World Library  
Flag as Inappropriate
Email this Article

Dynamic modulus

Article Id: WHEBN0003271052
Reproduction Date:

Title: Dynamic modulus  
Author: World Heritage Encyclopedia
Language: English
Subject: Complex modulus, Payne effect, Williams–Landel–Ferry equation, Dynamic mechanical analysis, Kelvin–Voigt material
Collection: Non-Newtonian Fluids, Physical Quantities, Solid Mechanics
Publisher: World Heritage Encyclopedia

Dynamic modulus

Dynamic modulus 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 1
    • Storage and loss modulus 1.1
  • See also 2
  • References 3

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.[1]

  • In purely elastic materials the stress and strain occur in phase, so that the response of one occurs simultaneously with the other.
  • In purely viscous materials, there is a phase difference between stress and strain, where strain lags stress by a 90 degree (\pi/2 radian) phase lag.
  • Viscoelastic materials exhibit behavior somewhere in between that of purely viscous and purely elastic materials, exhibiting some phase lag in strain.[2]

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

  • Strain: \varepsilon = \varepsilon_0 \sin(t\omega)
  • Stress: \sigma = \sigma_0 \sin(t\omega + \delta) \, [2]


\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.[2] The tensile storage and loss moduli are defined as follows:

  • Storage: E' = \frac {\sigma_0} {\varepsilon_0} \cos \delta

  • Loss: E'' = \frac {\sigma_0} {\varepsilon_0} \sin \delta [2]

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'' \, [2]

where i is the imaginary unit.

See also


  1. ^ PerkinElmer "Mechanical Properties of Films and Coatings"
  2. ^ a b c d e Meyers and Chawla (1999): "Mechanical Behavior of Materials," 98-103.
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.