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

presented in figure 2 the simulation correlates well with the experimental results. Small
deviations are only observed for higher load range in fiber direction.
S 11 [N/mm²]
6
5
4
3
2
1
x 10-4
0
0 0.1 0.2 0.3
E [-]
true
Fig. 2: Comparison of passive compression behavior in F (a) and XF (b)
Furthermore, the tensile properties have been investigated. In comparison with different
sources of experimental data an underestimate of the tensile behavior is found in the
simulation. Reflecting application scenarios of CASIMIR only tension in F due to
muscle activation is expected. As workaround these will be neglected for the volumetric
part and considered with the definition of the discrete spring elements.
3.2 Active Material Properties
For the discrete elements existing definitions of Blemker 8 are used which specify the
muscle force depending on the relative fiber length and on the level of activation.
Thereby the relative fiber length is defined by the quotient of the current to the initial
model state. Additionally, and as mentioned before, the passive tension behavior is also
considered, see figure 3. The implementation for the discrete spring elements is carried
out by nonlinear force-deflection curves. For this purpose the level of activation,
controlled by the nodal temperatures, is superimposed.
3.3 Model Setup
Measurement (F)
Simulation (F)
S 22 [N/mm²]
(a) (b)
F comb / F act @ l opt [-]
1
0.5
Combined Behaviour
Active Behaviour
Passive Behaviour
0 0.1 0.2 0.3
E [-]
true
Fig. 3: Nonlinear behavior of discrete model part
After defining each model part the coupling method using the Embedded Element
Formulation must be validated. Therefore we used experiments 9 with transversal
muscle loading performed on isolated rat M.gastrocnemius medialis. The measurement
consists of two steps: first the muscle is loaded transversally in XF by a rigid indenter
and then it is activated by an artificial stimulus, thereby performing an isometric
contraction at optimal muscle length (figure 3, l/lopt=1). Muscle force and lifting height
of the indenter are measured during the contraction. Considering the nonlinear tissue
behavior the indenter mass is varied (65, 115, 165, 215 and 265 g).
1
0.8
0.6
0.4
0.2
x 10-3
Measurement (XF)
Simulation (XF)
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
l / l [-]
opt