In continuum mechanics
, a Mooney-Rivlin solid
is a generalization of the Neo-Hookean solid
model, where the strain energy W
is a linear combination of two invariants
of Finger tensor
where and are the first and the second invariant of deviatoric component of the Finger tensor:
and , , and are constants.
If (where G is the shear modulus) and , we obtain a Neo-Hookean solid, a special case of a Mooney-Rivlin solid.
The stress tensor depends upon Finger tensor by the following equation:
The model was proposed by Melvin Mooney and Ronald Rivlin in two independent papers in 1952.
For the case of uniaxial elongation, true stress can be calculated as:
and engineering stress can be calculated as:
The Mooney-Rivlin solid model usually fits experimental data better than Neo-Hookean solid does, but requires an additional empirical constant.
Elastic response of soft tissues like that in the brain is often modelled based on the Mooney--Rivlin model.
- C. W. Macosko Rheology: principles, measurement and applications, VCH Publishers, 1994, ISBN 1-56081-579-5
Notes and References