Microstructure-Properties - Materials Science and Engineering

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6 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Elastic Anisotropy: 2 The definitions of the stress <strong>and</strong> strain tensors mean that they are both symmetric (second rank) tensors. Therefore we can see that ε 23 = S 2311 σ 11 ε 32 = S 3211 σ 11 = ε 23 which means that, S 2311 = S 3211 <strong>and</strong> in general, S ijkl = S jikl We will see later on that this reduces considerably the number of different coefficients needed.
7 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Stiffness in sample coords. • Consider how to express the elastic properties of a single crystal in the sample coordinates. In this case we need to rotate the (4 th rank) tensor from crystal coordinates to sample coordinates using the orientation (matrix), a (see lecture A): c ijkl ' = a im a jn a ko a lp c mnop • Note how the transformation matrix appears four times because we are transforming a 4th rank tensor! • The axis transformation matrix, a, is also written as λ.
Page 1 and 2: 1 Objective Linear Ferromagnets Non
Page 5: 5 Objective Linear Ferromagnets Non
Page 11 and 12: 11 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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