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:
U = PEP^(T) where P = matrix of eigenvectors of U, E = diag. matrix of eigenvalues of U
My uncertainty is what P & P^(T) represent physically.My ideas are as follows:
- a rigid rot'n of the basis vectors. By this, I mean that P rotates the basis vectors to align them with principal stretch directions, pure stretch occurs, & P^(T) rotates back.
- a pure shear but, if so, why both P & P^(T) ?
Any help / references would be great.
Thanks, John.