the reverse analysis once P , P , and S
are measured from an indentation test, their values will be substituted
into Eqs. 6-15 to 6-17 , and the set of candidate material properties which
could minimize the total error of the three equations is the identified
material. During this course, special attention needs to be paid to the
identification of global minimum and to avoid local minima, this can be
accomplished via an iteration process: first, the potential material
elastoplastic properties are varied in a large range, from which several
candidate materials who could lead to small total error of Eqs. 6-15 to
6-17 are identified. Next, from the established forward analyses, the

(2)
R

ε