summary17 - d 2.2 Surface normal / surface area change n r...

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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 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 = L 2 E + 1 1 relative length variation in the -direction L 0, 2.4 Angle change sin , = 2 E (1 + )(1 + )...
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