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

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

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

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Introduction to Elasticity