Elasticity/Principal strains

The principal values (eigenvalues) ${\displaystyle \textstyle \varepsilon _{1},\varepsilon _{2},\varepsilon _{3}}$ of a strain tensor ${\displaystyle \textstyle {\boldsymbol {\varepsilon }}}$ are called the principal strains.

If the corresponding principal directions (eigenvectors) are ${\displaystyle \textstyle \mathbf {n} _{1},\mathbf {n} _{2},\mathbf {n} _{3}}$, then

${\displaystyle {\boldsymbol {\varepsilon }}=\sum _{i=1}^{3}\varepsilon _{i}~\mathbf {n} _{i}\otimes \mathbf {n} _{i}}$

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

Introduction to Elasticity