Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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18<br />
Effect of symmetry on stiffness matrix<br />
Objective<br />
Linear<br />
Ferromagnets<br />
Non-linear<br />
properties<br />
Electric.<br />
Conduct.<br />
Tensors<br />
Elasticity<br />
Symmetry<br />
• Following Reid, p.66 et seq.:<br />
Apply a 90° rotation about the crystal-z axis<br />
(axis 3),<br />
C’ ijkl = O im O jn O ko O lp C mnop :<br />
C’ = C<br />
C ! =<br />
#<br />
%<br />
%<br />
%<br />
%<br />
%<br />
%<br />
%<br />
%<br />
$ %<br />
O 4 z =<br />
C 22 C 21 C 23 C 25 "C 24 "C 26<br />
C 21 C 11 C 13 C 15 "C 14 "C 16<br />
C 23 C 13 C 33 C 35 "C 34 "C 36<br />
C 25 C 15 C 35 C 55 "C 54 "C 56<br />
"C 24 "C 14 "C 34 "C 54 C 44 C 46<br />
"C 26 "C 16 "C 36 "C 56 C 46 C 66<br />
" 0 !1 0%<br />
$ '<br />
$ 1 0 0'<br />
$ '<br />
# 0 0 1&<br />
&<br />
(<br />
(<br />
(<br />
(<br />
(<br />
(<br />
(<br />
(<br />
' (
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