Page 328 - Mechanics of Asphalt Microstructure and Micromechanics

320 Ch a p t e r N i n e

DEMs are numerical techniques developed to simulate systems comprised of mul-
tiple distinct bodies that interact with one another through contact forces. However, in
some cases, it is useful to consider the deformation of the distinct bodies in order to
evaluate their stress and strain distributions (e.g., the mastics in asphalt concrete). The
combined finite-discrete element method is just a numerical method that could com-
bine aspects of both finite elements and discrete elements together. Starting from the
finite element method, a solid domain is discretized into finite elements; if this solid
domain fails or fractures, it would be transformed into several subsolid domains inter-
acting with one another and each of them could also be discretized into its own finite
element mesh. During this process, a transition from continua to discontinua algo-
rithms is involved, which is the main problem solved by the combined discrete-finite
element method.
The contact between these sub-solid domains is still considered the same as the
contact in the discrete element method. The difference is each of them could be dis-
cretized into finite elements, so the contact solutions of the finite element method could
also be utilized for both contact detection and contact interaction. The purpose of the
contact detection is to locate those domains that are close enough to be considered
contacting one another. The main challenge of this is CPU efficiency. The purpose of
the contact interaction is to evaluate the contact forces between interacting domains
and the major difficulty is the solution of contact kinematics, which is very complex,
especially in three dimensions. The existing FEM could help in solving the contact ki-
nematics and a potential contact force concept is introduced to solve the contact inter-
action problem.
The combined FEM/DEM method is becoming a wildly recognized tool utilized by
many researchers. Munjiza and his research group made great strides in this area. Mun-
jiza began research involving a large number of separate bodies that interact with one
another in 1999, which is a main problem in the large-scale discrete element simulations
or combined finite-discrete element simulations. In this work (Munjiza and John, 2002)
a fracture algorithm applicable to simultaneous multiple fracture of a large number of
bodies is developed and a fracture model is used in the combined discrete-finite ele-
ment method for both initiation and propagation of Mode I loaded cracks in concrete.
The algorithm is based on the approximation of experimental stress-strain curves for
concrete in tension. The standard finite element formulation for the hardening part of
the constitutive law is combined with the single-crack model for the softening part of
the stress-strain curve. Finite elements are used to model the behavior of the material
until the ultimate tensile strength and a discrete crack model is implemented through
crack openings and separation along edges of finite elements. Based on the conclusion,
the major advantages of this model are its ability to model both crack propagation and
crack initiation of multiple cracks allowing creation of a large number of distinct inter-
acting fragments without considerable additional CPU requirements.
Munjiza et al. (2000) published another piece of work utilizing the combined finite-
discrete element method to simulate the fracture of solid considering the effect of ex-
pansion of detonation gas to cracks. The proposed equation enables gas pressure to be
obtained in a closed form for both reversible and irreversible adiabatic expansion,
while the gas flow model proposed considers only 1D compressible flow through
cracks. When coupled with finite-discrete element algorithms for solid fracture and
fragmentation, the model enables gas pressure to be predicted and energy balance to
be preserved.