Page 261 - Mechanics of Asphalt Microstructure and Micromechanics

F inite Element Method and Boundar y Element Method 253

for the interfaces is often different from those of the bulk materials. Sometimes it is
necessary to develop interface elements to more efficiently and accurately model the
interface properties. A brief but comprehensive introduction on interface elements and
their application to pavement analysis and paving materials was given by Scarpas
(2004). The work presented here is based on Wang et al. (2006). The various finite ele-
ment techniques for analyzing an interface or joint proposed in recent years can be
basically divided into two categories. The first category contains nodal or point inter-
face elements that connect normal solid elements with each other using discrete springs
(Beer, 1985). A special joint finite element with zero thickness, which was developed by
Goodman et al. (1968), is a good example. Kaliakin and Li (1995) improved the zero-
thickness interface element to eliminate deficiency of spurious stress oscillations, which
might be caused by ill-conditioning of the interface element stiffness matrix due to
large off-diagonal terms (Wilson, 1977). Research by Day and Potts (1994) showed that
the ill-conditioning could be reduced by carefully selecting the size of the solid ele-
ments adjacent to the interfaces for 2D analyses. The idea of using continuous interface
elements with a finite thickness based on continuum mechanics appears to be another
choice (Desai et al., 1984), which falls in the second category to model joints/interfaces,
such as the continuous interface elements with a tiny thickness (Zienkiewicz et al.,
1970) and the thin elements (Desai et al., 1984) etc. Pande and Sharma (1979) found that
little ill-conditioning is experienced with the application of a very thin 2D element. It is
suggested that a thin element is numerically more reliable than an element with a zero
thickness.
Frequently, shear strains are concentrated through those interfaces within AC,
which produce large shear deformation along interfaces, but very small deformation
across interfaces. As such, a very small rigid body rotation will be generated if inter-
faces are nearly straight, which implies the possibility of the use of infinitesimal strain
theories. The localized large shear strains along interfaces will inevitably lead to dra-
matic distortion of the original interface elements, and the distortion will cause poor
element configuration if the mesh is kept unchanged. The distorted mesh is very likely
to result in incorrect displacements and stresses in these interface elements, and even
analysis failures due to the distortion-induced ill-conditioning of the stiffness matrix.
This section presents the development of interface elements using the work by
Wang and Wang (2006). In this special development, motions of an interface with as-
sumed thickness are treated as large deformation problems to which the continuum fi-
nite element analysis might be applied. All the node coordinates are updated at each
load step, and continuous interface elements are reconstructed based on the concept of
the contact band element approach developed by Wang et al. (1995, 2002) after con-
verged solutions are achieved at each load step. Infinitesimal strain theories are still
employed within each load step. As an example, strain descriptions in three-node and
four-node interface elements are formulated to harmonize the normal and shear stress-
strain relationships.
This continuous interface element is different from the thin-layer element (Desai et
al., 1984) in the sense that the continuous interface elements are continuously renewed
based on their current interface configuration subject to large shear deformation. Un-
like those rectangular thin-layer elements, they could be quadrilateral and triangular
elements. The continuous interface elements are equipped with the proposed strain
formulation and specific anisotropic Mohr-Coulomb yield criterion.