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

Within its application in the seat development process the question arose as to the
implementation of muscle forces caused by pedal operations influencing the seat
pressure distribution. As a first approach 2 the model was enhanced by a detailed
continuums model superimposed with discrete elements representing the muscle action
of the lower extremities (see figure 1).
The investigation showed that influences of the muscle activation on the global human
body behavior could be realized. However, local effects as e.g. tissue stiffening due to
muscle activation, as essential for the desired detailed analysis, were not captured so far,
as the direct link between both model parts is missing. Consequently the next step is the
development and implementation of an active and passive coupled modeling approach.
This paper presents the first step of an investigation on an isolated muscle. Thereby the
analysis with contracting muscle pre-loaded in cross-fiber direction +represents a real
driver scenario using thigh muscles for pedal operations. Finally an outlook on the
implementation of this approach in CASIMIR is given.
3. MODEL SETUP
Although in the last years methods 3 for combining active and passive behavior by one
continuum approach were presented, a realization by two modeled parts is here
preferred. This is due to a simpler final implementation in a detailed buttock model of
CASIMIR.
In the investigated setup of an isolated muscle the volumetric part is modeled via
tetrahedrons and the muscle fibers are represented by spring elements. The coupling is
defined via an Embedded Element Formulation with the FE-solver ABAQUS 4 internally
generating kinematic couplings.
Compared to a direct merging of the element nodes presented by Hedestierna 5 , this
procedure has the advantage that the two meshes are independent from each other and
that tetrahedrons can be used. Accordingly the volumetric mesh must not follow the
orientation of the muscle fibers. This simplifies the meshing process of complex muscle
geometries as automatic mesh generators are applicable.
3.1 Passive Material Properties
Before modeling the isolated muscle the material properties have to be defined. First the
passive properties of the volumetric part are reviewed. In the current setup of CASIMIR
a hyperelastic, incompressible and isotropic behavior following the material model of
Mooney-Rivlin is implemented. Regarding the setup of a detailed approach this must be
enhanced to represent the anisotropic behavior of muscle tissue. For implementation in
ABAQUS the generalized Fung 6 strain energy potential U, see Equation 1, is used:
c 1 J 1
Q
el
U e 1 lnJ
2 D
2
(Eq. 1)
Within the formula the shear and the compression behavior are represented by the
variables c and D. J el is the elastic volume ratio. The anisotropy comes into account by
the fourth order tensor Q, which combines all parts of the modified Green strain tensor
by dimensionless material constants.
For identifying the free parameters experimental data of compression tissue tests by Van
Loocke 7 are employed. The tests have been carried out on several porcine fresh samples
in fiber (F) and cross fiber (XF) direction. The material parameters are computed using
an optimization algorithm defined in Matlab. As optimization criteria the nonlinear
behavior in the tested directions and the incompressibility of the tissue are assumed. As
2
el