What is the Mooney Rivlin equation?

In finite elasticity, the Mooney–Rivlin material model for the Cauchy stress tensor T in terms of the left Cauchy–Green strain tensor B is given by $$T = -pI + s_1 B + s_2 B^{-1},$$where p is the pressure and s 1, s 2 are two material constants.

What is Mooney Rivlin model?

In continuum mechanics, a Mooney–Rivlin solid is a hyperelastic material model where the strain energy density function is a linear combination of two invariants of the left Cauchy–Green deformation tensor. . The model was proposed by Melvin Mooney in 1940 and expressed in terms of invariants by Ronald Rivlin in 1948.

What is incompressibility parameter?

This test characterizes the compressibility and volumetric expansion of the material by measuring the change in volume of the test sample due to a change in pressure (or temperature). Therefore; 2 divided by the slope of this line gives the incompressibility parameter “d”.

Is rubber linear elastic?

For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic, incompressible and generally independent of strain rate.

How to determine Mooney Rivlin constants for silicon rubber?

But my case is different which deals with “non-linear silicone rubber material” which can be approximated as following 3 parameter Mooney-Rivlin graphical curve. @Sankar Menon: I really appreciate if you can provide me the Mooney-Rivlin constants of silicone rubber.

Can a Mooney Rivlin model give insight into material behavior?

It’s important to understand that Mooney-Rivlin models do not give any special insight into material behavior. They are merely curve-fits of various polynomials to test data.

How is strain energy expressed in Mooney Rivlin model?

The Mooney-Rivlin class of models express the strain energy in terms of invariants, which are in turn expressed as functions of stretch ratios. The invariants are of the product of the deformation gradient with its transpose, F ⋅ FT. This result is symmetric because the product of any matrix with its transpose is always symmetric.

How are the mechanical properties of rubber determined?

Normally there are defined by Young’s modulus, possion’s ratio and shear modulus. Properties of rubber is very difficult, because it is time function, you can find some suggestion from this textbook, ” An introduction to the mechanical properties of solid polymers”. The authors are I. M. Ward and D. W. Hadley.