## Chapter 5: Elasticity / Hyperelasticity

### Contents

5.1 Introduction
5.2 Linear Elasticity
5.3 Isotropic Hyperelasticity
5.4 Summary of Predictive Capabilities of Isotropic Hyperelastaic Model
5.5 Anisotropic Hyperelasticity
5.6 Hyperelastic Foam Models
5.7 Mullins Effect Models
5.8 Use of Hyperelasticity in Polymer Modeling
5.9 Hyperelastic Code Examples
5.10 Exercises

### Errors in the Text

• Page 222, Equation 5.40: The first term on the right-hand side should start with 2/J, not J/2 as written.
• Page 223, Equation 5.44: The second term on the right-hand side should contain $$\lambda^4$$, not $$\lambda^2$$ as written.
• Page 224, Equation 5.55: Most of the time this equation is less useful than directly applying Equation 5.52.
• Page 225, on the middle of the page it says: “and $$\lambda = 2$$”, which should be “and $$\lambda = \sqrt{2}$$”.
• Page 225, Equation 5.58, the number 2 should be $$\sqrt{2}$$.
• Page 253, Equation 5.113, the left-hand-side of the equation should be $$\mathcal{L}^{-1}(x)$$.
• Page 253, Equation 5.114, the left-hand-side of the equation should be $$\mathcal{L}^{-1}(x)$$.
• Page 263, Equation 5.125, the equation should be:
$$\sigma_{planar} = \displaystyle\mu \left( \lambda^2 – \frac{1}{\lambda^2}\right) \frac{J_m}{J_m-(\lambda^2 + 1/\lambda^2 – 2)}$$
• Page 263, Equation 5.126, the equation should be:
$$\sigma_{biax} = \displaystyle\mu \left( \lambda^2 – \frac{1}{\lambda^4}\right) \frac{J_m}{J_m-(2\lambda^2 + 1/\lambda^4 – 3)}$$

Send me a message if you have found any other errors.