In a word, yes. But the elasticity is a way to characterize the
mechanical response of the material body for applied stresses that
stay within the linear regime. Very large stresses, which are high
enough to fracture the material, cause non-linear deformations. These
values vary greatly depending on the overall makeup of the concrete
mixture. Many of the non-fracture-related mechanical properties of
concrete are characterized by the elastic moduli. For example, in many
buildings the stiffness of the structure, made up of reinforced-steel
concrete beams, is more important than the strength of the
structure. The stiffness of the structure is directly related to the
stiffness of the concrete, which is a function of its elastic moduli.
The elastic moduli prediction code is set up to compute the
elastic moduli of an arbitrary material. As long as the microstructure
can be represented by a 3-D digital image, and the individual phase
elastic moduli are known, the program can be used to compute the
overall moduli. The overall elastic moduli are functions of the
microstructure as well as of the elastic moduli of the individual
chemical phases in the cement paste. These can be as many as 20 or 30,
since cement paste by itself is a chemically complex material.
The elastic moduli prediction code has been parallelized.
Why Parallelize these Calculations?
Part of the intrinsic error that comes about with the use of 3-D
digital images to represent microstructure is digital resolution
error. This can be quantified and eliminated by investigating the same
problem at several resolutions, looking at large enough systems to see
the asymptotic behavior. The parallel implementation of the elastic
code enables this to be easily and more accurately done.
How is the Parallelization Realized?
The parallelization was created using MPI and FORTRAN90 for a
distributed memory machine, ie. a PC-cluster running Linux. This new
code contains 3 predominant features which increase the speed and
allow the user to handle much larger problem sizes.
||Removal of ib array: This array is a hash table which needs
requires 27 times the memory the size of the data set. The new
parallel code allows one to address the needed array elements
directly by virtue of storing them in the "natural"
3-dimensional (x,y,z) manner which mimics the spatial
geometry of the actual sample.
Calculation of gb and Ah arrays: These calculations
consume over 90% of runtime due to the complexity of
These calculations are now in the form of:
The removal of the ib array
allows the computer to increase its access speed to the desired dk
array elements by removing a degree of indexing.
Increasing problem size/decreasing overall runtime: On a
single processor the entire data array must be loaded. However,
the use of parallel programming allows one to use approximately
1/nth the amount of memory per processing node or allows one
to run a problem that is essentially N times larger overall.
What is the Performance of the Parallel Code?
The time required to run a 300^3 (27 million voxels) job using
the serial version is nominally 120 hours. This new code is
able run the same calculation on 8 CPUs on an SGI Origin 2000
in about 6.42 hours; a speed-up of 18.69.
Besides some work on cement paste, the serial code has already
been applied to porous ceramics, porous glasses, rocks, open and
closed cell foams, and metal matrix composites. This parallel code
will allow calculations on much larger systems in a timely way, on the
order of 300-600^3 voxels in size, will allow many more applications
and not only to concrete. One important application is to quantify 3-D
microstructure using x-ray tomography. Various codes are then applied
to the resulting 3-D structure to compute various quantities. These
data sets are typically of size 512^3 or greater. In the past, a piece
had to be digitally cut out of the data set in order to be able to
compute quantities like elastic moduli, which induces finite size
error. Now such large data sets can be routinely processed with the
parallel elastic moduli code.
There also many problems that are not large in spatial size, but
require better digital resolution. One example is the early age
elastic properties of cement paste. To properly resolve the small
necks of material that are holding the solid backbone together
requires a fine digital resolution. The parallel code makes such fine