Title: loss modulus
Long Title: IUPAC Gold Book - loss modulus
DOI: 10.1351/goldbook.12782
Status: current

Definition
Ratio of the amplitude of the stress \(\pu{90\!^{\circ}}\) out of phase with the strain (\(\sigma_{0} \sin \delta\)) to the amplitude of the strain (\(\gamma_{0}\)) in the forced sinusoidal oscillation of a material. \[M^{\prime\prime} = \frac{\sigma_{0} \sin \delta}{\gamma_{0}}\]

Notes
1) For the definitions of the symbols used, see forced sinusoidal oscillation.
2) In a linear viscoelastic material, the strain \(\gamma = \gamma_{0} \cos \omega t\) produces a stress \(\sigma = \sigma_{0} \cos (\omega t + \delta) = \sigma_{0} \cos \delta \cos \omega t - \sigma_{0} \sin \delta \sin \omega t\).
3) The loss modulus characterises the viscous response of a material.

Related Term
- forced sinusoidal oscillation: https://goldbook.iupac.org//terms/view/12767

Source
- PAC, 2013, 85, 1017. 'Glossary of terms relating to thermal and thermomechanical properties of polymers (IUPAC Recommendations 2013)' on page 1032 (https://doi.org/10.1351/PAC-REC-12-03-02)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/12782/html
- json: https://goldbook.iupac.org/terms/view/12782/json
- xml: https://goldbook.iupac.org/terms/view/12782/xml

Citation: Citation: 'loss modulus' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.12782
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Accessed: 2026-06-04T10:56:34+00:00