Dynamic modulus

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

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 (π / 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[1].

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

  • Strain: ε = ε0sin(tω)
  • Stress:  \sigma = \sigma_0 \sin(t\omega + \delta) \, [1]


ω is frequency of strain oscillation,
t is time,
δ is phase lag between stress and strain.

Storage and loss modulus

The storage and loss modulus in viscoelastic solids measure the stored energy, representing the elastic portion, and the energy dissipated as heat, representing the viscous portion [1]. 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 [1]

Similarly we also define shear storage and 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'' \, [1]

where i is the imaginary unit.

See also


  1. ^ a b c d e Meyers and Chawla (1999): "Mechanical Behavior of Materials," 98-103.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Dynamic mechanical analysis — Dynamic Mechanical Analyzer Acronym DMA Classification Thermal analysis Manufacturers Bose Electroforce Group, Mettler Toledo, Netzsch Instruments, PerkinElmer, TA Instruments, Triton Technology Ltd, Gabo Other techniques Related Isothermal… …   Wikipedia

  • Dynamic mechanical spectroscopy — In the technique of Dynamic Mechanical Spectroscopy a material (usually a slab of polymer) is exposed to a periodical deformation. The deformation can be in tensile, compression or bending mode but torsional deformations are the most practical… …   Wikipedia

  • Shear modulus — SI symbol: G SI unit: gigapascal Derivations from other quantities: G = τ / γ …   Wikipedia

  • Elastic modulus — An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance s tendency to be deformed elastically (i.e., non permanently) when a force is applied to it. The elastic modulus of an object is defined as… …   Wikipedia

  • Complex modulus — may refer to: Absolute value (mathematics), the numerical value of a real number without regard to its sign. Dynamic modulus (materials engineering), the ratio of stress to strain under vibratory conditions.[1] Notes ^ The use of the term complex …   Wikipedia

  • High strain dynamic testing — is a method of testing deep foundations to obtain information about their capacity and integrity, and in some cases, to monitor their installation. It is codified by D4945 00 Standard Test Method for High Strain Dynamic Testing of Piles. High… …   Wikipedia

  • Maxwell material — A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. It is named for James Clerk Maxwell who proposed the model in 1867. It is also known as a Maxwell fluid. Contents 1 Definition 2 Effect of a… …   Wikipedia

  • Viscoelasticity — is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain… …   Wikipedia

  • Palierne equation — connects the dynamic modulus of emulsions with the dynamic modulus of the two phases, size of the droplets and the interphase surface tension. The equation can also be used for suspensions of viscoelastic solid particles in viscoelastic fluids… …   Wikipedia

  • Kelvin-Voigt material — A Kelvin Voigt material, also called a Voigt material, is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the British physicist and engineer William Thomson, 1st Baron Kelvin and after German… …   Wikipedia