# Advanced elasticity/Mooney-Rivlin material

A **Mooney-Rivlin solid** is a generalization of the w:Neo-Hookean solid model, where the strain energy **W** is a linear combination of two invariants of the w:Finger tensor :

- ,

where and are the first and the second invariant of w:deviatoric component of the w:Finger tensor:^{[1]}

- ,

- ,

- ,

where: and are constants.

If (where G is the w:shear modulus) and , we obtain a w: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 w:Melvin Mooney and w:Ronald Rivlin in two independent papers in 1952.

## Uniaxial extension edit

For the case of uniaxial elongation, true stress can be calculated as:

and w:engineering stress can be calculated as:

The Mooney-Rivlin solid model usually fits experimental data better than w:Neo-Hookean solid does, but requires an additional empirical constant.

## Rubber edit

Elastic response of rubber-like materials are often modelled based on the Mooney-Rivlin model.

## Source edit

- C. W. Macosko
**Rheology: principles, measurement and applications**, VCH Publishers, 1994, ISBN 1-56081-579-5