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A purely elastic body when subjected to cyclic stress input results strain (or deformation), which is proportional to stress amplitude and are in in phase with the input stress, as shown in the Figure 1 here. In this case no energy is lost or dissipated and the total energy stored by elastic material is conserved when the load is removed and the material returns to its original position. Whereas, for a purely viscous material all the energy is dissipated once the load is removed. The amount of dissipated energy is quantified as the damping of the material and they are characterized by how the energy is being dissipated from the materials or structures (underdamped, critically damped, over-damped, friction etc.). Such linear viscous materials when subjected to cyclic stress yields proportional to the strain rate which are 90 degree out of phase with the input stress.
Viscoelastic materials exhibits both elastic and viscous behavior (refer to “Viscoelastic Materials: Introduction” section for fundamental properties and models of viscoelastic materials). Therefore, for a given stress input, they recover some of the stored energy and dissipate the rest of the energy. When they are subjected to cyclic loading (as shown in the Figure 1, the phase angle (or lag) $\phi $ between the stress input and strain response is between the purely elastic and purely viscous case ranging from $\left( {0 < \phi < {\pi \mathord{\left/{\vphantom {\pi 2}} \right.\kern-\nulldelimiterspace} 2}} \right)$. This phase angle $\phi $ is the measure of dissipation (or damping level) in the material. Such linear viscoelastic materials are often defined by their storage modulus $E’$ representing the elastic response of the material and their loss modulus $E”$which represents their viscous response. They are often represented as a complex modulus ${E^*} = E’ + iE”$ with the following stress-strain relationship:
$\sigma \left( t \right) = {E^*}\varepsilon \left( t \right){\rm{ }} \Rightarrow {\rm{ }}\sigma \left( t \right) = \left( {E’ + iE”} \right)\varepsilon \left( t \right)$
In general these complex modulus and damping properties are dependent on frequency as well as temperature. DMA tests are conducted to estimate these material properties.
The following video links demonstrates the capabilities of a representative DMA instrument as well as provides an overview of DMA testing protocols.
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What Is Dynamic Mechanical Analysis: http://www.youtube.com/watch?v=ohw6PfOIyIs
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TA Instrument’s RSA-G2 Model: http://www.youtube.com/watch?v=BAlOE5rNSgs
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