MIT2_094S11_lec11

MIT2_094S11_lec11 - 2.094 Finite Element Analysis of Solids...

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Unformatted text preview: 2.094 Finite Element Analysis of Solids and Fluids Fall 08 Lecture 11- Deformation, strain and stress tensors Prof. K.J. Bathe MIT OpenCourseWare We stated that we use Reading: Ch. 6 t V t ij e ij d V t = V t S t V = t R (11.1) t ij ij d The deformation gradient We use t x i = x i + t u i t x 1 t x 1 t x 1 x 1 x 2 x 3 t x 2 t x 2 t x 2 t X (11.2) = x x x 1 2 3 x t 3 x t 3 x t 3 x 1 x 2 x 3 t d x 1 d t x (11.3) t d x = 2 t d x 3 d x 1 d x (11.4) (11.5) d x 2 d x 3 Implies that d t x = t X d x = ( t X is frequently denoted by t F or simply F , but we use F for force vector) We will also use the right Cauchy-Green deformation tensor t C t X T t X = (11.6) Some applications 45 MIT 2.094 11. Deformation, strain and stress tensors The stretch of a fiber ( t ): 2 t t t 2 d x T d x d s t = = (11.7) d x T d x...
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MIT2_094S11_lec11 - 2.094 Finite Element Analysis of Solids...

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