Page 105 - MODELING OF ASPHALT CONCRETE

Overview of the Stif fness Characterization of Asphalt Concr ete 83

Dissipated
pseudostrain
energy
Measured stress s x x x x x x

x x x x x
x
R
e = s LVE /E = “Pseudo’’ or reference strain
R
FIGURE 3-11 Illustration of dissipated pseudostrain energy.

is the result, it means that the material is behaving as a linear viscoelastic material. On
the other hand, if a closed, curved figure such as is also shown in Fig. 3-10 is the result,
then the material is behaving as a nonlinear viscoelastic material.
If the calculated linear viscoelastic stress is divided by a reference modulus, the
result has the dimensions of strain and is called pseudostrain. By this means, the graph
of measured against calculated linear viscoelastic stress has been converted into a stress
versus pseudostrain graph and the area within the closed, curved loop has been
converted into dissipated pseudostrain energy, as illustrated in Fig. 3-11.
This dissipated pseudostrain energy is the energy that has been lost in loading and
unloading the material minus the energy that has been lost in overcoming the viscous
resistance of the material, and therefore it represents the energy that is available to do
damage to the material. However, if the material is loaded and unloaded repeatedly and
the closed loop does not change its size or area, then that is an indication that the material
is not changing and is not being damaged. Damage to the material is indicated by a
change in the shape and area of the dissipated pseudostrain energy loop. Figure 3-12
illustrates a slight change in the dissipated pseudostrain energy loop.

Dissipated Pseudostrain Energy
Change

Actual stress Dissipated
pseudostrain
energy

Linear viscoelastic stress (from strain history)
Pseudostrain =
Reference modulus
FIGURE 3-12 Change in dissipated pseudostrain energy indicating damage.