Microstructure-Properties - Materials Science and Engineering

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10 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry “matrix notation”, contd. • Similarly for strain: " $ # ! 1 1 ! 1 2 ! 1 3 ! 2 1 ! 2 2 ! 2 3 ! 3 1 ! 3 2 ! 3 3 The particular definition of shear strain used in the reduced notation happens to correspond to that used in mechanical engineering such that ε 4 is the change in angle between direction 2 <strong>and</strong> direction 3 due to deformation. % ' & ( ) * " $ $ # ( * ) ( ! 1,! 2,! 3,! 4,! 5,! ) 6 ! 1 1 2 ! 6 1 2 ! 5 1 2 ! 6 ! 2 1 2 ! 4 1 2 ! 5 1 2 ! 4 ! 3 % ' ' &
11 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Work conjugacy, matrix inversion • The more important consideration is that the reason for the factors of two is so that work conjugacy is maintained. dW = σ:dε = σ ij : dε ij = σ k • dε k Also we can combine the expressions σ = Cε <strong>and</strong> ε = Sσ to give: σ = CSσ, which shows: I = CS, or, C = S -1
Page 1 and 2: 1 Objective Linear Ferromagnets Non
Page 9: 9 Objective Linear Ferromagnets Non
Page 13 and 14: 13 Objective Linear Ferromagnets No
Page 17 and 18: 17 Effect of symmetry on stiffness
Page 41: 41 Objective Linear Ferromagnets No

Microstructure-Properties - Materials Science and Engineering

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