ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

t
1 ⎧⎪ ⎫
2 2
⎪
ττττ ( t) : = ⎨J − 1+ κ ( t′ ) ⎡J ( t − t′ ) − 1⎤dt′
⎬ +
D ∫ ⎣ ⎦
I
⎪ ⎪
⎩ t′=
0
⎭
t
2 ⎧⎪ ⎡ 1
−1
⎤ ⎫⎪
+ ⎨ γ ( t′ ) Φ ( t − t′ ) tr ( t) − Ψ ( t − t′ ) ( t − t′ ) dt′
3 ∫
⎢
B C ⎬
3
⎥
I
1
⎪⎩ t′=
0
⎣ ⎦ ⎪⎭
t t
⎡ ⎤ 2
−1
+ 2 ⎢Φ 1 ( t) + ∫ γ ( t′ ) Φ1 ( t − t′ ) dt′ ⎥ B ( t) − γ ( t′ ) 1 ( t t′ ) ( t t′ ) ( t t′ ) dt′
3 ∫ Φ − Ψ − C − .
⎢⎣ t′ = 0 ⎥⎦
t′
= 0
In (7) the definitions hold
k2 k
BI
3
1 9
1 c1 B 3 e
9
( I )
( ) 2
−
⎡ ⎤
⎣
C B
⎦
(8)
−1
Φ ≡ + − and Ψ ( t − t′ ) ≡ tr ( t − t′ ) ⋅ ( t)
T -2/3
where B : = F ⋅ F ≡ J B is the left deviatoric CAUCHY strain tensor with its first
invariant B := trB
.
I
5. PARAMETER ESTIMATION AND VERIFICATION
Long-term elastic material parameters, as well as Prony series parameters, were
established for gluteal adipose and passive, transversally loaded muscle tissue, Table-1
and Table-2.
Table 1
Established material parameters representing long-term gluteal skin/fat tissue and passive
muscle tissue behaviour
c 1[MPa]
D [M -1 Pa -1 ] 1 k [MPa] 2
skin/ fat 9.27942E-004 2.78050E+000 6.56340E-009 1.50920E+002 1/3
(passive) muscle 4.40712E-004 2.58623E+001 1.30769E-002 4.68772E+001 1/3
k [-] κ [-]
Table 2
Established Prony series material parameters representing transient gluteal skin/fat and passive
skeletal muscle tissue behaviour
skin/ fat (passive) muscle
i i g [-] i k [-] i g [-] i k [-] τ i [s]
1 1.33240411e-002 1.32003205e-002 7.67035335e-001 1.16768944e-002 2.0
2 3.64287819e-003 3.24971069e-004 6.44394623e-002 2.29042100e-004 40.0
3 3.85165666e-004 5.60416576e-004 6.08481439e-004 3.73646787e-004 80.0
4 1.59997251e-002 1.89029712e-005 2.17789168e-002 1.28511319e-005 200.0
Verification of the approach was done by simulating the indentation test scenarios at 10,
20, 30 and 40 mm ramp displacement. The simulated indenter force-time data was then
compared to the test data, Figure-1b.
6. FE MODELLING AND BODY-SUPPORT INTERACTION SIMULATION
Based on MRI data, anatomically adequate FE buttock models were generated in the
recumbent and seated position. These included unloaded buttocks in the supine and
seated position. To insure unloaded buttocks in the seated position, the subject was
(7)