The Mooney-Rivlin (MR) model for incompressible hyperelastic material as well as its extended version proposed by Kawamura, Urayama, Kohjiya in 2001 can be shown not to be in agreement with the Landau theorem about expansion of a scalar function of a symmetric positive definite tensor of 2nd rank with respect to the tensor invariants. The theorem states that expansion of the scalar function up to some power of the tensor elements has to include all terms of the same power. However, this is not what the models look like. E.g., the MR model accounts for I1 and I2 invariants of the Finger tensor, but misses the I1^2 term. Similarly, the extended version includes I2^2 term, but doesn't include I1^3. Having fixed that, one can find the one-to-one correspondence between the model coefficients C1, C2 [ also, C3-5 for the extended version ] with the Lame moduli [ and the Murnaghan moduli ] . Partially, the result is C1 = -2 * C2 = mu, where mu is the shear modulus. This means that the MR model is a particular case of the linear elasticity theory, whereas its extended version is a particular case of the general non-linear elasticity theory. Question: does this mean that the MR model is less trustworthy than the linear elasticity theory and does not capture nonlinear effect already bc of this circumstance?
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