Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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24<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 />
• This can be further simplified with the aid of the<br />
st<strong>and</strong>ard relations between the direction cosines,<br />
a ik a jk = 1 for i=j; a ik a jk = 0 for i≠j, (a ik a jk = δ ij ) to read as<br />
follows.<br />
s 1! 1 = s1 1 "<br />
2( s1 1 " s1 2 " 1<br />
2<br />
s ) 4 4 # 1<br />
{ 2 2 2 2 2 2<br />
#2 + # 2#3<br />
+ }<br />
#3#1<br />
• By definition, the Young’s modulus in any direction is<br />
given by the reciprocal of the compliance, E = 1/S’ 11.
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