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Subsubsection 4.1.2.6: Holzapfel-Gasser-Ogden Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.8: Muscle Material

#### 4.1.2.7 Mooney-Rivlin

The material type for uncoupled Mooney-Rivlin materials is Mooney-Rivlin. The following material parameters must be defined:
 Coefficient of first invariant term [P] Coefficient of second invariant term [P] Bulk modulus [P]
This material model is a hyperelastic Mooney-Rivlin type with uncoupled deviatoric and volumetric behavior. The strain-energy function is given by: and are the Mooney-Rivlin material coefficients. The variables and are the first and second invariants of the deviatoric right Cauchy-Green deformation tensor . The coefficient is a bulk modulus-like penalty parameter and is the determinant of the deformation gradient tensor. When , this model reduces to an uncoupled version of the neo-Hookean constitutive model.
This material model uses a three-field element formulation, interpolating displacements as linear field variables and pressure and volume ratio as piecewise constant on each element [48].
This material model is useful for modeling certain types of isotropic materials that exhibit some limited compressibility, i.e. 100 < (/ < 10000.
Example:
<material id="2" type="Mooney-Rivlin">
<c1>10.0</c1>
<c2>20.0</c2>
<k>1000</k>
</material>


Subsubsection 4.1.2.6: Holzapfel-Gasser-Ogden Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.8: Muscle Material