summary17 - d Ω 2.2 Surface normal surface area change n...

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Lecture 17 - summary Topic: How to describe deformation (cont’d from lecture 16) Goal is to develop a mathematical language to describe deformation Topics covered: 1.) Review and example – deformation gradient tensor (main tool) Deformation gradient: Deformation β ∆ x x y y β 0 0 () = 0 1 0 F ij 0 0 1 2.) Applications to: 2.1 Volume change J = d d = det F J = Jacobian
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Unformatted text preview: d Ω 2.2 Surface normal / surface area change n r da = J ( F T ) − 1 ⋅ N r dA r r r r L 2 d − L 2 = dX ⋅ ( F T F − 1 ) ⋅ dX = dX ⋅ 2 E ⋅ dX E = F T F − 1 Strain 2.3 Length change tensor λ α = ∆ L α 2 E αα + 1 − 1 relative length variation in the -direction L 0, 2.4 Angle change sin θ , β = 2 E αβ (1 + λ )(1 + λ )...
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This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

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