SVD

Hello !

I have been reading quite a bit about decomposing deformation gradients into F=RU = vR where R = rigid rot'n, U = right stretch & v = left stretch. Since the principle stretch axes & basis vectors don't usually coincide, such stretches produce both stretch & shear as shown in animation at link below.

A singular value decomposition of U (or v) can be used to isolate the pure stretches. In my case, U is postive semi-definite so SVD given by eigenvalue decompostion as follows: