Yeoh hyperelastic model

The Yeoh hyperelastic material model[1] is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber.

The model is based on Ronald Rivlin's observation that the elastic properties of rubber may be described using a strain energy density function which is a power series in the strain invariants

of the Cauchy-Green deformation tensors.

[2] The Yeoh model for incompressible rubber is a function only of

For compressible rubbers, a dependence on

Since a polynomial form of the strain energy density function is used but all the three invariants of the left Cauchy-Green deformation tensor are not, the Yeoh model is also called the reduced polynomial model.

The original model proposed by Yeoh had a cubic form with only

dependence and is applicable to purely incompressible materials.

The strain energy density for this model is written as where

can be interpreted as the initial shear modulus.

Today a slightly more generalized version of the Yeoh model is used.

For consistency with linear elasticity the Yeoh model has to satisfy the condition where

is the shear modulus of the material.

, Therefore, the consistency condition for the Yeoh model is The Cauchy stress for the incompressible Yeoh model is given by For uniaxial extension in the

Therefore, The left Cauchy-Green deformation tensor can then be expressed as If the directions of the principal stretches are oriented with the coordinate basis vectors, we have Since

The engineering stress is For equibiaxial extension in the

Therefore, The left Cauchy-Green deformation tensor can then be expressed as If the directions of the principal stretches are oriented with the coordinate basis vectors, we have Since

The engineering stress is Planar extension tests are carried out on thin specimens which are constrained from deforming in one direction.

direction constrained, the principal stretches are

Therefore, The left Cauchy-Green deformation tensor can then be expressed as If the directions of the principal stretches are oriented with the coordinate basis vectors, we have Since

The engineering stress is A version of the Yeoh model that includes

dependence is used for compressible rubbers.

The strain energy density function for this model is written as where

is interpreted as half the initial shear modulus, while

is interpreted as half the initial bulk modulus.

the compressible Yeoh model reduces to the neo-Hookean model for incompressible materials.

The model is named after Oon Hock Yeoh.

Yeoh completed his doctoral studies under Graham Lake at the University of London.

[4] Yeoh held research positions at Freudenberg-NOK, MRPRA (England), Rubber Research Institute of Malaysia (Malaysia), University of Akron, GenCorp Research, and Lord Corporation.

[5] Yeoh won the 2004 Melvin Mooney Distinguished Technology Award from the ACS Rubber Division.