Theory Manual Version 3.4
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Section 5.3: Nearly-Incompressible Materials Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.2: Ogden Hyperelastic

### 5.3.1 Mooney-Rivlin Hyperelasticity

This material model is a hyperelastic Mooney-Rivlin type with uncoupled deviatoric and volumetric behavior. The uncoupled strain energy W is given by: Here, and are the Mooney-Rivlin material coefficients, and are the invariants of the deviatoric part of the right Cauchy-Green deformation tensor, , where , is the deformation gradient and is the Jacobian of the deformation. When , this model reduces to an uncoupled version of the incompressible neo-Hookean constitutive model.
The Cauchy stress is given by The spatial elasticity tensor is given by where, This material model uses a three-field element formulation, interpolating displacements as linear field variables and pressure and volume ratio as piecewise constant in each element [67].
Section 5.3: Nearly-Incompressible Materials Up Section 5.3: Nearly-Incompressible Materials Subsection 5.3.2: Ogden Hyperelastic