This document discusses hyperelastic constitutive models for incompressible isotropic materials. It presents the strain energy function for such materials and derives the second PK stress tensor and Cauchy stress tensor from it. It then focuses on the Humphrey hyperelastic material model, giving its strain energy function involving parameters c1 and c2, and showing how to derive the stresses. Finally, it notes this model was used to predict the stress-stretch behavior of porcine stomach tissue, optimizing parameters c1 and c2 to match experimental data.

1. Hyperelastic constitutive
model

2. Hyperelastic constitutive model
• The strain energy function for an ncompressibleisotropic hyperelastic
material can be written as:
where p is the hydrostatic pressure required to satisfy the
incompressibility condition.

3. Hyperelastic constitutive model
• The second PK stress tensor can then be derived as follows.

4. Hyperelastic constitutive model
• Using index notation, T can be written as

5. Hyperelastic constitutive model
• The Cauchy stress tensor can be derived as

6. Humphrey hyperelastic material
• The strain energy function for the material is
where c1 and c2 are the material parameters.
• The stresses can be written as

7. Result
Model predicted stress-stretch behaviour of a
porcine stomach tissue strip along with the
experimental data. The optimized parameters for
the Humphrey material are c1= 0.11 kPa and c2=
3.4.