EN0175-15

EN0175-15 - EN0175 10 24 06 Review of deformation tensors F...

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Unformatted text preview: EN0175 10 / 24 / 06 Review of deformation tensors: F , C , B , U , V , R , E , * E Given F , one can follow the following standard procedure to determine the other strain measures. 1) Most simply, F F C T = , T F F B = , ( ) I C E − = 2 1 , ( ) 1 * 2 1 − − = B I E 2) To fine U , V , R , we need to perform the eigenvalue analysis of C and B (diagonalization of matrices): III III III II II II I I I III II I m m m m m m C m m C v v v v v v v v ⊗ + ⊗ + ⊗ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⇒ = 2 2 2 2 2 2 2 λ λ λ λ λ λ λ III III III II II II I I I III II I n n n n n n B n n B v v v v v v v v ⊗ + ⊗ + ⊗ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⇒ = 2 2 2 2 2 2 2 λ λ λ λ λ λ λ 3) III III III II II II I I I m m m m m m U v v v v v v ⊗ + ⊗ + ⊗ = λ λ λ III III III II II II I I I n n n n n n V v v v v v v ⊗ + ⊗ + ⊗ = λ λ λ j i ij e U e U v v ⋅ = , j i ij e V e V v v ⋅ = ⇒ U and V 4) R V U R F = = F V U F R 1 1 − − = = Generalized Hooke’s law...
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

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EN0175-15 - EN0175 10 24 06 Review of deformation tensors F...

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