Cauchy–Green deformation tensor

Summary

The right Cauchy–Green deformation tensor is $C = F^T F$ and the left one is $b = F F^T$, where $F$ is the deformation gradient. They remove the rotation part of $F$ and keep only the stretching. The tensor $C$ gives the squared length of a deformed line element in terms of the undeformed one. They are symmetric and positive definite, and they equal the identity exactly when the deformation is locally rigid.