Dynamic modulus (sometimes complex 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.

• 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 radian) phase lag.

• Viscoelastic materials exhibit behavior somewhere in between that of purely viscous and purely elastic materials, exhibiting some phase lag in strain.

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

where

1. is frequency of strain oscillation,

2. is time,

3. is phase lag between stress and strain.

,

which is the time-dependent generalization of Hooke's law converges to the equilibrium shear modulus:

1. .

The Fourier transform (see below).

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. The tensile storage and loss moduli are defined as follows:

.

as follows:

is the imaginary unit.

Ratio between loss and storage modulus

) between the storage and loss modulus.

greater than 1, the energy-dissipating, viscous component of the complex modulus prevails.

See also

• Dynamic mechanical analysis

• Elastic modulus

• Palierne equation

References