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December 1st, 2014, 07:49 AM  #1 
Newbie Joined: Dec 2014 From: London Posts: 1 Thanks: 0  Proof that V/V0 = det(F)
I wish to prove in index notation that the change in volume expressed as a ratio is equal to the determinant of the deformation tensor, F. x1' = F x1 x2' = F x2 x3' = F x3 Original volume = V0 = x1 . (x2 x x3) = Ɛijk x1i x2j x3k Deformed volume = V = x1' . (x2' x x3') = Ɛlmn x1i x2j x3k Fli Fmj Fnk Which is as far as i've gotten so how does V/V0 = det(F) i.e., Ɛijk Fi1 Fj2 Fk3 Many thanks 