Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
Microstructure-Properties - Materials Science and Engineering
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17<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 />
• Why do we need to look at the effect of symmetry?<br />
For a cubic material, only 3 independent coefficients<br />
are needed as opposed to the 81 coefficients in a 4th<br />
rank tensor. The reason for this is the symmetry of<br />
the material.<br />
• What does symmetry mean? Fundamentally, if you<br />
pick up a crystal, rotate [mirror] it <strong>and</strong> put it back<br />
down, then a symmetry operation [rotation, mirror] is<br />
such that you cannot tell that anything happened.<br />
• From a mathematical point of view, this means that<br />
the property (its coefficients) does not change. For<br />
example, if the symmetry operator changes the sign<br />
of a coefficient, then it must be equal to zero.
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