Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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5<br />
Objective<br />
Linear<br />
Ferromagnets<br />
Non-linear<br />
properties<br />
Electric.<br />
Conduct.<br />
Tensors<br />
Elasticity<br />
Symmetry<br />
Elastic Anisotropy: 1<br />
• First we restate the linear elastic relations for<br />
the properties Compliance, written S, <strong>and</strong><br />
Stiffness, written C (!), which connect stress, σ<br />
, <strong>and</strong> strain, ε. We write it first in vector-tensor<br />
notation with “:” signifying inner product (i.e.<br />
add up terms that have a common suffix or<br />
index in them):<br />
σ = C:ε<br />
ε = S:σ<br />
• In component form (with suffixes),<br />
σ ij = C ijkl ε kl<br />
ε ij = S ijkl σ kl