Page 361 - Mechanics of Asphalt Microstructure and Micromechanics

Digital Specimen and Digital T est-Integration of Microstructure into Simulation 353

methods are usually used for minimizing the objective function. In this section, an im-
proved trial-and-error optimization algorithm was selected to obtain the model param-
eters. For a model with a few parameters, the trial-and-error method is usually very te-
dious and time-consuming. However, for the developed method, this disadvantage can
be overcome through conducting the sensitivity analysis to the model parameters. The
improved method needs no more complicated mathematics for solving the inverse prob-
lems, and avoids the tedious iteration process of the trial-and-error method. The sensi-
tivity analysis determines the moving directions and amounts of changes for the model
parameters. Therefore, it saves numbers of iterations for seeking the minima of the ob-
jective function. The procedure of the parameter optimization is related with a series of
calls between ABAQUS and a developed program, Param Opti, to minimize the defined
objective function, which is the function of measured and simulated deformations taken
from the experimental measurements and FEM simulations with different loading cy-
cles. The function defined in Equation 10-5 is used for simulative tests as well. If u rep-
resents a function of the vector of model parameters, D is the function of vector u.
The following is the optimization procedure:
Step 1. Guess an initial set of parameters. Do simulations to obtain an initial de-
formed profile with different loading cycles.
Step 2. Perform sensitivity analysis of the parameters.
Step 3. Input the deformed profile to the Param Opti program to calculate the value
of the objective function. If the value of the objective function does not satisfy the se-
lected convergence criteria, the program will generate a new set of parameters.
Step 4. Input the new set of parameters into ABAQUS input file to do simulations to
obtain the deformed profiles corresponding to the new set of parameters.
Step 5. Repeat steps 3 and 4 until the selected criterion is satisfied.
Step 6. Output the parameter set.
The objective of parameter optimization is to find a set of parameters to minimize
the objective function. For the two-layer elasto-viscoplastic model, there are 10 param-
eters: E, n, A, n, m, f, Y 0 , B, C, D, that need to be characterized. According to Huang
(2004), the typical value of the Poisson’s ratio for AC was given as 0.35. In this study,
this value was used in the simulations. From the studies conducted by Perl et al. (1983)
and Huang (2004), the parameter n is related to the contact pressure between the pres-
surized hose and the specimen in the APA test. In Huang (2004), the value 0.8 for n was
used under the contact pressure of 95 psi. In this study, the contact pressure is 100 psi.
Therefore, the same value will be used. After fixing two parameters, there are eight
parameters for the optimization.
To minimize the number of trials in the optimization process, a sensitivity analysis
needs to be carried out before the optimization. The purpose of the sensitivity analysis
is to study the influence of the change of the parameters on the deformation. Through
the sensitivity analysis, the percent of change for each parameter in every iteration call
between the ABAQUS and the Param Opti program can be determined. The values will
be input into the Param Opti program. After obtaining the simulation result using the
parameter set, if the convergence criterion of the objective function is not satisfied, the
program will generate a new set of parameters to obtain new deformed profiles. Other-
wise, the program will output the parameter set. The following are steps for the sensi-
tivity analysis. The result of the sensitivity analysis is shown in Figure 10.37.