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

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

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The overall dimensions 10 of the muscle are: length: 24 mm, volume 928 mm³. As shown<br />

in figure 4 the modeling is carried out by tetrahedrons (initial length 1.0 mm). The<br />

fibers are represented by spring elements which are concentrically arranged in rows of 8<br />

lines. Considering a continuous coupling each line consists of several elements in series<br />

(length 1.5 mm).<br />

Indenter<br />

Movement<br />

(a) (b) (c)<br />

Fig. 4: Experimental setup, complete model setup and cross section<br />

4. SIMULATION AND RESULTS<br />

Outer row<br />

lines<br />

The simulation procedure corresponds to the real measurements. By using the<br />

ABAQUS explicit solver geometrical and material nonlinearities are considered. The<br />

several modeling parts are connected to each other by a general contact definition using<br />

a penalty formulation. Friction is assumed with a coefficient of 0.2.<br />

In a first test the passive tension behavior is neglected. Thereby instabilities occur while<br />

contracting the muscle, see figure 5. Background is the influence of the local strain resp.<br />

differences of local strain states of the discrete elements. This effect is reduced by the<br />

passive behavior, but still exists.<br />

Fig. 5: Instabilities while muscle contraction due to local strain influence<br />

In order to solve this problem a global control of the influence of the fiber length on the<br />

activated force is introduced. It is implemented by a sensor, measuring the average<br />

strain of the muscle as feedback of the simulation. Finally the force-displacement curves<br />

of all discrete elements are controlled globally by this value. An additional benefit is<br />

that the discrete element length has no influence on the muscle force, i.e. it can be<br />

chosen arbitrarily.<br />

The evaluation of the simulation is carried out by the measured muscle force and the lift<br />

up of the indenter (see figure 4). In figure 6 the results of the simulation are compared to<br />

the measurements. Regarding the indenter stroke there is a qualitative correlation<br />

between simulation and measurement. With a quantitative comparison of the results,<br />

however, the computation seems to be less sensitive. Similar effects are observed for the<br />

muscle force.

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