Strain

• Deformation gradient \(F\) describe both
• • - Rigid transformation (rotation) - not related to material effort
  • - Any other deformation inducing local length change - related to material effort

• Strain \(\epsilon\) is a measure of deformation ignoring rigid transformation.

• Several possible measure of strain
• • - Green strain tensor \(\epsilon=\frac{1}{2}\,(F\,F^T-\mathrm{Id})\)
  • • (+) If \(\varphi\) is a rotation \(F=R\) \(\Rightarrow\) \(\epsilon=0\)
    • (-) Non linear in \(p\)

• • - Linearized Cauchy strain \(\epsilon=\frac{1}{2} (F^T+F)-\mathrm{Id}\)
  • • Used for small deformations