Examples of Hyperelastic Strain Energy Density Functions - Lesson 4

In this video, the discussion will continue with examples of hyperelastic strain energy functions. The example first discussed is the elastic strain energy function for non-linear elasticity. It is the St. Venant – Kirchhoff model. It depends upon Lame’s parameters which can be written in terms of Young’s Modulus and Poisson’s ratio which are more familiar terms in linear elasticity. It is discussed that the strain energy function should satisfy the requirement of frame invariance. Stress derivation is shown. The stress-strain relation is linear, but the strain is non-linear in the displacement gradient.

The previous discussion continues and the partial derivative of stress with respect to strain is evaluated which will give the elasticity parameter or the material elasticity tensor. It is a fourth-order tensor. The major and minor symmetry of this tensor is discussed. The elasticity for St. Venant- Kirchhoff model is positive definite.

Response to a Question

In this lesson the response is provided to the following question:

  • Is there a reason that this particular form of the St. Venant Kirchhoff model was chosen?