Page 329 - Mechanics of Asphalt Microstructure and Micromechanics

Applications of Discrete Element Method 321

Munjiza et al. (2004) reported the work to use combined finite-discrete element
model to investigate the failure and collapse of reinforced concrete beam and column.
Algorithms specific to reinforced concrete structures and beam type structural elements
were developed. These solutions have two main characteristics: 1) finite element dis-
cretizations are able to capture pre-failure behavior accurately; and 2) after the failure
and collapse have occurred, the same finite element discretizations are able to capture
interaction between failing and collapsing structural elements. A simple two-node fi-
nite element was proposed together with numerical integration, which enables the non-
linear behavior of both concrete and reinforcement to be captured. The proposed nu-
merical solution was compared with an analytical solution for linear elastic behavior.
Experimental verification of the proposed numerical solution for non-linear behavior
and collapse was conducted using existing experimental results. Based on the conclu-
sion of this work, the results obtained using the combined schemes compare well with
analytical and experimental results.
Bangash and Munjiza (2003) conducted a comparison between an experimental re-
sult, undertaken at the Swiss Federal Institute, and a combined finite discrete element
simulation to model the pre-failure and post-failure transient dynamics of reinforced
concrete structures. In this work, a novel beam element is introduced in order to in-
crease CPU and RAM efficiency. The accuracy and reliability of this element is assessed
when used in dynamic loading conditions. Based on the conclusion, the element intro-
duced is capable of accurately modeling inertia and contact effects in pre- and post-fail-
ure dynamics. Komodromos and Williams (2002) used a combined DEM and FEM to
simulate deformable multi-body systems. In this work, an updated Lagrangian finite
element formulation and an explicit time integration scheme were used together with
some simplifying assumptions to liberalize this highly nonlinear contact problem. In
particular, the DEM is employed to identify, at each simulation step, the bodies in con-
tact and determine the contact forces. Then, either an FE or a DE formulation, depend-
ing on whether the body under consideration is deformable or rigid, respectively, is
used for the individual body to describe the equations of motion. In case of a deform-
able body, the strains are assumed to be sufficiently small to permit a small strain anal-
ysis. The deformability of individual bodies is considered using a displacement-based
updated-Lagrangian FE formulation.
Finally, an explicit time-integration method, specifically the central difference meth-
od, is used to perform the numerical direct integration of the equations of motion and
determine new displacements, as well as the deformations and stresses wherever need-
ed, of each body. After computation of the motion for each discrete body at a new time
step, the positions of all discrete bodies are updated and a new contact detection pro-
cess determines the new contacts and evaluates the corresponding contact forces, which
are then used in the following time step of the simulation. A wave propagation simula-
tion is presented as a very simple example that demonstrates a software implementa-
tion of the combined DEM and FEM to simulate deformable bodies using Java and da-
tabase technologies. An extendable, object-oriented, and portable computational tool,
which enables numerical simulations of multiple distinct bodies that interact through
contact forces while allowing selected bodies to be deformable, is used for this verifica-
tion example.
Lewis et al. (2005) used the combined finite-discrete element method to simulate the
pharmaceutical powder and tableting process and contact dynamics for irregular-shaped
particles. The main achievement is that a particle-scale formulation and two-stage