To characterize the viscoelastic behavior of plastics, including the idealized components of the viscoelastic models, a special terminology is needed, which is explained here:
Elastic response: An elastic body is represented by the Hookean solid, as modelled by the linear spring. The stress is proportional to the strain and independent of time; the response to stress is instantaneous. There is no permanent or irrecoverable deformation, all energy used to deform the spring is accumulated and is fully recoverable.
Viscous response: A viscous body is represented by the Newtonian fluid as modelled by the dashpot. The stress is proportional to the strain rate, making the behaviour time-dependent. The recovery is nil when the stress is removed. The energy to deform the dashpot is completely dissipated during the deformation process.
Creep: Creep is the time-dependent increase in strain of a viscous or viscoelastic material under the sustained stress. The time-dependent deformation is partially recoverable with time after the release of the stress.
The creep experiments are usually performed under the constant load conditions. When stresses are high, the sample may “neck” and the cross-section supporting the load may be significantly reduced at some point during the test. Unless otherwise indicated, the creep stress (or “an engineering” stress), based on the original cross-sectional area, will be used, rather than the "true" creep stress which is based on the reduced cross-sectional area, that occurs on necking. This reflects the typical practice, which is to report the engineering stress rather than the true creep stress in creep experiments. This practice is not universal, particularly in scientific behavioral investigations.
Relaxation is the time-dependent decay in stress of a viscoelastic material under the sustained strain. Some of the deformation is recoverable with time after the release of the sustained strain. Unless the imposed initial strain is above the yield point, the cross-section remains fairly close to the original one, throughout the test. This differs from the creep behaviour as noted earlier.
Recovery is the extent to which an element returns to its original configuration after the release of the stress or strain.
The linear viscoelastic response refers to the viscoelastic response in which the stress and strain are related by a single modulus, which depends only on the duration of the applied stress and strain at a given temperature. This differs from the non-linear viscoelastic response in which the modulus depends on the value and duration of the stress or strain.
Viscoelastic stiffness response has been traditionally expressed in terms related to the manner of loading. That is, to the time dependent apparent modulus or to the ratio of the (decaying) stress to the (constant) strain, imposed during the relaxation experiments. This is defined as the "relaxation modulus" E(t).
If the test is performed in creep, the "creep compliance" or the ratio of (increasing) strain to the applied stress D(t) , is used to define the response. This observation is extremely useful for the study of the non-linear viscoelastic behavior, which occurs at the stresses and the temperatures above the range
of the interest in the structural engineering.
It can be shown that for the small strains at the temperatures within the useful range, E(t) similar to 1/ D(t) . Thus, provided that one knows the range over which this assumption can be made, a single modulus can be used to describe the time-dependent stiffness response under both the creep and the relaxation loading conditions.
A new term, the "Viscoelastic Modulus" is coined here, which defines the ratio between the stress and the strain after any duration of the stress or strain. This ratio is frequently referred to as the "Apparent Modulus". The "Viscoelastic Modulus" terminology, however, appears to be a more descriptive and appropriate companion to the term "elastic modulus", which is well known to the Structural Designer.