Dynamic modulus

Dynamic modulus (sometimes complex modulus[1]) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free or forced vibration tests, in shear, compression, or elongation). It is a property of viscoelastic materials.

Viscoelastic stress–strain phase-lag

Viscoelasticity is studied using dynamic mechanical analysis where an oscillatory force (stress) is applied to a material and the resulting displacement (strain) is measured.[2]

Stress and strain in a viscoelastic material can be represented using the following expressions:


 \omega =2 \pi f where f is frequency of strain oscillation,
t is time,
 \delta is phase lag between stress and strain.

Storage and loss modulus

The storage and loss modulus in viscoelastic materials measure the stored energy, representing the elastic portion, and the energy dissipated as heat, representing the viscous portion.[3] The tensile storage and loss moduli are defined as follows:

Similarly we also define shear storage and shear loss moduli, G' and G''.

Complex variables can be used to express the moduli E^* and G^* as follows:

E^* = E' + iE'' \,
G^* = G' + iG'' \, [3]

where i is the imaginary unit.

See also


  1. The Open University (UK), 2000. T838 Design and Manufacture with Polymers: Solid properties and design, page 30. Milton Keynes: The Open University.
  2. PerkinElmer "Mechanical Properties of Films and Coatings"
  3. 1 2 3 4 5 Meyers and Chawla (1999): "Mechanical Behavior of Materials," 98-103.
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