Elasticity/Principal strains

The principal values (eigenvalues) ${\epsilon }_1,{\epsilon }_2,{\epsilon }_3$ of a strain tensor $\mathit{\epsilon }$ are called the principal strains.

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

$\mathit{\epsilon }=\sum _{i=1}^3{\epsilon }_i{𝐧}_i\otimes {𝐧}_i$

is called the spectral decomposition of $\mathit{\epsilon }$.

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Introduction to Elasticity