Microstructure-Properties - Materials Science and Engineering

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30 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Supplemental Slides • The following slides contain some useful material for those who are not familiar with all the detailed mathematical methods of matrices, transformation of axes etc.
31 Objective Linear Ferromagnets Non-linear properties Electric. Conduct. Tensors Elasticity Symmetry Notation F Stimulus (field) R Response P Property j electric current E electric field D electric polarization ε Strain σ Stress (or conductivity) ρ Resistivity d piezoelectric tensor C elastic stiffness S elastic compliance a rotation matrix W work done (energy) I identity matrix O Y Young’s Young s modulus δ Kronecker delta e axis (unit) vector T tensor αα direction cosine symmetry operator (matrix)
Page 1 and 2: 1 Objective Linear Ferromagnets Non
Page 11 and 12: 11 Objective Linear Ferromagnets No
Page 17 and 18: 17 Effect of symmetry on stiffness
Page 29: 29 Objective Linear Ferromagnets No
Page 41: 41 Objective Linear Ferromagnets No

Microstructure-Properties - Materials Science and Engineering

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