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Subsubsection 4.1.2.7: Mooney-Rivlin Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.9: Ogden

#### 4.1.2.8 Muscle Material

This material model implements the constitutive model developed by Silvia S. Blemker [18]. The material type for the muscle material is muscle material. The model is designed to simulate the passive and active material behavior of skeletal muscle. It defines the following parameters:
 along fiber shear modulus [P] cross fiber shear modulus [P] exponential stress coefficients [P] fiber uncrimping factor [ ] optimal fiber length [ ] maximum isometric stress [P] fiber stretch for straightened fibers [ ] bulk modulus [P] activation level
The main difference between this material formulation compared to other transversely hyperelastic materials is that it is formulated using a set of new invariants, originally due to Criscione [23], instead of the usual five invariants proposed by A.J.M. Spencer [52]. For this particular material, only two of the five Criscione invariants are used. The strain energy function is defined as follows: The function is the strain energy contribution of the muscle fibers. It is defined as follows: where, and The values and are determined by requiring and continuity at .
The parameter is the activation level and can be specified using the active_contraction element. You can specify a loadcurve using the lc attribute. The value is interpreted as a scale factor when a loadcurve is defined or as the constant activation level when no loadcurve is defined.
The muscle fiber direction is specified similarly to the transversely isotropic Mooney-Rivlin model.
Example:
<material id="1" type="muscle material">
<g1>500</g1>
<g2>500</g2>
<p1>0.05</p1>
<p2>6.6</p2>
<smax>3e5</smax>
<Lofl>1.07</Lofl>
<lambda>1.4</lambda>
<k>1e6</k>
<fiber type="vector">1,0,0</fiber>
</material>


Subsubsection 4.1.2.7: Mooney-Rivlin Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.9: Ogden