Elasticity/Principal strains

The principal values (eigenvalues) $$\textstyle \varepsilon_1, \varepsilon_2, \varepsilon_3$$ of a strain tensor $$\textstyle \boldsymbol{\varepsilon}$$ are called the principal strains.

If the corresponding principal directions (eigenvectors) are $$\textstyle \mathbf{n}_1, \mathbf{n}_2, \mathbf{n}_3$$, then


 * $$ \boldsymbol{\varepsilon} = \sum^3_{i=1} \varepsilon_i ~

\mathbf{n}_i\otimes\mathbf{n}_i $$

is called the spectral decomposition of $$\textstyle \boldsymbol{\varepsilon}$$.

Related Content
Introduction to Elasticity