June 2014
Intermediate to advanced
502 pages
17h 39m
English
Content preview from Biomaterials for Bone Regeneration
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278 Biomaterials for Bone Regeneration
In terms of stretch and Cauchy stress, we have
TR
UR
I
=+
R
UR
2
μ
q
p
qT
R
R
[9.18]
The response to a uniaxial test is, accordingly,
σ
μ
λλ
=
λ
(
)
2
2
q
q
λλ
λ
λ
λ
−
/
[9.19]
4. Logarithmic strain (one invariant, two parameters)
Finally, we propose here a phenomenological model based on loga-
rithmic strain ε = ln( U ). On account of incompressibility, the rst invari-
ant of this strain is zero ( I
1
= tr( ε ) = ln( J )). The second invariant is simply
I
2
2
12
=
−
(
)
/t
2
r
ε
.We assume the free energy in the form:
F
q
qI
=−
(
)
2
2
μ
exp
[9.20]
The conjugate stress of ε is, in this case, the rotated Cauchy stress ...