Strain tensor

Summary

A strain tensor measures how a deformation changes lengths and angles near each point, ignoring rigid motion. In the theory of small deformations it is the symmetric part of the displacement gradient, $\varepsilon = \tfrac12 (\nabla u + (\nabla u)^T)$. Its diagonal entries are relative changes of length along the axes, and its off-diagonal entries are half the changes of right angles.