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Reconfiguring Steel Structures: Energy Dissipation and Buckling
Mitigation Through the Use of Steel
Foams
Principal Investigators:
Sanjay R. Arwade (University of Massachusetts)
Jerome F. Hajjar (Northeastern University)
Benjamin W. Schafer (Johns Hopkins University
Project Proposal
Authors:
Sanjay R. Arwade
Jerome F. Hajjar
Benjamin W. Schafer
Date: 12/6/10
Grants: CMMI-1000334, CMMI-1000167, CMMI-0970059
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Collaborative Research: Reconfiguring Steel Structures: Energy
Dissipation and Buckling Mitigation Through the Use of Steel
Foams
1 Introduction
Steel buildings and bridges are designed such that elastic or
inelastic buckling occurs in key components during major loading
events (AISC 2005a, 2005b; AISI 2007; AASHTO 2009). However, such
buckling has complications such as (a) low-cycle fatigue failures
in the buckling components (Uriz and Mahin 2004), (b) requirements
for expensive local stiffening to control where the buckling
occurs, and (c) limited energy dissipation in the buckling modes
triggered. Cellular and foamed steel (Fig. 1) is a new and
potentially revolutionary material that allows for (i) components
to be replaced with elements capable of large energy dissipation,
or (ii) components to be stiffened with elements which will
generate significant supplementary energy dissipation when buckling
occurs. Steel foams provide a means to explore reconfiguring steel
structures to mitigate cross-section buckling in many cases and
dramatically increase energy dissipation in all cases.
Though aluminum and titanium foams are utilized in aerospace and
automotive applications that require materials that are light and
stiff, stiff and permeable, or energy absorbent, the potential
application of steel foams in civil structures has not been
adequately explored. Steel foams offer the following key advantages
for use in civil structures:
• Steel foams have a high stiffness-to-weight ratio and
therefore can be designed as stockier members having similar weight
but much lower local slenderness ratios than comparable steel
members. Members that commonly buckle now, such as steel braces or
flanges of girders in flexure may be replaced by energy-dissipating
steel foams. These members will not be exposed to the low cycle
fatigue fractures and irregular load-deformation curves that are
common in current steel members that now buckle cyclically, with
this cyclic local or member buckling now being fundamental to the
primary energy dissipation mechanism in a large majority of
present-day steel structures.
• Steel foams absorb large amounts of energy at lower stress
levels and will not attract large additional loads through
increased strength making steel foams ideal to use in
energy-dissipating devices.
• Steel foams are weldable to other steel components (Kremer et
al. 2004) using comparable if not identical methods to current
steel. This puts steel foams in stark contrast to other methods
that are being investigated for enhancing ductility (e.g., shape
memory alloys).
• Steel foams should have enhanced thermal properties compared
with regular steel on a pound-for-pound basis, due to the internal
voids and increased conductive path.
• Steel foams have low specific weight, thus these components
will not add undue weight to the structure in comparison to their
energy-dissipation capabilities.
Mass production of steel foam does not yet exist, yet recent key
advances in the manufacture of steel foams present the first
opportunity to develop practical applications for metallic foams in
civil structures. Through an agreement with the American Iron and
Steel Institute, the investigators can obtain the necessary steel
foam members and components as produced by a powder metallurgy
process developed by Kremer et al. (2004). This process has, for
the first time, produced steel foam of high enough quality that it
can be considered for use as a structural material, and the
investigators will have ample access to the specimens necessary to
conduct this research. By utilizing a less expensive base material
(i.e., steel as opposed to titanium) the cost penalty of using
foamed materials will be reduced. Further, by providing
!"# $
!%# $
! $
Figure 1: Steel foam (a)-(b) microstructures ~ 4cm and (c)
sections (Kremer et al. 2004).
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initial characterization and applications, the case for
developing mass production methods and more dramatic cost
reductions can be established as a necessary step towards common
use.
The goal of this work is to provide the foundational
experimental results, validated complementary simulations, and an
initial assessment of appropriate implementation strategies to
enable the basic engineering of steel foam as a structural
component in steel structures. This project, through physical
testing and computational simulation, will deliver (1) a
constitutive model for the complete, quasistatic, monotonic and
cyclic response of steel foam; (2) computational tools for the
simulation of the micromechanical response of steel foams; (3)
candidate designs of steel foam elements that can serve as energy
dissipators in civil structures; (4) quantitative demonstration of
the ability of steel foam to mitigate buckling instability in steel
structural components; and (5) recommendations on possible new
designs for the microstructure of steel foam to render it more
suitable for civil structural applications.
The research team is described in Tab. 1. See Section 5 for
additional details.
Table 1: Research team participants, affiliation and
expertise
Researcher Affiliation Expertise/Role
Asst. Prof. Sanjay R. Arwade
University of Mass. Amherst
PI: Materials characterization, micro-scale modeling,
constitutive models, stochastic simulation
Assoc. Prof. Benjamin W. Schafer
Johns Hopkins University
co-PI: Cold-formed steel structures, structural stability,
component modeling, modeling energy dissipation
Prof. Jerome F. Hajjar
University of Illinois Urbana-Champaign
co-PI: Hot-rolled steel structures, fuse-based structural
systems, structural system modeling, experimental testing
To ensure the developed work has maximum impact on industry and
practice, an Industrial Advisory Board (IAB) has been created for
this proposal (Tab. 2). See Section 5 for additional details. The
individuals named in the table, representing essentially all the
major organizations in the steel construction industry, have agreed
to participate in the IAB. The American Iron and Steel Institute
(AISI) and the American Institute of Steel Construction (AISC) have
provided supporting letters (included in the supplementary docs).
AISI specifically endorses the “potential in the application of
steel foam for structural use,” and states that the proposal “takes
genuine steps towards providing analytical tools and specific real
applications,” that will motivate the adoption of steel foam in
practice. AISC advises of the need for a “product form that would
eliminate the buckling” that often causes failure in steel
structures.
Table 2: Industrial Advisory Board participants, title and
organization
Participant Title Organization
Jay Larson Director Construction and Technical American Iron and
Steel Institute
Don Allen Technical Director Steel Stud Manufacturers
Association
Lee Shoemaker Director of Research Metal Building Manufacturers
Association
Tom Schlafly Director of Research American Institute of Steel
Construction
David Mar Principal Tipping Mar Associations, Berkeley, CA
Tom Trestain Principal Trestain Structural Engineering, Toronto,
ON
2 Background
In the seminal edited volume Metal Foams A Design Guide, (Ashby
et al. 2000) Ashby, Gibson and others argue that industrial take-up
of advanced materials lags far behind research development, and
that the route to accelerating the take-up of advanced materials is
to focus early in material development on “development of design
rules, research targeted at characterizing the most useful
properties, and demonstrator projects” (Ashby et al. 2000, Fig.
1.2). Ashby and co-authors (Salimon et al. 2005) specifically
identified the wide range of possible transformative applications
for steel foam. This proposal is a direct response to the
opportunity the identify, and is focused specifically on
“characterizing the most useful properties”, and developing
“demonstrator” applications for the new material, steel foam.
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2.1 Mechanics of metal foams
The mechanics of low-density (relative density less than 0.2)
open- and closed-cell foams is essentially mature at this point,
with results available for important material properties such as
the elastic and shear moduli, Poisson’s ratio, yield stress and
plasticity parameters (Gibson & Ashby 1997, and, selected from
a very deep literature, Silva & Gibson 1995, Gong et al. 2005,
Jang et al. 2008, Warren & Kraynik 1987, 1997, Luxner et al.
2007, Papka 1994, Papka & Kyriakides 2008a,b, Silva et al
1995). The mechanics indicate that relative density of the foam
controls virtually all of the material properties. The mechanics,
however, are developed from the beam or plate-like behavior of the
cell ligaments and walls in low-density metallic foams, this
behavior does not predominate in steel foams, which have relative
densities between 0.3 and 0.8 (Kremer et al. 2004). For higher
density foams bending does not dominate the local microstructural
response, and further study is needed.
Nevertheless, the knowledge base from low-density foams provides
a strong foundation from which we will develop our treatment of
steel foams. For example, the engineering community now knows that
material stiffness decreases less rapidly than weight when a metal
is foamed so that foams have high stiffness to weight ratios, that
foams are able to develop very large compressive strains at low
stress levels, that response is asymmetric in tension and
compression, and that relative density is the most important, if
not the only, parameter that determines material properties.
Basic design guides are provided for low density foams subject
to fatigue loads (Ashby et al. 2000), and some experimental
investigations of the fatigue response of metal foams have been
published (Harte et al. 1999, Ingraham et al. 2008) but there
remain significant gaps in our understanding of metal foam
mechanics (Tab. 3). To apply steel foams to civil structures these
gaps must be filled because steel foams are high density and
seismic fatigue loads are low cycle.
2.2 Steel foams
Metallurgists and materials scientists in Europe and the United
States have fabricated steel foams using three main: powder
metallurgy (Kremer et al. 2004, Park & Nutt 2000, 2001a,b,
2002, Motz et al. 2005), sintering hollow steel spheres (Tuchinsky
2005), and chemical reduction of ceramic foams (Verdooren 2005
a,b). These methods are similar to those reviewed by Banhart (2001)
for the processing of metal foams, and each yield different
microstructures. We will focus on steel foams prepared by the
powder metallurgy method developed by Fraunhofer USA (Kremer
et al. 2004; Fig. 1 a,b,c in this proposal) in a project
supported by the Dept. of Energy and the American
Iron and Steel Institute. The close association of the
investigators with AISI is evidenced by the letter of
support, which states, “AISI strongly supports the goals of this
research and will work with the
researchers to help them achieve those goals, including securing
samples, should the project be funded.”
This firm support of the group that participated in the
development of the Fraunhofer process assures that
this project will have access to sufficient material
samples, and also that the work will remain firmly
grounded in the realities of the production process.
Kremer et al. (2004) completed preliminary experimental
characterization of the tensile and compressive properties of steel
foam and the response of hollow steel tubes filled or partially
filled with foam. The material characterizations indicate
substantial differences between the response of high density steel
foams (relative
Table 3: Summary of state of knowledge of foam mechanics.
Foam
Monotonic
Fatigue
Medium-High Cycle
Fatigue
Low Cycle
Low density Well understood
Several experimental results
Fewer than 10 tests reported, no models
High density Preliminary experiments
No known character-izations or models
No known character-izations or models
Figure 2: Bending tests on tubes filled (green, higher load and
ductility) and empty (blue) (Kremer et al. 2004)
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density about 0.5) and low density foams made of other metals.
The tests on filled tubes demonstrate the potential of foam to
shift buckling modes in the direction of higher strength and
ductility (Fig. 2)
3 Material Characterization and Constitutive Modeling
The steel foams that we propose to investigate have
microstructures that are qualitatively different from those in
currently produced metal foams. The key difference is the high
relative density, in the range of 0.5, and the resulting thick cell
walls (Fig 1). The thickness of the cell walls renders invalid the
assumption of beam- or plate-like behavior for the cell walls.
Since essentially all previous analytical and computational work on
the mechanics of metal foams has been built upon the assumption of
beam- or plate-like behavior of the cell walls, we must develop
novel models for the microstructure and mechanics of steel foams.
Our material characterization efforts concentrate in four
areas:
1. Experimental characterization of the material
microstructure
2. Experimental characterization of the mechanical
properties
3. Numerical modeling of the material and material response
4. Development of constitutive models for the material
Development of validated numerical modeling techniques will
enable, (a) careful examination of steel foam applications as
described in Section 4 and (b) the extension of this work from
material characterization to material design, in which simulation
will be used to optimize the material microstructure to specific
structural applications.
Working with AISI (see support letter), who have previously
performed research on steel foams, we will secure a variety of
steel foam samples for testing. Because steel foam is not in
regular commercial production, bars and cold-reduced sheet are
selected as sample components for this project due to their
relative ease of manufacture. Based on the work sponsored by AISI
and DOE at Fraunhofer (Kremer et al. 2004) it is anticipated that a
carbon-strontium carbonate composition will be used for the foaming
agent and hot uniaxial pressing for mechanical drawing of the
specimens. Many of the developed procedures are proprietary to
AISI, but AISI’s support of this project insures that successful
steel foam samples can be created and explored for structural use
herein. AISI has specifically stated in their supporting letter
that it will “ensure those companies [that produce steel foams] are
receptive to material requests.”
The steel foam bars will be 41mm x 92mm (essentially equivalent
to a timber “2x4” or a 362S162 cold-formed steel stud, SSMA 2001
nomenclature) in cross-section with length dependent on the test of
interest. Such a specimen size is within the known capabilities of
the specimens produced at Fraunhofer (Kremer et al 2004). Void
density ranges between 43% and 55% were demonstrated in that work,
target void densities of 50%, 65% and 80% will be sought for the
bar specimens here.
3.1 Microstructure characterization
Characterization of the microstructure of steel foam requires
imaging of the complex three-dimensional geometry of the solid and
void phases of the material. We will employ two techniques at
opposite ends of the technological spectrum to obtain such images,
serial sectioning and x-ray computed tomography (CT), and will
follow the recommendations of Banhart (2001) to establish a
systematic characterization plan. In serial sectioning,
two-dimensional images of cross sections through the material
microstructure are obtained by grinding the material to reveal
successive sections. The advantages of serial sectioning are that
it requires no specialized equipment and the grinders and imaging
tools are readily available at UMass. The disadvantages are that
considerable skill is required to grind material so as to reveal
successive layers, reconstruction of the three-dimensional geometry
from the serial sections is a subtle operation, and the process is
extremely time consuming, cannot be automated, and is destructive.
X-ray CT imaging, on the other hand, is fully automated,
non-destructive, and directly delivers a three-dimensional
reconstruction of the microstructure. The disadvantage of CT
imaging is that it requires highly specialized equipment usually
available only at medical institutions, and can be expensive.
Access
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to CT scanning equipment is available at UMass through
arrangement with Cooley-Dickinson Hospital. Given the relative
advantages and disadvantages of the two methods we propose to
investigate CT scanning as the primary imaging tool, with serial
sectioning available as a backup method to ensure viability of the
project. Successful CT scanning of steel foams has already been
demonstrated (Fig. 3)
In characterizing the microstructure we will evaluate the
following features: void size distribution, void shape, and spatial
distribution of the voids. Quantification of the void size can be
conducted by a relatively straightforward thresholding operation
because of the high contrast ratio between the solid and void
phases in the material. Quantifying the shape of the voids is
somewhat more challenging since the shape of the voids is in
general random. Recent work on the analysis has indicated that
moment invariants are the best way to characterize the shape of
irregular three-dimensional volumes (MacSleyne et al. 2008). We
will employ standard methods for characterizing the spatial
distribution of the void phase including 2- and 3- point
correlation functions and the lineal path and chord length density
functions (Torquato 2002).
3.2 Mechanical property experiments
A thorough investigation of the mechanical properties of steel
foams is proposed since the high relative density of steel foams
renders their mechanics qualitatively different from those
conventionally understood for low density metal foams. We propose
to characterize the compressive, tensile, and cyclic response of
steel foams, and make preliminary investigations into the thermal
and vibrational characteristics. Furthermore, we will make
preliminary investigations into the dependence of mechanical
properties on average void size and will determine whether any size
effect can be discerned in the response of the material. The tests
described here will allow us to develop constitutive models for
steel foams that will then be implemented in the finite element
analysis packages ABAQUS and ADINA. These models are a major
contribution of this project because no constitutive models
currently exist for the class of high density foams such as steel
foam.
3.2.1 Tension tests: We will conduct tension testing on
specimens designed to conform to ASTM standard E8 (ASTM 2008) for
tension testing of metallic materials. The specimens have reduced
cylindrical cross sections in the gage length. The tension tests
are designed to define the overall stress-strain response of the
material during tensile loading, to establish the elastic modulus
and ultimate stress of the material and the dependence of the
modulus and ultimate stress on the void size and specimen size.
Also important are the strain at ultimate stress and the post-peak
response of the foam. We propose to conduct tension tests on
specimens with the three target relative densities, 50%, 65%, and
80%. At each relative density we will investigate specimens with
three different diameter to void size ratios, 5, 10, 20. These
values are chosen because for low density aluminum foams a specimen
to void diameter ratio of 10 is usually treated as a minimum. Our
goal is to determine whether this lower bound on specimen size also
applies to high density steel foams. We will determine in
conjunction with the manufacturer whether variation in the diameter
to void size ratio will be varied by changing the specimen diameter
or the average void size. If the material characterization tests
reveal substantial orthotropy in the void structure we will conduct
the full set of experiments in each of the three principal material
directions. With three test replications for each specimen design
we will conduct 27 tests if the material is found to be isotropic,
and 81 tests if the material is found to be anisotropic. The test
matrix for
Figure 3: X-ray CT image of steel foam (Kremer et al. 2004)
Table 4: Test matrix for tension tests on steel foams. Numbers
in the table cells indicate number of test replications at each
specimen design
Specimen diameter/void size
Relative density 5 10 20
50% 3 3 3
65% 3 3 3
80% 3 3 3
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each relative density and material direction is summarized in
Tab. 4.
3.2.2 Compression tests: The compression testing program has
essentially the same objectives as the tension testing program so
the experimental design is similar. These tests are necessary
because the response of metallic foams is highly asymmetric in
tension and compression. The test matrix is identical to that shown
in Tab. 4. The specimen geometry is as specified in ASTM E9 (ASTM
1989). An additional parameter to be studied in the compression
tests is the strain to densification.
3.2.3 Shear tests: Shear deformation is the primary local
deformation mode used in energy dissipating devices in civil
structures. We will therefore conduct an investigation of the shear
properties of steel foams, again following the test matrix of Tab.
4. We will use the compact shear specimen proposed by Barr &
Liu (1983) due to the small volume of material required and robust
performance cited in the paper. The specimen diameter / void size
ratio for the shear specimens should be interpreted as the ratio of
the minimum specimen dimension to the void size.
3.2.4 Fatigue tests, low and high cycle: In many of the example
applications discussed in Section 4 the steel foam must sustain
non-monotonic loads, such as are generated in an earthquake. The
response of metal foams to cyclic loading is much less well
understood than their response to monotonic loads, and the initial
report on steel foam fabrication and properties (Kremer et al.
2004) did not report any cyclic tests. Our objective is to obtain
characterizations of the mechanical response of steel foams to
cyclic loading of large and small amplitudes, corresponding to low
and high cycle fatigue cases respectively. The responses of
interest are the fatigue life and also the hysteretic behavior of
the material which is critical to evaluating the potential cyclic
energy dissipating performance of the material. We will perform
fatigue tests under strain control at strain amplitudes ranging
from 0.05% to 2% strain, for three values of relative density, 50%,
65%, and 80%, and for fully reversed loading,
compression-compression loading, tension-tension loading and fully
reversed shear loading.
3.2.5 Size effect: Statistical size effect is known to occur in
materials with heterogeneous microstructures such as steel foams.
The tests described above interrogate specimens of three different
sizes relative to the average void size in the material to provide
an indication of the size of the representative volume element and
any tendency for the material to exhibit a size effect. Any
potential size effect in the material is important to our study
because, as is described in the following sections, some of our
example applications use relatively large volumes of steel foam to
directly absorb energy and some use small volumes of steel foam to
attempt to beneficially modify the response of thin-walled steel
members.
3.2.6 Other properties: Steel foams have potentially
advantageous thermal, vibrational, and acoustic properties. They
should prove less thermally conductive than solid steel, and foams
are known to substantially dampen vibrations. To investigate
vibrational properties we will conduct free vibration tests on
steel foam beams to evaluate the damping coefficient by logarithmic
decrement methods. The beams tested will have span to depth ratio
of about 15, will be square in cross section, and will be
fabricated at the three relative densities of interest, 50%, 65%,
and 80%. They will be instrumented with an accelerometer during the
test so that the damping coefficient can be estimated. A full
fledged thermal conductivity study is beyond the scope of this
project, but we will make some preliminary measurements of the
conductivity by heating one end of one of the beams and measure the
heat conduction using thermocouples.
3.2.7 Weldability: Connection design will be a major challenge
in the eventual commercialization of steel foam for civil
structural applications. Kremer et al (2004) demonstrated the
feasibility of welding steel foams, but used filler wire and rods
more typical in aerospace applications. UMass has an established
relationship with a steel fabricator where a small scale program of
test welding will be conducted. The program will consist of cutting
five to ten specimens of the same geometry as the tensile
specimens, welding them back together. The specimens will be
returned to UMass to undergo the tensile testing protocol to
evaluate the tensile strength of welded butted connections. Results
of this preliminary
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evaluation will include the quantitative tensile testing results
and the qualitative report of the welder on material
weldability.
3.3 Material modeling
Our material modeling efforts are focused on developing models
that can predict the macroscopic material properties of a steel
foam from an explicit representation of the material
microstructure. In addition to these homogenization efforts, which
we propose to conduct both by numerical simulation and approximate
analytical methods, we will use numerical simulation to evaluate
the thermal and vibrational properties, as well as bolt bearing, a
problem that arises in a many structural steel connections. We
build our modeling on the experience of Prof. Arwade with modeling
random microstructures and simulating their response (Arwade &
Grigoriu 2003,2004; Schafer & Arwade 2004; Tan & Arwade
2008; Louhghalam & Arwade 2009).
3.3.1 Material microstructure model: The microstructure of steel
foams consists of solid and void phases. The void phase is often
spherical, and is typically at least approximately elliptical. The
problem of generating sample microstructures for use in analysis,
therefore, amounts to placing voids of random size and shape in a
defined domain that is otherwise filled with the solid phase. Many
packing algorithms are available for performing such simulations in
two and three dimensions, including the Poisson hard core field
(Torquato 2002). We prefer the Poisson hard core field as a model
on which to base simulations because of its straightforward
implementation and flexibility in allowing for control of the void
shape, void size distribution, and void spatial distribution.
Figure 4 shows some of the degrees of control available in
simulating microstructures using a Poisson hard core field. The
illustrations are two dimensional, and the algorithm is easily
extended to three dimensions. If voids of random shape are desired,
as opposed to elliptical voids with random size, we will use a
recently developed method for generating three dimensional volumes
of arbitrary shape with specified statistical properties (Grigoriu
et al. 2006). Although the Poisson hard core field is very
flexible, it is not well suited to generating microstructures that
match statistical measures of phase spatial distribution such as
the n-point correlation functions, lineal path and chord length
density functions. Iterative methods are, however, available for
simulating such microstructures with specified higher order
statistics (Graham-Brady & Xu 2008), and these will be adapted
to our purpose.
3.3.2 Analytical approaches to homogenization: In the
applications we describe in the following sections, plastic
deformation in the steel foam is used as an energy absorbing
mechanism. The homogenization problem, therefore, involves the
plastic and elastic properties of the steel foam microstructure.
Although homogenization for elastic properties of heterogeneous
microstructures are well developed, only recently have techniques
become available for homogenization of plastic properties (Acton
& Graham-Brady 2009). While these techniques are suitable for
characterizing the elastic properties and compressive plastic
properties, no techniques are currently available for
homogenization of fracture properties or ultimate stress. We will
investigate adapting the method of Acton & Brady for
homogenization of ultimate stress of the steel foam microstructures
so that a full characterization of the elastic and inelastic
properties of the foam can be approximated by analytical methods.
The research challenges posed by applying approximate analytical
homogenization techniques to steel foam microstructures
include:
1. The void phase has zero material stiffness, and this zero
value can pose numerical challenges to averaging based
homogenization methods.
2. Homogenization for ultimate stress is even more challenging
than for yield stress since ultimate stress of a heterogeneous
material with voids in it is highly dependent on the local
arrangement of
Figure 4: Simulated 2D steel foam
microstructures; circular and
elliptical voids, both with 70%
relative density and random void
size.
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the phases, and consideration of such local geometry is
particularly difficult to include in homogenization methods.
3.3.3 FE mechanics modeling: To the degree that analytical
homogenization approaches do not provide the necessary
characterization of the steel foam material properties we will seek
recourse to finite element analysis of steel foam microstructures
to establish the link between the steel foam microstructures and
macroscopic properties. Such simulations can be treated as
quasi-static and must incorporate material nonlinearity to capture
yielding of the base metal and geometric nonlinearity to account
for the large displacements that occur at the cell walls. Figure 5
shows simulations of the tensile elasto-plastic response of a steel
foam with oriented elliptical voids.
In modeling the large deformation response of steel foams in
tension and compression, some significant challenges are presented,
namely:
1. Densification of the foam is caused by self-contact of the
material as the voids close and the cell walls come into contact
with one another. This is a challenging phenomenon to model since
the geometry of the contact and target surfaces is not known a
priori for a steel foam with random void geometry.
2. Fracture of the foam under tensile loading occurs by
progressive fracture or tearing of the cell walls. Modeling this
phenomenon is challenging because the locations of the local
fractures are not known a priori. Two options are available for
simulating the tensile failure of steel foams, the use of cohesive
elements at all possible locations of fracture (Ortiz &
Pandolfi 1999) or the use of a strain based element rupture
criterion to determine when fracture occurs in individual elements.
We will investigate both of these methods to gauge their
suitability to this modeling problem.
The primary purpose of the finite element modeling is to develop
a model for the mechanical response of steel foam that has been
validated against the experimental results described in the
previous section. This modeling capability will be used in the
successive parts of the proposal, specifically in efforts to design
steel foam microstructures that are optimized to the desired
structural performance and as plug-in components to the simulations
used to explore possible structural applications of steel foams.
For example, the structural advantages of forming the web of a
steel plate girder from steel foam cannot be evaluated if
constitutive models for the steel foam are not available. While the
material characterization experiments will provide constitutive
models for the as-produced foams, the computational models are
critical to evaluating the constitutive relations of novel
candidate microstructural designs.
3.3.4 Constitutive modeling: The ultimate goal of the material
testing program is to motivate and calibrate constitutive models
for steel foams that can be used in the computational simulations
of steel foam applications. Standard material properties (E, Est,
fy0.2, !y, fu, !u, etc.) as well as phenomenological
properties (Ramberg-Osgood parameters, etc.) will be developed
from the test results. Models for the monotonic constitutive
response and the cyclic constitutive response are required to allow
investigation of the intended breadth of applications.
Ramberg-Osgood, crushable foam (similar to von Mises plasticity),
and hyperfoam models (energy functionals similar to Mooney-Rivlin
models), all of which are readily available in commercial finite
element codes such as ABAQUS/ANSYS/ADINA, will be investigated as
potential monotonic models. The challenges in fitting a model to
the monotonic response center on the asymmetric response of foams
to tensile and compressive loading.
Figure 5: Simulated stress strain curves for steel
foam microstructures with elliptical voids. Bold
(red) line is reference continuum stress-strain
curve. Dashed lines are stress strain curves for
different material orientations. Light solid line is
reference stress strain curve for steel foam with
circular voids.
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Preliminary tests performed at UMass on aluminum foams show a
reasonably straightforward, symmetric, cyclic hysteretic response
under fully reversed loading, but under tension-tension and
compression-compression loading strain ratcheting has been observed
(Harte et al. 1999). This ratcheting is not reproduced by the
classical cyclic plasticity models. Bari and Hassan (2000) report
on the suitability of the Prager, Armstrong and Frederick,
Chaboche, Ohno-Wang and Guionnet models for modeling ratcheting,
and indicate that the Chaboche, Ohno-Wang, and Guionnet models
perform well. We will use these results to guide our cyclic
constitutive modeling in response to the experimental results.
3.3.5 Bolt bearing: A critical step in making steel foams useful
as a structural material is developing strong and ductile
connection details. Although preliminary studies on the structural
use of steel foam (Kremer et al. 2004) have shown that good quality
welds can be achieved and that adhesives provide another possible
connection method, the bolting of steel foams has not yet been
investigated. Because this proposal is focused on material
characterization and the demonstration of possible structural
applications, the scope does not include comprehensive testing of
connection details. The simulation tools described in the above
sections, which allow the comprehensive inelastic modeling of steel
foam response far past the elastic limit in tension and
compression, provide an opportunity to conduct preliminary
numerical investigations into the possibility of using bolts to
connect steel foam components to other steel foam components or to
solid steel components. We will investigate through simulation the
multiple bolt configuration shown in Fig. 6, with and without the
steel face sheets. Only the relatively high density of steel foams
makes bolted connections conceivable.
3.3.6 Model validation: The material characterization tests
described above provide the data required for validation of the
computational models we propose to develop. The models must be
validated with respect to their ability to predict the elastic
properties, yield points, densification strains, and tensile
failure strains measured in the experiments.
3.4 Computational material design
One of the objectives of this project is to demonstrate that
structural elements can be made of steel foam that deliver better
performance characteristics than their solid steel counterparts. We
intend that this demonstration, disseminated to the steel industry
through AISI and AISC, our industrial partners, will spur more
intense research and development on the metallurgical and
manufacturing aspects of steel foam. The materials design research
task makes preliminary exploration into the possibility of
designing the material microstructure to deliver desired
macroscopic material properties. Three specific material design
parameters are of interest to us in this project, the void size
distribution, void orientation distribution, and the possibility of
functionally grading the void size distribution and volume fraction
within a steel foam component.
For low density metallic foams the properties have been shown to
depend nearly completely on the relative density. This has not been
verified for higher density foams such as steel foams, leaving open
the possibility that, at the same relative density, different void
size distributions may deliver different macroscopic properties.
This seems particularly likely for fracture properties which are
known to depend on defect size. In steel foams the voids play the
role of defects. Figure 1 shows that anisotropic voids can be
generated in steel foams, and Fig. 5 shows how the properties
differ in the material directions of steel foams with anisotropic
voids. There may arise applications in which anisotropy of steel
foams with anisotropic voids can be advantageous to the material
performance. Finally, and potentially most importantly, functional
grading of the void size distribution could significantly enhance
the performance of steel foam components. For example, functional
gradation opens the possibility for tailoring the stiffness,
strength, and energy dissipation potential to the demands not only
component by component, but within components. Furthermore, the
possibility of generating, during the manufacturing process,
regions of very low or zero porosity would solve many challenges
relating to painting, corrosion
Fig. 6: Schematic bolt testing arrangement
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11
resistance, and fireproofing of the material. Figure 1 shows a
steel foam cylinder that is functionally graded by virtue of having
the foam expanded within a solid steel tube so that the porous
steel foam transitions to nonporous steel at the surface. Our
objective is to demonstrate how functional grading of a steel foam
could be beneficial to performance, and motivate development of a
process for directly manufacturing steel foams with functionally
graded void structures.
4 Application of Steel Foams to Steel Components and Systems
To understand the potential transformative benefits of steel
foams, the second major part of this proposal focuses on
applications, both at the component and system level. The materials
characterization and constitutive models from Section 3 provide a
means to meaningfully simulate steel foam. This ability will be
integrated with our existing research expertise in performing
material and geometric nonlinear analysis of steel components and
systems to provide accurate simulations demonstrating the resulting
behavior of structural systems comprised of, or modified by, steel
foams. The use of steel foams to significantly increase energy
dissipation and to mitigate local (cross-section) stability modes
will be the focus at the component level. The integration of steel
foams into braced frame systems (both cold-formed and hot-rolled)
and modern fuse-based framing systems will be the focus at the
systems level. The objective here is to use computational
simulation to explore and identify the most promising
applications for steel foams and then use these findings to
motivate future experimental studies in a continuing
collaboration with the industrial partners.
The primary activities within this task include:
• Calibration of baseline archetypes: A series of baseline
archetype steel structures will be defined, and parametric
variations will be established for a computational study of both
member archetypes and system archetypes that will benefit from
steel foam. Specific instances of what will be explored are
discussed below.
• Development of comparative performance metrics: Metrics will
be established to compare progression of damage and performance of
traditional steel structures versus those with foam. Future
cost/benefit assessments will also be included. Through this study,
the most effective uses of steel foam will be identified based on
the material characterizations of Section 3.
• Computational analysis of steel foam alternatives: We will
conduct both three-dimensional continuum analysis of members and
components as well as system-level analyses based on fiber analysis
procedures to study the detailed progression of damage, comparing
existing steel construction to the proposed, optimized use of steel
foam.
• Identification of target alternatives for future testing: This
research will establish a clear basis for the necessary next steps
in structural system testing needed to facilitate broader adoption
of steel foams.
The research team has significant experience both modeling and
testing the member archetypes: including steel plates, (e.g., Moen
and Schafer 2009; Schafer et al. 1998; Yu and Schafer 2006b; Hajjar
et al. 1998; Ye et al. 2000; Tort and Hajjar 2007), hot-rolled
W-sections (e.g., Schafer et al. 2000; Schafer and Seif 2008), and
cold-formed C-sections (e.g., Moen and Schafer 2008; Yu and Schafer
2003; Yu and Schafer 2006a; Yu and Schafer 2007) as illustrated in
Fig. 7. This experience will be utilized to build baseline
(a) FE model of hot-rolled steel FR
connection using shell and solid elements (Schafer et al.
2000)
(b) Testing and simulation of purlin-metal
shheeting, distortional failure (Yu and Schafer 2007)
Figure 7: FE modeling examples
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12
models (ABAQUS and/or ADINA FE models utilizing predominately
shell elements) for the performance of the archetypes that will
subsequently be modified through the use of steel foams.
The team also has extensive experience in static and dynamic
system analyses using stress-resultant space distributed plasticity
formulations that discretize the cross section into a grid of
fibers and track uniaxial stress-strain constitutive relations at
each fiber (Hajjar et al. 1998; Tort and Hajjar 2007). This
formulation includes a comprehensive bounding surface steel
plasticity model, already calibrated to baseline models of steel
beam-column strength, including the debilitating effects of local
buckling (Tort and Hajjar, 2007). The formulation will be
recalibrated to the constitutive response found in Section 3 for
appropriate foamed materials, thus enabling parametric
differentiation of the global static and dynamic response of
complete systems with and without the use of foamed components. In
the applications below, both static and dynamic loadings may be
investigated depending on the specific needs of the application. To
provide a basis for comparison, solutions that are generally
equivalent or lesser in weight (i.e., amount of material employed)
will be investigated. Detailed simulation will track damage
progression for example through the use of incremental dynamics
analysis (e.g., Vamvatsikos and Cornell 2004) in line with ATC-63
protocols (ATC 2009) to assess damage up to and include collapse
potential. We will examine the relative effects of mitigation of
buckling modes and favorable tension, compression, and shear cyclic
yielding capabilities for energy dissipation as compared to
traditional structural systems.
4.1 Member archetypes
To provide a means for baseline comparison a series of member
archetypes are selected for analysis and simulation: plate/sheet
steel, a hot-rolled steel W-section, and a cold-formed steel
C-section. Plate steel is a fundamental building block for existing
steel structures and provides a means to examine local buckling in
an isolated context. The W-section and C-section are the most
commonly used sections in hot-rolled and cold-formed steel
construction, respectively.
Two major modifications will be explored for the member
archetypes: (1) foaming the basic shape, and (2) adding foam
inserts to the member at critical locations. The local slenderness
of a steel plate in compression may be defined as
where ! = 0.7 typically defines the slenderness limit at
which
plates can develop their full yield capacity (! > 0.7 implies
a plate
with reduced capacity due to local buckling) and is found to be
a function of material properties: E, ", fy; loading and
boundary
Figure 8: Hot-rolled W-section (a) standard, (b) equal area
foamed to
50% relative density
Figure 10: (a) BRB braced frame after Sabelli et al. (2003) with
(b) BRBs replaced with steel foam links (c) buckling of a hollow
tube brace and (d) buckling of a steel foam filled brace – note
shorter wavelength buckling and a buckling resistance increased by
more than a factor of two.
Figure 9: Cold-formed steel stud buckling modes and potential
steel foam modifications: (a) global flexural-torsional buckling,
(b) distortional buckling, (c) local buckling, (d) full height foam
core insert, (e) end-only foam insert, and (f) intermediate foam
insert.
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13
conditions, k; and the basic geometry width, w, and thickness,
t. A foamed plate can have a significantly reduced ! for the same
amount of base material – consider the ratio of the slenderness of
a foamed plate,
!*, to the original plate, !.
While the effective properties (E*, "#, fy*) of the foamed plate
all change (and exact determination of this
change is an important outcome of the work of Section 3) the
dominant change is of the thickness, resulting in a stockier plate
for the same amount of material. As Fig. 8 illustrates for a
W-section foaming a cross-section can provide a steel member with
remarkably different properties: chief among them an increased
resistance to local buckling and the potential for much greater
energy dissipation.
Foaming the archetypal shape itself may not be necessary or
cost-effective in some situations. Instead, targeted application of
the steel foam may provide a more efficient use. In deep W-sections
or plate girders it may be advantageous to make the stiffeners of
steel foam bars, so that when buckling of the flanges occurs
compression in the stiffening bars will be engaged and significant
energy expended. In cold-formed steel sections a number of
potential uses for supplementary steel foams are envisioned as
shown in Fig. 9. Different foam inserts may be appropriate for
mitigation of each of the dominant cross-section buckling modes and
provide a means to stabilize the offending buckling modes, and to
expend far greater energy in such deformation modes when they
occur.
4.2 System (braced frame) archetypes
A systems-level archetype selected for additional study is the
braced frame. Hot-rolled steel braced frames suffer from a number
of difficulties that may be removed through innovative inclusion of
steel foam components. Similarly, cold-formed steel strap braced
shear walls (the braced frame analog in low-rise construction) have
poor seismic performance and deserve attention.
In seismic zones the conventional hot-rolled steel Special
Concentrically-Braced Frames (SCBF) suffer from having their
primary energy dissipation include cyclic buckling and tensioning
of the brace, often resulting in low cycle fatigue fractures (Uriz
and Mahin 2004; Uriz 2005). For this reason, buckling-restrained
braces (BRBs) have gained popularity in recent years (Sabelli 2004;
Xie 2005), including being incorporated into the national seismic
specifications for steel structures (AISC 2005). BRBs are highly
resilient members with strong potential to improve seismic
performance as compared to SCBFs. However, they are found to fail,
sometimes prematurely, either due to overall buckling of the brace
(Takeuchi et al. 2009) or, more likely, due to premature buckling
of the gusset plate (e.g., Takeuchi et al. 2004). Preliminary
exploration of an SCBF where steel foam links replace the brace or
BRB (Fig. 10) show the potential for excellent performance. In
addition, eccentrically braced frames currently rely upon heavily
stiffened shear links to dissipate energy. Recent research has
shown sensitivity of these links to premature fracture (Okazaki et
al. 2005). Preliminary assessment of the use of foamed links
without stiffeners, spliced into the girder outside link region,
will be conducted to explore an attractive alternative to the
fabrication and alleviation of stress concentrations seen in
current shear links.
For cold-formed steel construction the braced frame analog is
the strap braced shear wall (Fig. 11). Though a commonly used
system the failure mode in the absence of careful weld details or
reduced section braces is connection fracture. Even when the strap
remains intact, large strap deformations lead to severe pinching in
the hysteretic loops under even low numbers of cycles (Al-Kharat
and Rogers 2008). The inclusion of steel foams introduces the
possibility to provide inelastic deformations in the chords as well
as the diagonals. More radically, rather than include interior
studs, a foamed track distribution
strap braced shear wall
Figure 11: Light steel frame shear walls (Al-Kharat and Rogers
2008)
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14
member along with an optimally designed foam core might be
utilized in the plane of the shear wall. A variety of options will
be explored, including steel foam modifications to the corrugated
sheet steel shear wall pioneered by Tipping-Mar (Tipping and
Stojadinovic 2008) from our Industrial Advisory Board.
4.3 System (fuse-based) archetypes
The second system-level archetype selected for study is the new
modular fused-based framing system. A number of these new
structural systems have recently been proposed as alternatives to
conventional lateral-resistance systems in building structures,
particularly for seismic force resisting systems (SFRS). Modular
fused-based systems offer an attractive and robust alternative to
traditional systems concentrating damage in replaceable fuse
elements. The SFRS may often be decomposed into modular components,
permitting both the fuses and the SFRS as a whole to be optimized
for desired performance at progressively higher intensities of
loading. These systems are frequently coupled with a self-centering
mechanism, such as post-tensioning, thus eliminating residual
lateral drifts, facilitating replacement of the damaged fuses, and
ensuring the integrity of the lateral-resistance system after major
seismic events.
The use of modular, fused-based systems in steel structures
represents a fundamental departure from current seismic design
methods in which the girders, braces, columns, walls, and their
connections, all made from construction-grade materials, are relied
upon to absorb energy through inelastic deformations. Fused systems
are being explored both in hot-rolled and cold-formed steel
construction, we will explore the use of foamed material to form
the primary fuse mechanisms, as these can depend fundamentally on
reliable cyclic yielding for energy dissipation. Since the damage
is focused within the fuses, these fuses permit optimization for
the desired performance. Specifically, the fuse systems enable
tuning of the structural system to achieve stiff response (minimal
damage) under frequent loadings, inelastic energy dissipation under
moderate loadings, and pinched degrading response that preserves
self-centering under large (rare) loadings. Outside of the fuses,
the remainder of the SFRS structural system is then detailed to
avoid structural damage. With appropriate design and detailing a
variety of modular subassemblies may be developed to offer new
capabilities for efficient construction and safe designs.
Fuse-based systems thus offer a new opportunity for developing
simple design strategies and optimized configurations that ensure
outstanding structural performance with high reliability. An
example of a fused-system was studied by Prof. Hajjar and others
(Deierlein et al. 2009), consisting of two braced frames with
energy-dissipating fuses bolted between them and absorbing the
energy through cyclic inelastic shear (see Fig. 12). The fuses
consist of steel plates with diamond-shaped cutouts used to enhance
shear ductility. This research provides a foundation for
computational exploration in this work of fuse topologies that will
capitalize on the specific characteristics of steel foams to
provide primary energy dissipation in steel structures.
5 Administration
Work Plan: The research tasks are shown in Tab. 5. Prof.
Arwade’s primary tasks are materials characterization and
constitutive modeling of steel foams, while Profs. Schafer and
Hajjar focus on
Figure 13: Research team composition
Figure 12: Example of fuse-based structural system, (a)
schematic, (b) under test at Illinois, (c) hysteretic performance
and time history
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15
computational simulations to demonstrate the advantages of
introducing steel foams into conventional steel construction and
entirely new members and systems that fully utilize the advantage
of steel foams.
Research Team: The research team is described in Tab. 1 and Fig.
13. The Postdoctoral Researcher will be co-mentored by Profs.
Schafer and Hajjar (see supplementary mentoring plan). The research
team will utilize web conferencing, i.e., Adobe Acrobat Connect,
and virtual research spaces, e.g., Groupsite, (JHU provides free
subscriptions to both) to ensure smooth collaboration within the
research team.
Industrial Advisory
Board: An Industrial Advisory Board (IAB) has been assembled for
this project (Tab. 2). (All members have agreed to serve on the
IAB.) The IAB includes the major parties involved in constructional
steel for building structures (AISC, MBMA, AISI, SSMA), as well as
practicing engineers with significant expertise in cold-formed
steel structures (Trestain) and in hot-rolled steel structures,
rocking systems, and fused-based systems (Mar). The IAB will meet
in-person once a year and quarterly via web conference to ensure:
(a) industry feedback is provided and incorporated throughout the
project, (b) research findings are immediately shared with key
impacted industries, and (c) an initial consensus is achieved for
continuing this intensive two year project into a 2nd phase with
significant member and systems testing, and meaningful financial
involvement from industry.
6 Broader Impacts
The research team strongly believes in the importance of both
intellectual and sociological broader impacts. The intellectual
broader impacts stem from integration with engineering practice and
industry. The sociological broader impacts focus on an organized
cohort of undergraduate researchers and specific efforts to include
underrepresented minorities in the research team. A vertically
integrated research team spanning from high school (JHU),
undergraduate researchers (an organized cohort from all 3
universities), a Ph.D. student (UMass), a postdoctoral researcher
(Hopkins) and faculty at the Assistant (Arwade), Associate
(Schafer), and Full (Hajjar) levels is realized.
Integration with engineering practice and industry: The research
will be specifically disseminated outside of academia to practicing
engineers through the research team’s involvement with the IAB and
the specification committees that create the building design
standards for hot-rolled steel (AISC) and cold-formed steel (AISI),
which will be provided regular updates on the research, and have
indicated their support, specifically promising to support
“commercial delivery to the marketplace” (AISI), and to “help
provide fabrication expertise” (AISC). The research seeds an
intellectual partnership across the institutions, and across the
steel (hot-rolled and cold-formed steel) industry and research
communities. This project will demonstrate the practical
application of steel foams, jump starting their uptake in industry
and helping to bring an important material manufacturing
development to the civil infrastructure.
Table 5: Project GANTT Chart
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16
Undergraduate research cohort: an undergraduate will be part of
the research team at each school (UMass, JHU, UIUC). In addition to
working with their research mentor during the year, during the
summer after the first and second year the 3 students will be
combined and spend 1 month, as a cohort, at each of the three
schools. The students will therefore be engaged with the entire
project. The investigators will support this experience with other
funds if supplemental REU funds cannot be obtained.
Baltimore Polytechnical High School (Poly) Students Research
Practicum: a high school student from Poly will be included on the
research team at JHU. Prof. Schafer has a strong working
relationship with Ms. Sally Kutzer who runs the Research Practicum
program at Poly, a majority-minority public high school in
Baltimore City. This program pairs Poly students with research
experiences in universities. The students spend 20 hours a week in
the laboratory for an entire academic year. At the end of the two
semester sequence they provide an original research paper and oral
presentation. Prof. Schafer has hosted students in the past three
years, and is working with a student this academic year. The two
graduates from the program in Prof. Schafer’s group, both minority
women, contributed original research and are enrolled as full
scholarship students at JHU. Ms. Kutzer will help us identify a
Poly student for the research team.
Northeast Alliance for Graduate Education and the Professoriate
(NEAGEP): Recruiting for the graduate research positions at
UMass-Amherst will include a specific focus on underrepresented
minorities through UMass’s role as the lead institution in NEAGEP.
The NSF-funded NEAGEP includes dedicated staff for recruitment and
retention, funds for recruiting, summer programs, stipend support,
and support in mentoring programs, amongst other activities.
7 Results of Prior NSF support
Prof. Arwade: DMI-0423582 (9/04-8/07, $286,000) A framework for
microstructural design using Bayesian classifiers. The project aims
to develop techniques based on pattern recognition algorithms that
can be used in the rapid evaluation of the mechanical response of
material microstructures. Prof. Arwade, and co-PI T. Igusa and one
M.S. and one Ph.D. student (one a woman), developed reduced order
representations of random material microstructures that can render
microstructural design approaches more efficient. The project, has
resulted in 4 journal publications, 8 articles in peer-reviewed
conference proceedings, 8 conference presentations, and 4 invited
departmental seminars at various universities.
Prof. Schafer: CMMI-0448707 (5/2005-6/2010, $400,000) CAREER:
Structural Stability and Thin-walled Structures. The project
investigates (i) a novel decomposition technique of use in model
reduction and modal identification in structural stability
problems, and (ii) the practical extension and verification of
computational structural stability into design of thin-walled steel
members. Publications include fundamental advances in stability as
well as a re-examination of coupled instabilities in thin-walled
members and inelastic buckling of thin-walled bending members
totaling 7 journal publications and 13 refereed conference
proceedings. This grant supports 2 Ph.D. students, high school and
undergraduate researchers, and has led to the construction of a new
testing facility for thin-walled members.
Prof. Hajjar: CMS-0084848 (9/2000-8/2006, $206,142) Performance
Based Design Methodology for Composite Construction with
Application to Concrete-Filled Steel Tube Structural Systems. A 3D
fiber-based distributed plasticity mixed finite beam element
formulation was developed to simulate the nonlinear dynamic
response of rectangular concrete-filled steel tube (RCFT)
beam-columns, steel girders, and steel braces as part of frame
structures. The finite element has separate translational
degrees-of-freedoms defined for the concrete core and the steel
tube to simulate slip deformation. Cyclic constitutive relations
were derived accounting for slip, confinement and local buckling.
The work was validated against over one hundred experiments in the
literature. Representative composite frames were analyzed under a
suite of ground motion records to quantify the demand imposed on
the RCFT columns. The project supported one Ph.D. student and one
M.S. student and 6 journal articles have appeared.
See the investigator biographical sketches for representative
publications resulting from these projects.
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1
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