Dynamic mechanical analysis: Difference between revisions

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:<math> \delta </math> is phase lag between stress and strain.
 
Consider the purely elastic case, where stress is proportional to strain given by [[Young's modulus]] <math>E</math> . We have <br>
<math>
\sigma(t) = E \epsilon(t)
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*Phase angle: <math> \delta = \arctan\frac {E''}{E'} </math>
 
Similarly, in the shearing instead of tension case, we also define [[Shear modulus|shear storage]] and loss moduli, <math>G'</math> and <math>G''</math>.
 
Complex variables can be used to express the moduli <math>E^*</math> and <math>G^*</math> as follows:
:<math>E^* = E' + iE'' = \frac {\sigma_0} {\varepsilon_0} e^{i \delta} \,</math>
:<math>G^* = G' + iG'' \,</math>
where