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5.2.5 Ogden Unconstrained
The Ogden unconstrained material is defined using the following hyperelastic strain energy function: Here, are the principal stretches and , and are material parameters.
The Cauchy stress tensor for this material may be obtained using the general formula for isotropic elasticity in principal directions given in (2.4.2-7), with Similarly, the spatial elasticity tensor is given by where and are the eigenvectors of . In the limit when eigenvalues coincide, In the reference configuration the elasticity tensor reduces to which has the form of Hooke's law for infinitesimal isotropic elasticity (see Section 5.1↑), with equivalent Lamé coefficients and .