AAB Proposal : Large scale simulation of dynamic fracture
events
P.I. : Philippe H. Geubelle
Department
of Aeronautical and Astronautical Engineering
University
of Illinois at Urbana-Champaign
1. Summary of research.
The field of dynamic fracture constitutes
one of the most challenging current research topics in theoretical,
computational and experimental solid mechanics. At the experimental level, the
problem complexity is associated with the visualization and measurement of very
fast cracks running at speeds of hundreds of meters per second, in fracture
events typically lasting only a small fraction of a second, which requires very
sensitive optical techniques and high speed recording devices. The theoretical
analysis of dynamic fracture effects has proven to be much more complex than in
the quasi-static situation due to the appearance of complex stress wave
patterns associated with the hyperbolic equations of motion and the inherent
nonlinearity created by continuously evolving geometries. These facts have
limited most analytical investigations to two-dimensional geometries, simple
(linearly elastic) material models, prescribed crack motion and time domains
often limited to the early dynamic events (Freund, 1990).
The computational approach has therefore
provided an alternative to extend the analysis to more complex geometries, more
realistic material models, spontaneous crack propagation problems with longer
duration of the simulations. Among the various methods used in dynamic fracture
problems during the past two decades, the finite element method has proven to
be the most versatile to tackle complex geometries and material behaviors while
the boundary integral scheme has been shown to be more efficient in handling dynamic
fracture problems of larger size but simpler geometries and material models
(see Geubelle and Rice, 1995, for a review of previous numerical work).
The computational approach is, however, also
confronted with many challenges associated with the following conflicting
requirements : On one hand, a high degree of refinement in both the space- and
time-discretizations is needed to accurately represent arbitrarily moving
singularities and discontinuities associated with the traveling crack tips and
stress waves, while, on the other hand, large domains of analysis are required
to reduce the interactions due to finite boundaries. Furthermore, if the use of
non-uniform spatial discretization, refined in singularity and discontinuity
regions and coarser in the rest of the domain, appears as a natural way to
reduce the size of the problem, the complexity of remeshing procedures needed
to cope with continuously evolving geometries is often overwhelming, especially
in three-dimensional situations. These facts have once again limited most
numerical analyses to two-dimensional situations or to very coarse (and thereby
rather imprecise) three-dimensional discretized domains.
We propose to further develop, implement and
optimize two distinct methods specially adapted to study large complex dynamic
fracture events. The first one, based on a spectral form of the elastodynamic
boundary integral formulation and referred to as spectral scheme, aims
at the simulation of a class of fundamental dynamic fracture problems involving
the spontaneous initiation, propagation and arrest of planar cracks and
faults embedded in homogeneous or bimaterial (visco)elastic infinite domains.
The second scheme is an extension of a special finite element scheme (referred
hereafter as the cohesive/volumetric finite element (CVFE) scheme),
which also allows for the simulation of a wide range of dynamic fracture events
and has been successfully used by various research groups over the past few
years (Camacho and Ortiz, 1996; Xu and Needleman, 1994, 1996ab; Geubelle and
Baylor, 1998). These two methods are described in the second section of this
proposal.
In the remainder of this section, we
describe three applications in which we plan to use these two methods. The
first one is related to the NSF funded investigation of the mechanics of fiber
pull-out and push-out in a composite materials. The second project, also funded
by NSF through the CAREER Young Faculty Development Program, aims at the
numerical simulation of the high speed grinding of structural ceramic
materials. The third and final project, currently funded by the P.I.'s start-up
funds, aims at extending the aforementioned spectral scheme to two classes of
fundamental elastodynamic problems: the mechanics of rigid-punch impact and
that of crack propagation in a layered material.
Application 1 : Dynamic fiber pull-out in
model composite systems
The failure of continuous fiber reinforced
polymeric (CFRP) and ceramic (CFRC) composite structures subjected to dynamic
loading is a very complex process involving five basic mechanisms :
matrix cracking, delamination, fiber/matrix debonding, fiber breakage and
fiber pull-out. The relative importance of these five mechanisms depends on
loading rate : while matrix cracking and delamination are the primary
mechanisms leading to dynamic failure of polymeric matrix composites under low
velocity impact (i.e., impact for which the duration of loading is much longer
than the travel time of elastic waves in the structure), fiber/matrix debonding
and subsequent fiber pull-out are the two leading sources of energy absorption
under high velocity impact conditions (Abrate, 1991).
In the latter situation, the energy
absorption mechanisms are similar to those observed during quasi-static
propagation of a crack perpendicular to the fiber direction. These mechanisms
are associated with bridging of the crack by partially debonded, unbroken
fibers present in its wake. Because of the important effect it has on the
fracture toughness of a composite, the process of progressive debonding and
pull-out of the bridging fibers has been the subject of extensive experimental
and analytical work. On the experimental side, both fiber pull-out and push-out
tests are most often conducted with model composites involving fibers two
orders of magnitude larger than actual ones. However, the vast majority of
existing work on this topic has been limited to quasi-static loading
situations. The few investigations involving dynamic loading recently performed
on certain composite systems seem to indicate that the dynamic fiber pull-out
process presents some unusual and sometimes contradictory characteristics
(Khanna and Shukla, 1994; Klopp and Crocker, 1994; Lankford et al.;
1992).
The present proposal aims at obtaining the
computational resources needed to support the computational part of a combined
experimental/analytical research project dedicated to dynamic fiber pull-out.
The primary objective of this project is to enhance, through detailed
experiments and numerical simulations, the current understanding of dynamic
fiber debonding and frictional pull-out in CFRP and CFRC composites. An
improved understanding of how these two failure mechanisms take place and how
they are affected by key loading, material and geometry-related parameters is a
mandatory step toward the successful design of impact tolerant composite
structures.
With regards to the numerical aspects of the
problem, the problem of debonding and fiber pull-out/push-out is intrinsically
non-linear, since the domain of investigation changes continuously as the
debonding crack front propagates along the fiber/matrix interface. Furthermore,
the incorporation of the inertial effects associated with the high strain rate
transient loading conditions render the problem particularly complex, and numerical
simulations are the only recourse to study this problem.
In the proposed computational project, the
most challenging analytical task is undoubtedly the simulation of the failure
process itself, which, as was mentioned before, includes two distinct phases:
fiber debonding and frictional sliding. An accurate description of each
of these two phenomena is essential to determine their relative
importance in the energy absorption process, as was emphasized in a recent
paper dedicated to the quasi-static fiber pull-out/push-out process in a model
polyester/epoxy composite system (Lin, Geubelle and Sottos, 1998),
All existing quasi-static models of the
fiber pull-out process have emphasized the primordial role of the friction
model (Povirk and Needleman, 1993; Tsai and Kim, 1996; Tandon and Pagano,
1996). The classical constant coefficient Coulomb friction model is inadequate
to capture the observed stick/slip process and more complex models including a
dependence of the friction coefficient on the slip rate are required. One of
the main objectives of the proposed analytical work will be to investigate the
behavior of these various models under dynamic conditions and to correlate them
to the dynamic fiber pull-out/push-out experiments performed at the University
of Delaware by Prof. Lambros' group.
Another important aspect of the simulation
of the fiber debonding process is the capture of the stress concentration
associated with the advancing debond front. This approach is more involved than
the so-called "shear lag" theory (Hutchinson and Jensen, 1990; Liang
and Hutchinson, 1993) based on a uniform distribution of the shear stress at
the fiber/matrix interface, but is needed to accurately model the spontaneous
propagation of the debond crack from one or sometimes both ends of the fiber
(Morrison et al., 1988; Bechel and Sottos, 1996).
The successful completion of the research
project will be an important preliminary step in the design of more impact
resistant composite structures, especially in situations where a dynamic crack
is expected to propagate perpendicularly to the fiber. As in the quasi-static
loading situation, fracture resistance of fiber reinforced composites
under high speed impact will only be improved through a detailed understanding
of the fiber bridging process, and in particular, the crucial role of the
fiber/matrix interface : if the latter is chosen too weak, the composite will
offer very little resistance to the fiber pull-out; if the interface is too
strong, very little energy will be absorbed in the debonding and pull-out
process, thereby decreasing the overall toughness of the composite (Kim and
Mai, 1991). The proposed work will shed new light on the fundamental role that
loading rate is expected to play in this composite design process.
Application 2 : High speed grinding of
ceramics
Due to their high specific strength and
their excellent thermal, chemical and wear resistance, ceramic materials are
increasingly considered for a wide range of high temperature and high stress
applications such as engine parts, turbine blades and cutting tools, in
addition to their well established role in optical and electronic components.
The use of advanced ceramics for structural applications alone is expected to
represent more than $1 billion in 2000, growing annually at an average rate of
13% (Li and Liao, 1996).
Many
of the applications in which this class of materials are involved require high
dimensional accuracy and/or surface finish. Although new techniques such as
ultrasonic, electro-discharge and laser beam machining have been proposed, the
most common approaches are still fairly conventional : grinding, lapping and
polishing (Klocke, 1996). However, the brittleness of ceramic materials renders
their machining more complicated than in metals, as the material removal
process is often accompanied with residual radial micro-cracks appearing in the
vicinity of the machined surface, and even macro-cracks penetrating deeper
inside the component. This residual damage may have a strong influence on the performance
of the machined part (Li and Liao, 1996; Liu et al., 1996; Esposito et
al., 1997) and extensive efforts have been spent over the past couple of
decades to understand, predict and eventually minimize the appearance of these
detrimental residual cracks.
High
speed grinding, involving wheel rotation speed in excess of 20,000 rpm and
contact times in the 10...100 ms range, is increasingly being considered not only to
improve the productivity of the surface machining process, but also as a way to
reduce the amount of residual damage(Malkin and Ritter, 1989). However, the
high strain rates (greater than 1000/s) involved in this class of processes
render most of the existing analytical tools inadequate: additional effects
such as inertia, frictional heating and rate dependence must be included in the
analysis. Furthermore, the existing analytical models, mostly based on static
continuum-level indentation solutions, are often oversimplified in their
description of the complex interactions between the various damage processes
taking place in the vicinity of the tool/part interface, and always involve a
single grit system.
This
particular research project aims at providing a more realistic description of the
ceramics grinding process, by including dynamic thermo-mechanical effects, by
accounting for the granular microstructure of the ceramics and by allowing the
presence of more than one abrasive particle. It is clear that the capture of
effects as diverse and complex as 3D crack interaction, ceramics
microstructure, rate sensitivity, frictional heating, localized plasticity and
inertia requires the use of advanced numerical methods. The development and
implementation of an advanced numerical tool able to capture the spontaneous
initiation, propagation and arrest of a large number of cracks during a scratch
test under high strain rate conditions is the primary objective of the research
project.
Application 3 : Fundamental problems in
rigid punch impact and failure of a layered structure
As indicated earlier, the spectral scheme
has proven over the past few years to be an extremely valuable tool to study
various fundamental 2D and 3D dynamic fracture problems involving planar crack
and faults of arbitrary shapes, embedded in an infinite homogeneous or
bimaterial medium and subjected to any combination of space- and time-dependent
tensile and shear loading conditions. With the successful completion of the
parallel optimization efforts achieved over the past few months by Scot
Breitenfeld and Geubelle (1998) (see Section 3 and attached paper), the
spectral code is probably the most powerful numerical tool available to date to
simulate this class of problems, providing an unprecedented amount of details
on the failure process taking place in the immediate vicinity of the rapidly
advancing crack front.
The objective of this third project is to
extend the range of applicability of the spectral scheme to two new class of
dynamic fracture problems. In the first one, the domain containing the planar
crack will not be required to be of infinite extent, but of finite
"thickness" perpendicular to the fracture plane. This would be of
great interest for geophysical applications for which the wave reflections due
to the presence of the earth surface, and in applied mechanics for the
treatment of the dynamic failure of layered media often used in vibration
absorbing structures.
The second extension of the spectral scheme
is concerned with a very precise simulation of the classical problem is the
dynamic impact of a rigid punch of arbitrary shape with a (visco)elastic
medium. Although this problem does not exactly constitute a dynamic fracture
event per se, it shares many similarities with the fracture problems.
For example, both problems are characterized by the presence of strong stress
concentrations, and sometimes of stress singularities. While the basic spectral
formulation of the (visco)elastodynamic boundary integral relations will need
to be modified as indicated in the next section, we believe that the resulting
impact spectral scheme will be very similar to that developed for the dynamic
fracture problem.
2. Computational methodology.
As indicated before, the first numerical
method is a cohesive/volumetric finite element scheme (CVFE) recently used by
Xu and Needleman (1994) and Camacho and Ortiz (1996) to simulate various
dynamic fracture events in brittle materials. The method is based on a surface
cohesive model in which the continuum is characterized by two constitutive
relations : a volumetric constitutive model describing the "bulk
behavior" of the material, and a cohesive surface constitutive relation
between the tractions and displacement jumps which characterizes the behavior
of the bond surfaces between elements. By providing the "element
boundaries" with a cohesive-type model, the scheme allows for the spontaneous
creation of new surfaces, including non-coplanar crack extension. In essence,
each finite element is "tied" to its neighbors though a series of nonlinear
"springs" which governs its interaction with its surrounding (Figure
1). The creation of an internal surface is thus associated with the failure of
a number of these springs. Since the failure of the bonds will involve both
tensile and shear loading, special care must be taken to allow for the
mixed-mode decohesion process. Triangular elements are typically used to
maximize the number of potential crack extension sites.
The cohesive failure is described by a
traction-separation law which can take various forms : Xu and Needleman (1994)
used a phenomenological potential-based relation in which the tractions are
expressed as derivatives of a scalar potential with respect to the displacement
jump across the cohesive element.
Camacho and Ortiz (1996) introduced a simple linear
decohesion law in which the normal and shear tractions acting on the
inter-element surfaces decrease linearly with the normal and tangential
displacement discontinuities. Unlike Xu and Needleman, Camacho and Ortiz
introduced an internal variable to characterize the maximum damage level
previously achieved and to prevent rehealing of the fracture surfaces. However,
their formulation "decoupled" the tensile and shear responses of the
cohesive elements. The P.I. and his co-workers (Geubelle and Baylor, 1998; Lin et
al., 1998) have instead adopted the following coupled quasi-linear
traction-separation law
(2)
where Tn and Tt
denote the tensile and shear tractions, respectively; Dn and Dt are the normal and tangential displacement jumps; dn and dt are critical values of the displacement
discontinuities beyond which complete failure is assumed; smax and tmax
are the maximum attainable values of the tensile and shear tractions; S
is the coupling internal damage variable ranging from 0 to 1
, (3)
where 
denotes a if a is
positive and 0 otherwise. The cohesive failure model described by (2) and (3)
is illustrated in Figure 2.
Figure
2. Cohesive failure model described by (2) and (3).
The remainder of CVFE implementation is
fairly conventional : it involves an explicit time stepping scheme (Belytschko et
al., 1976) and large deformation kinematics, as large rotations of elements
can take place as cracks propagate spontaneously in the discretized domain.
The combination of volumetric and cohesive
finite elements has been shown to be very successful in capturing a wide range
of phenomena taking place in the dynamic failure of homogeneous and bimaterial
brittle systems, including the onset of crack branching (Xu and Needleman,
1994), the spontaneous dynamic debonding of bimaterial interfaces (Xu and
Needleman, 1996ab), the fragmentation of brittle ceramic specimen under impact
(Camacho and Ortiz, 1996), the effect of viscoplasticity on spontaneous dynamic
fracture (Siegmund and Needleman, 1997), and the impact-induced delamination of
composite plates (Geubelle and Baylor, 1997). As shown by Camacho and Ortiz
(1996), this scheme can be combined with a contact algorithm to capture
frictional contact. The implementation of an efficient contact algorithm able
to capture the possible interaction between the spontaneously created
fracture surfaces is often one of the most challenging aspects of a dynamic
fracture code. This task is however simplified in the fiber pull-out/push-out
case since the fracture surfaces (i.e., the cohesive elements) will be limited
to the fiber/matrix interface (for adhesive failure cases), or its immediate
vicinity (for cohesive failure of the interphase region). Finally, if experimental
observations indicate that the friction-induced thermal effect plays an
important role in the process, a thermal component will be added in the finite
element simulations, converting the frictional energy into heat following the
scheme employed by Camacho and Ortiz (1996).
The second numerical scheme to be used in
this project is an extension of a spectral scheme recently developed and
implemented by Geubelle and Rice (1995) to investigate a wide range of 2D and
3D dynamic fracture problems. The numerical scheme is a special form of the
boundary integral method and is based on an exact spectral representation of
the elastodynamic relations between the traction stresses acting on the
fracture surface and the associated displacement discontinuities. The scheme is
based on the following form of the elastodynamic equations expressed on the
fracture plane 
, (4)
where 
are the traction stress
components on the fracture plane; 
are the externally applied traction stresses; 
are the
displacement discontinuity (or crack opening displacement COD) components; 
is a material
dependent diagonal matrix and 
are linear functionals of the history of the COD
up to the present time. In most boundary integral formulations, these
functionals take the form of a triple convolution integral (over time and over
the two spatial coordinates 
and 
spanning the fracture plane). However, in the
spectral formulation, these functionals are expressed in the spectral domain,
and only a convolution integral in time (over the past COD history) is needed. The
convolution kernels for the fracture modes I, II and III have been derived
analytically in the homogeneous linearly elastic situation by Geubelle and Rice
(1995), and the formulation has been recently extended by Geubelle and
Breitenfeld (1997) and Breitenfeld and Geubelle (1997) to 2D and 3D dynamic
fracture problems of interfaces, and by Geubelle and co-workers (Geubelle et
al., 1997; Danyluk et al., 1998) to viscoelastodynamics.
One of the main advantages of the method is its
great flexibility in the choice of failure and friction models. The spectral
scheme has for example been successfully used by Perrin et al. (1995) to
investigate the effects of a special form of the aforementioned state- and
rate-dependent friction model on the propagation of a pulse in the simpler
homogeneous 2D anti-plane shear condition. Other advantages of the spectral
scheme are its relative simplicity compared to other boundary integral schemes,
and its adaptability to massively parallel computing architectures, which
allows for the simulation of large scale detailed problems, as discussed in the
summary of the extensive optimization work described in next section.
3. Preliminary results and optimization
efforts.
This section describes some of the early
results obtained with the two numerical schemes with regards to the code
development and optimization.
3.1. Cohesive/volumetric finite element
scheme
Over the past few years, our group has
gained of lot of experience with the CVFE scheme which we have applied it to
various quasi-static and dynamic fracture problems (Geubelle and Baylor, 1998;
Lin et al., 1998). An example of these applications can be seen on
Figure 3 which presents a snapshot of the failure process taking place during
the impact-induced delamination of a [06/904/06]
graphite epoxy composite plate.
Figure
3. Delamination of a cantilever composite plate subjected to an impact line
load.
The
cohesive elements placed in the 90• plies and along the interfaces are able to
capture
both
the initiation and propagation of the delamination fronts. (Taken from Geubelle
and Baylor, 1998)
During the past few months, our efforts have
been dedicated to adapting the CVFE to applications described in Section 1.
Typical preliminary result obtained in the dynamic fiber pull-out/push-out
project is shown in Figure 4. Although these results have been obtained with a
fairly coarse mesh and do not account for the frictional contact taking place
between the newly created fracture surfaces, these preliminary studies seem to
indicate that the numerical scheme can provide valuable information on the
failure process. Also missing in the current numerical model are the thermal
effects associated with the frictional heating generated during the sliding of
the fiber out of the surrounding matrix. These effects will be particularly
important in the fiber pushout case.
The use of finer discretization, the
incorporation of more complex thermo-mechanical model and the capture of the
frictional contact will undoubtedly greatly increase the computational
requirements of this type of simulations. Furthermore, a systematic parametric
study will have to be performed to study the effects of material mismatch,
residual stresses, interfacial properties, fiber roughness, ... The parallel
implementation of the CVFE explicit structural code is therefore an important
part of our current efforts. While our initial approach (used by Jeff Baylor in
the numerical simulation of impact-induced delamination of composites) was
based on explicit optimization directives available on the Exemplar, we have
decided to orient our optimization efforts toward a more portable MPI
implementation and a mesh partitioning technique (we are currently using METIS,
the public-domain partitioning code).
Figure 4. Dynamic fiber pull-out in a model
polyester/epoxy composite, showing the rapid spontaneous propagation of a
debonding crack along the fiber/matrix interface. As shown by the contour of
the shear stress, the numerical scheme is able to capture the stress
concentration associated with the rapidly propagating crack front.
Dimensions are given in mm, and the shear stress in MPa.
With regards to the second project in which
the CVFE scheme will be used, i. e., the simulation of high-speed grinding of
structural ceramics, the initial implementation efforts have been mostly
dedicated to the mesh generation issue, as cohesive elements must be introduced
along the grain boundaries, while conventional volumetric elements are used to
discretize the grains themselves. Since the presence of a granular
microstructure introduces a new length scale in the problem, preliminary
simulations performed on a small domain have been dedicated on a convergence
study of the grain-based CVFE scheme. A typical result is shown in Figure 5,
which shows the extent of intergranular fracture damage associated with a
sudden tensile loading of a ceramic plate.
The efficient implementation of the CVFE
scheme on a massively parallel computing platform is also essential in this
particular problem, especially as larger domains and fully 3D simulations are
planned in the future.
Figure 5. Integranular failure process associated with the
sudden tensile loading of a pre-notched ceramic plate. The thicker segments
correspond to the grain boundarties which failed as the intergranular cracks
propagated through the domain.
3.2. Spectral scheme
Initial progress has also been achieved in
the further development of the spectral scheme. To address the issue of a
spectral formulation for finite domains, preliminary efforts have been
dedicated to the computation of quantities off the fracture planes. A spectral
formulation, similar to that described by (4), has been derived to compute the
displacement and stress fields along planes parallel to the fracture plane. An
example of some recent results obtained with the spectral scheme for a mode III
bimaterial problem is shown in Figure 6, which presents a snapshot of the
stress and displacement distribution in the vicinity of an spontaneously
propagating interfacial crack. Note the presence of the stress singularity
associated with the non-moving crack tip (left) and the stress concentration
present in the vicinity of the propagating right crack tip.
Figure 6. Full-field d stress distribution in the vicinity
of a spontaneously propagating mode III interfacial crack, showing the emission
of waves from the advancing crack. Note the precision with which the numerical
scheme captures the various wave fronts appearing in the stiffer (top) and more
compliant (bottom) materials.
As indicated earlier, we have achieved major
progress over the past year or so in the parallel implementation of the
spectral dynamic fracture code. The details of the parallel implementation
approach are summarized in a recently completed paper (Breitenfeld and
Geubelle, 1998) attached to this proposal, and will not be repeated in this
proposal. Let's just indicated that the parallel implementation has allowed us
to investigate problems involving an extremely fine spatial discretization of
the fracture plane (with a spatial grid involving more than 16 million grid
points) and long durations (more than 20,000 time steps). This undoubtedly
makes the spectral scheme the most efficient boundary integral-based numerical
scheme for this class of problem.
4. Justification for service units
requested.
Although both the CVFE and spectral schemes
are basically explicit structural numerical methods, their "computing
resource requirements" are quite different.
On one hand, the CVFE scheme requires a very
large number of degrees of freedom, as the presence of the cohesive elements
greatly increases the number of nodes present in the discretization, and
thereby the number of degrees of freedom. In order to accurately capture the
cohesive failure process, including the stress concentration present in the
vicinity of the spontaneously propagating crack tip(s), a fine discretization
is also usually needed. Finally, the use of the explicit time stepping scheme
needed to capture the various elastic waves and to "follow" the
cohesive failure process requires the introduction of very small values for the
time step (typically, a fraction of the well known Courant stability condition,
i.e., a fraction of the time needed for a wave to travel across the smallest
element). A CVFE simulation therefore requires a substantial amount of degrees
of freedom and time steps (both typically well over 106), and the
method is particularly suitable for very detailed numerical analyses of very
short dynamic fracture events (with a total duration of less than 1 msec.).
Based on previous experience with the first parallel implementation of the CVFE
code (using parallel directives) and on our need to perform many runs needed to
investigate the effects of the many parameters involved in the dynamic fiber
pull-out process (normal load, friction law, material mismatch, loading rate,
...) and in the ceramics grinding grinding problem (grain size, grit motion,
...), about 10,000 S.U. are requested for the CVFE part of the project.
However, since the numerical method involves an explicit time stepping scheme,
and therefore does not necessitate the creation and storage of a large
stiffness matrix, the memory requirement associated with this scheme is
relatively limited (approximately 5 GB). This should be largely sufficient to
handle the large vectors containing the displacements, velocities,
accelerations, internal forces and cohesive forces at each node, together with
the coordinate and connectivity table arrays, even in the 3D situation.
As indicated earlier, the main limitation of
the 3D spectral scheme is the associated memory requirement. This has motivated
some of our recent optimization efforts (see previous section). A typical size
run involving a spatial grid with 1024*1024 points and 10,000 time steps
requires approximately 16 GB of memory on 128 nodes and "consumes"
approximately 240 S.U. (for about 1 hour on a dedicated queue). Since the main
objective of the spectral code part of this project is the development of the
method, we do not expect to run many very large problems during the next twelve
months. About 2000 S.U. are requested for this part of the project.
5. Local computing environment and
post-processing.
The P.I. and his research group have access
to 7 HP C180 (each with 128 MB RAM, 4 GB disk space and 24 bit accelerated
graphic card) UNIX workstations on which the code development and the pre- and
post-processing work will be performed. An additional 16 GB harddrive has also
been purchased recently.
One of the main difficulties associated with
the finite element simulations of dynamic problems is the vast amount of data
generated by a single run, which need to be processed. This task will be
performed locally using the TECPLOT post-processing package (with 3D
extension), which has animation capabilities.
6. Other supercomputing support for this
or related projects.
A year ago, the P.I.'s research group was
allocated 18,000 S.U. on the NCSA Origin 2000 and 6666 S.U. on the Exemplar
under the project name 'qme'. The applications involved in the 'qme' project
were somewhat different than those presented here, with more emphasis on the
impact-induced delamination of composites and on the fiber pull-out process.
But the basic objectives of the 'qme' project are similar to those of the
present proposal, i. e., the development, implementation, optimization and
application of the CVFE and spectral schemes for large scale dynamic fracture
simulations. The project has resulted in various publications which have been
attached to this proposal. Slightly over 10,000 S.U. have been used on the
Origin 2000, where most of the optimization work described in Breitenfeld and
Geubelle (1998) have been performed. This explains why we have decided to
reduce our request to 12,000 S.U. for this year.
One of the main difficulties associated with
the finite element simulations of dynamic problems is the vast amount of data
generated by a single run, which need to be processed. This task will be
performed locally using the TECPLOT post-processing package (with 3D
extension), which has animation capabilities.
7. Qualifications of principal
investigator
The postdoctoral research fellow (Dr.
Changyu Hwang) and the graduate students (Scot Breitenfeld, Dhirendra Kubair,
Spandan Maiti, Xiaopeng Bi) involved in the project already have extensive
experience in numerical simulations of complex solid mechanics problems. Most
of them have already attended the parallel computing workshops organized at
NCSA and/or have received a formal training on parallel computing by taking the
CSE 302 course offered on campus.
As described in the biographical data
attached to this proposal, the P.I. has an extensive experience in various
aspects of fracture mechanics and in the development of numerical methods and
their implementation on various supercomputing platforms.
8. References
Abrate, S. (1991) "Impact on laminated
composite materials". Appl. Mech. Rev., 44 (4), 155-190.
Bechel, V. T. and Sottos, N. R. (1996)
"Measuring debond length in the fiber pushout experiment". TAM Report
832, University of Illinois at Urbana-Champaign, submitted to J. Mech. Phys.
Solids.
Belytschko, T., Chiapetta, R. L. and Bartel,
H. D. (1976) "Efficient large scale non-linear transient analysis by
finite elements". Int. J. Numer. Meth. Eng., 10, 579-596.
Breitenfeld, M. S. and Geubelle, P. H.
(1997) "Numerical analysis of dynamic debonding under 2D in-plane and 3D
loading". To appear in Int. J. Fracture.
Breitenfeld, M. S. and Geubelle, P. H.
(1998) "Parallel implementation of a spectral scheme for the simulation of
3D dynamic fracture events". Submitted to Int. J. Supercomp. Appl.
& High Performance Computing.
Camacho, G. T. and Ortiz, M. (1996)
"Computational modelling of impact damage in brittle materials", Int.
J. Solids Structures, 33 (20-22), 2899-2938.
Esposito, L., Tucci, A. and Andalo, G.
(1997) "Surface finish and mechanical properties of commercial
Aluminas". J. Eur. Ceram. Soc., 17, 479-486.
Freund, L. B. (1990) "Dynamic fracture
mechanics", Cambridge University Press.
Geubelle, P.H., (1994), "Implementation
of a 3D elastodynamic boundary-integral code on the CM-5". Harvard
Mech-240 Report, Harvard University.
Geubelle, P. H. and Baylor, J. (1998)
"Impact-induced delamination of composites: a 2D simulation". Composites
B, 29B, 589-602.
Geubelle, P. H. and Breitenfeld, M. S.
(1997) "Numerical analysis of dynamic debonding under anti-plane shear
loading". Int. J. Fracture, 85, 265-282.
Geubelle, P.H. and Rice, J.R. (1995) "A
spectral method for 3D elastodynamic fracture problems". J. Mech. Phys.
Solids, 43:11, 1791-1824.
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"Surface/subsurface damage and the fracture strength of ground
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(1998) "Simulation of fiber debonding and frictional sliding in a model
composite pushout test". Submitted to Int. J. Solids Structures.
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ATTACHMENTS
A.1 P.I.--Philippe H. Geubelle:
curriculum vitae
Education :
6/93 Ph.D. in Aeronautics, California Institute
of Technology, Pasadena, CA
Minor
in Material Sciences
Thesis
: "Nonlinear effects in interfacial fracture"
Advisor
: Professor Wolfgang G. Knauss
6/89 M.Sc. in Aeronautics, California Institute
of Technology, Pasadena, CA
6/88 B.Sc. in Mechanical Engineering,
Louvain-la-Neuve, Belgium
Thesis
: "Numerical modeling of diaphragm forming of composite plates"
Research Experience :
1/95
- Assistant Professor, Department of
Aeronautical and Astronautical Engineering, University of Illinois at
Urbana-Champaign; CSE Faculty Member
Joint
appointments in Mechanical and Industrial Eng. Dept., Theoretical and Applied
Mechanics Dept. and at NCSA
Class
taught : Aircraft Structures II (AAE221), Computational Methods in Aerospace
Engineering (AAE391CM), Finite Element Analysis of Aerospace Structures
(AAE320), Fracture Mechanics (AAE493FM).
93-94 Post-Doctoral Research Associate, Harvard
University, Cambridge, MA
In
collaboration with Professor James R. Rice
Research
topics : analytical and numerical analysis of three-dimensional dynamic
fracture problems and adaptation to a massively parallel computer
89-93 Graduate Research Associate, California
Institute of Technology, Pasadena, CA
Research
topics : theoretical (asymptotic) and numerical (finite element) analysis of
geometrical and material-related nonlinearities in quasi-static homogeneous and
bimaterial fracture
Honors and Awards :
NSF
CAREER Award 98
AIAA
Teacher of the Year Award 98
List
of Teachers Recognized as Excellent by their Students 95, 96, 97
NATO
Postdoctoral Fellowship 93-94
Ballhaus
Prize for Oustanding Doctoral Dissertation, Caltech 6/93
Sechler
Prize for Oustanding Contribution to Research, Caltech 6/92
Josephine
de Karman Fellowship 91-92
Belgian
American Educational Foundation Fellowship 88-89
List of Publications: (the publications
involving large scale computations performed on supercomputer are denoted by an
asterisk)
Geubelle,
P. H. and Knauss, W. G. (1994) "Crack propagation at and near bimaterial
interfaces : linear analysis". ASME J. Appl. Mech., 61,
560-566.
* Geubelle,
P. H. and Knauss, W. G. (1995) "Crack propagation at and near bimaterial
interfaces under general loading : nonlinear analysis". ASME J. Appl.
Mech., 62:3, 601-606
* Geubelle,
P. H. and Knauss, W. G. (1994) "Finite strains at the tip of a crack in a
sheet of hyperelastic material : 1. Homogeneous case". J.
Elasticity, 35, 31-98.
* Geubelle,
P. H. and Knauss, W. G. (1994) "Finite strains at the tip of a crack in a
sheet of hyperelastic material : 2. Special bimaterial cases". J.
Elasticity, 35, 99-137.
* Geubelle,
P. H. and Knauss, W. G. (1994) "Finite strains at the tip of a crack in a
sheet of hyperelastic material : 3. General bimaterial case". J.
Elasticity, 35, 139-174.
Geubelle, P. H. and Knauss, W. G. (1995)
"A note related to energy-release rate computations for kinking interface
cracks". ASME J. Appl. Mech., 62:1, 266-267.
Geubelle,
P. H. (1995) "Finite deformation effects in homogeneous and interfacial
fracture". Int. J. Solids Structures, 36:6/7, 1003-1016.
* Geubelle,
P. H. (1994) "Implementation of a 3D elastodynamic boundary-integral code
on the CM-5". Mech-240 Report, Division of Applied Sciences, Harvard
University.
* Geubelle,
P. H. and Rice, J. R. (1995) "A spectral method for 3D elastodynamic
fracture problems". J. Mech. Phys. Solids, 43:11, 1791-1824.
Morrissey,
J. W. and Geubelle, P. H. (1997) "A numerical scheme for mode III dynamic
fracture problems". Int. J. Numer. Meth. Eng., 40,
1181-1196.
Geubelle, P. H., Danyluk, M. J. and Hilton,
H. H. (1997) "Dynamic mode III fracture in viscoelastic media". Int.
J. Solids Structures, 35, 761-782.
Geubelle, P. H. and Breitenfeld, M. S. (1997)
"Numerical analysis of dynamic debonding under anti-plane shear
loading". Int. J. Fracture, 85, 265-282.
*
Danyluk, M. J., Geubelle, P. H. and Hilton, H. H. (1998) "2D and 3D
dynamic fracture in viscoelastic media". Int. J. Solids Structures,
35:28-29, 3831-3853.
*
Geubelle, P. H. (1997) "A numerical method for elastic and viscoelastic
dynamic fracture problems in homogeneous and bimaterial systems". Computational
Mechanics, 20:1-2, 20-25.
*
Breitenfeld, M. S. and Geubelle, P. H. (1997) "Numerical analysis of
dynamic debonding under 2D in-plane and 3D loading". To appear in Int.
J. Fracture.
Jung, D., Hegeman, A., Sottos, N. R.,
Geubelle, P. H. and White, S. R. (1997) "Self-healing composites using
embedded micro-spheres," Composite and Functionally Graded Materials,
Jacob, K., Katsube, N., and Jones, W., Eds., Vol. MD-80, in Proceedings of the
ASME International Mechanical Engineering Conference and Exposition, pp.
265-275. Also submitted to Polymer Composites.
* Geubelle,
P. H. and Baylor, J. (1998) "Impact-induced delamination of composites: a
2D simulation". Composites B, 29B, 589-602.
*
Breitenfeld, M. S. and Geubelle, P. H. (1998) "Parallel implementation of
a spectral scheme for the simulation of 3D dynamic fracture events". Submitted
to Int. J. Supercomp. Appl. & High Performance Computing.
Lin,
G., Geubelle, P. H. and Sottos, N. R. (1998) "Simulation of fiber
debonding and frictional sliding in a model composite pushout test".
Submitted to Int. J. Solids Structures.
A.2. Publications
Attached with the proposal are copies of 2
recently completed papers which have involved a substantial amount of parallel
computing on the NCSA paltforms:
• "Impact-induced delamination of
composites: a 2D simulation" by Geubelle and Baylor, Composites Part B,
29B(1998), 589-602.
This paper has resulted from Jeff Baylor's
M. Sc. Thesis dedicated to the use of cohesive/volumetric finite element scheme
for the simulation of impact-induced delamination in composites. Most of the
simulations have been performed on the Exemplar
• "Parallel implementation of a
spectral scheme for simulations of 3D dynamic fracture events" by
Breitenfeld and Geubelle. Submitted to Int. J. Supercomputing Appl. &
High Perf. Computing (1998).
This recently completed paper summarizes our
parallel optimization efforts with the spectral scheme.
