Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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23<br />
Objective<br />
Linear<br />
Ferromagnets<br />
Non-linear<br />
properties<br />
Electric.<br />
Conduct.<br />
Tensors<br />
Elasticity<br />
Symmetry<br />
Rotated compliance (matrix)<br />
• Given an orientation a ij , we transform the<br />
compliance tensor, using cubic point group<br />
symmetry, <strong>and</strong> find that:<br />
S 1! 1 = S1 1 a1 1<br />
( 4 4 4<br />
+ a1<br />
2 + ) a1<br />
3<br />
+ 2S 1 2 a 1 2<br />
( 2 2 2 2 2 2<br />
a1 3 + a1 1a1<br />
2 + ) a1 1a1<br />
3<br />
( )<br />
2 2 2 2 2 2<br />
+ S4 4 a1 2a1<br />
3 + a1 1a1<br />
2 + a1 1a1<br />
3