Page 273 - Mechanics of Asphalt Microstructure and Micromechanics

F inite Element Method and Boundar y Element Method 265

condition for this method was found by Cormeau (1975) to be very critical and requires
very small time steps. Another scheme using explicit method with subincrementation
to enhance the accuracy was successfully applied by Kumar et al. (1980) and Banthia
et al. (1985). This scheme usually has to combine with error checking and automatic
time stepping. As both time stepping and error checking are model and loading process
dependent, the criteria for time stepping and error checking should be established for
different problems.
The fully implicit method is believed to be the most accurate method. The consis-
tent tangent moduli method by Simo et al. (1985) for rate-independent elastoplasticity
and the method by Lush et al. (1989) are quite popular. However, for this method, the
backward operator requires the solution of a set of nonlinear equations with a Newton-
type iteration procedure and can be computationally intensive. For large-scale FE simu-
lation or long-sequence FE simulation, computation expenses could be critical. Also,
according to Busso et al. (1994), the complexity of the iteration expressions can limit its
implementation into finite element codes for some elaborate constitutive models with
tensorial internal variables.
To avoid the problems encountered in both explicit method and implicit method,
the implicit method combined with Taylor series approximation (Kanchi et al., 1978;
Marques et al., 1983) can be used. By this approach, the finite incremental constitutive
equations were derived from first order Taylor series expansion. The simultaneous so-
lution of the evolution equations placed this procedure on a robust foundation. Exam-
ples of this procedure were given by Dombrovsky (1992), where he applied this proce-
dure to derive the finite incremental stress-strain relation for two popular visco plasticity
models: the Miller model (Miller, 1976) and the Bodner-Partom model (Bodner et al.,
1975). This method was proved to be stable, accurate, and efficient. It allows a much
larger time step than the explicit method without encountering stability problems and
is computationally less intensive than the fully implicit method.

8.6 Semi-Implicit Implementation of the
SHRP Viscoplasticity Deformation Model

8.6.1 Introduction to the SHRP Model
AC has long been recognized as a viscoplasticity material (Lai et al., 1973; Huschek,
1977; Brown and Bell 1979). However, in the conventional design and analysis, it is still
treated either as a nonlinear elasticity material or as a viscoelasticity material. The lack
of a proper constitutive model and its corresponding numerical implementation are the
principal barriers to advance in this field. In the last decade, a research program under
SHRP (SHRP-A-415, 1994) investigated the permanent deformation mechanism of AC
and identified the following significant permanent deformation characteristics:
• Dilation
• Shearing stiffening under hydrostatic pressure
• Temperature dependence
• Residual permanent deformation
• Negligible volumetric creep deformation