Using Eshelby's energy-momentum tensor, we compute the forces
acting on a moving crack front. The resultant of forces is
found to be not necessarily in the direction of crack propagation.
We propose a generalization of Griffith's approach that takes
into account this fact. In this framework, we prove that below a
critical crack speed, the crack propagates in a direction that keeps
a pure opening mode at its tip. Above this critical velocity,
such a configuration of crack propagation is no more favored. This
leads to a dynamic instability of the crack tip. Various
experimental manifestations are discussed under the light of this model.
It is well-known that fractal-like objects appear in many
engineering, environmental and technological processes. In particular,
in solidification processes a mushy region (zone between solid and
liquid) emerges, and includes solid phase
elements in the form of dendrites, grains, etc.
In general, the density of a solid phase into the mushy region
may vary with spatial coordinate like a fractal cluster.
In this case, the formation of solid and the mechanical
characteristics of patterns are dependent on the fractal dimension.
The purpose here is to develop the theoretical approach
for investigation of such an influence. Suggested model of the mushy
region is based on the deduced fractal diffusion equation for impurity
concentration including the boundary conditions at the moving
interfaces. This model is solved with the help of self-similar
variables and transition to the effective fixed boundaries. It was
shown that an increase of the fractal dimension gives rise to the
solidification velocity. This is due to the fact that the fractal
dimension increase correspons to the decrease of a free space filled
with a liquid. Possible ways of generalizing of the developed
approach to similar fractal systems seem to be quite obvious.
Delamination process remains a challenge to macroscopic modelisation,
because it has been impossible till now to understand how it works:
micromechanical descriptions of the mode-dependant interface toughness
of an interfacial crack are not far advanced. I will show that,
because of the geometry of the crack, the usual 1/sqrt(r)
divergence of the stress near the crack tip is changed into a less
diverging behavior, which appears to be strongly dependant on mode
mixity.
The study of delamination cracks in terms of K_I/sqrt(r) and
K_{I\I}/sqrt(r) expansions of the stress near the crack tip is not
self-consistent because it yields negative values of K_I and thus
ignores the non-interpenetrability of the crack lips. As I show, this
corresponds physically to a macroscopic contact zone between the
crack lips. The interaction of the lips over this contact zone is
modeled by a Coulomb law of friction. The usual 1/sqrt(r)
divergence is then regularised, yielding a vanishing energy release
rate on the crack tip G_t=0, no matter how small the friction. This
is interpreted as a mode-dependant shielding of the interfacial crack.
I will discuss new propagation criteria for the crack. 2D finite
elements simulations are presented.
We consider the possibility of using diffusion as a mechanism for
efficient mixing in granular systems. To study this we study
numerically the diffusion of a disc in a sea of discs as a function of
its radius both in the elastic and the agitated inelastic cases. With
periodic boundary conditions the coefficient of diffusion depends on
the size of the system. We explain this finite size effect and remedy
it by working in a system with hard walls. The results of the elastic
case can be explained analytically but not for the inelastic case. We
also show prelimenary results for mixing. The experiments will be done
on the air table at the University of Rennes I.
The Saffman Taylor instability in the linear Hele Shaw cell has been
the subject of extensive studies. Classically the theorists have focused
in the explanation of the low surface tension limit giving a finger width
of 1/2. This 1/2 limit remained a challenge during several decades, but
nowadays it is perfectly understood. In this presentation we take a different
point of view. We basically show that the Hele-Shaw cell is an excellent
model system to study the dynamical properties of complex fluids. It gives
enlightement into both, interfacial properties in systems such as surfactants,
and bulk behavior like in polymers presenting effects such as shear thinning.
Variation in morphology makes an interesting study. Fascinating among them
are the ones in which a crossover from fractal to
non-fractal structures are observed
by varying different parameters. Growth of bacterial colonies[1]
by varying agar and nutrient concentration, aggregation of
potassium dichromate[2]
in gelatin are some of the interesting examples showing the above transition.
In this paper we present a study of variation of morphology of polyethylene
oxide (PEO) films (thickness approx. 150 micron) complexed with ammonium
perchlorate (NH4ClO4)
formed by evaporating a methanolic solution. Films with salt concentration
x=0 - 0.35 (x is the weight fraction of salt) were prepared for the morphology
study. We present a series of photographs and micrographs
showing the transition
in morphology from pure PEO spherullites at x=0, through macroscopic
diffusion limited aggregates (DLA) from x=0.10-0.15 to large
compact
spherullite(x=0.18-0.35). For high salt fraction some fraction
of salt remains unreacted. To identify the species present in the films,
preliminary
studies of variable temperature polarising microscopy (VTPM) and X-ray
diffraction (XRD) studies have also been done.
PEO-NH4ClO4 complexes are ion conducting material
and are used commercially
as solid electrolytes[3]. As morphology affects different properties such as
crystallinity, ionic conductivity etc., our main objective is to find out the
most suitable composition for use as a polymer elctrolyte. Work is in progress
for estimation of crystallinity and ionic conductivity of films possessing
different morphology.
[1] A. Nakahara, Y. Shimada, Jun-ichi Wakita, M. Matsushita and T. Matsuyama, J. Phys. Soc. Jpn. 65, 2700 (1996).
[2] Jun-ichiro Suda, T. Nakayama, A. Nakamura and M. Matsushita, J. Phys. Soc. Jpn. 65, 771 (1996).
[3] M. Armand, Solid State Ionics 69, 309 (1994).
We present experiments showing that a granular system of small
beads does exhibit ageing properties: its maximum stability angle is
measured to increase logarithmically with resting time, i.e. the time
elapsed before performing the measure. We show that humidity is the crucial
ingredient responsible for this behaviour: while ageing effects are
important at intermediate humidity, they
disappear at vanishing humidity. On the basis of these experimental results, we propose a model based on the activated
condensation of liquid bridges between the beads. Within this picture,
we are able to reproduce both the waiting-time and humidity dependence of the
ageing properties. Extensions of this work to ``dry'' solid friction shall be
discussed.
We study dynamics of a bead on a forced vibrating string. In large frequency
intervals, the bead adjust its position so that the system is at resonance
with the driving. These domains are linked by a set of bifurcations. We
show the selection process linked to nonlinearities when there is more
than one bead. The agreement between the experiment and the theory is very
good. Then, we discuss the use of such discrete models to study the vibration
of soap membranes.
It is well known that granular flows do not obey classical law of hydrodynamics [1]. For example, the rate of discharge of a hopper is known to be virtually independent of the height of granular matter situated above the aperture. This effect contradicts the usual Bernouilli's law where the transfer from potential energy to kinetic energy basically determines the rate of discharge. This particular rheology is the results of the lack of energy conservation for the ``microscopic'' interactions between the grains which leads to a very special state of matter at a macroscopic level. At the moment, the knowledge of the basic mechanisms controlling the dynamics of flowing granular matter is very fragmented. In previous experimental work on vertical chutes, a regime of global packing acceleration was evidenced and studied [2]. Depending on the roughness of the boundaries the trigger of a rising fracture wave was found. here, for a similar experimental design, a set of new results on the flows in vertical chutes is presented [3]. This work is based on the visualization of a 2D model media using millimeter size beads with rather well controlled mechanical properties. A fast-speed video camera as well as extensive image processing techniques are used. For the first time, in a vertical configuration and without the effect of air [4], a regime of stationary kinetic waves in evidenced which is compared to previous numerical simulations [5] and to recent experimental results on inclined planes [6,7]. The mass fluxes and the local densities are measured as well as their fluctuations, in different experimental conditions. A phase diagram is presented for the onset of the kinematic wave regime. Questions concerning the modes of mass and momentum transfer and the central role of boundary conditions (geometry, roughness etc....) are addressed and in particular the limits of validity of a kinetic theory is at the center of the discussion [8,9].
[1] R. M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992).
[2] J. Duran, T. Mazozi, E. Clement and J.Rajchenbach, Phys. Rev. E 50, 3092 (1994); S. Luding, J. Duran, T. Mazozi, E. Clement and J.Rajchenbach, J. Physique I 6, 823 (1996).
[3] E. Clement, F.Rioual, G.Reydellet and J.Lanuza, in preparation.
[4] T. Raafat, J. P. Hulin and H. J. Herrmann, Phys. Rev. E 53, 4345 (1996).
[5] K. Nagel, Phys. Rev. E 53, 4655 (1996); T. Poschel, J. Physique I 4, 499 (1994); J. Lee and M. Liebig, J. Physique I 4, 507 (1994).
[6] C. T. Veje and P. Dimon, Phys. Rev. E 56, 4376 (1997); Phys. Rev. E 54, 4329 (1996).
[7] S. Horlyck, Master's Thesis, University of Copenhagen (1998).
[8] R. Bagnold, Proc. Roy. Soc. Lond. A295, 219 (1954); J. Jenkins and S. Savage, J.Fluid Mech. 130, 187 (1983).
[9] J. Jenkins, ``Kinetic theory for nearly elastic spheres'', in Physics
of Dry Granular Materials, ed. by J. P. Hovi, S. Luding and H. J. Herrmann
(Kluwer Acad. Publ. Dordrecht, 1998).
We have investigated the flow of a single layer of uniform brass ball
bearings in a small-angle funnel. The behavior of the flow depends in a
sensitive way on the geometry. For example, when the funnel opening angle
greater that two degrees, the flow is dense and steady, but when it is
less than one degree, the flow is irregular and kinematic shock waves are
present. Using a video camera, we have studied the creation of the shock
waves and followed their evolution and interactions. We have also examined
how such a flow responds to an excitation. In a smaller version of the
shock wave experiment, we vibrated the system and found, for example, that
there is a critical acceleration necessary to maintain the flow, below
which the balls jam (the well-known Muesli Effect).
The Sneppen model is modified to include an inertia effect. The
roughness exponent is found to depend continuously on this "inertia" and
interpolates between the Sneppen value of 0.63 and unity.
Percolation of small particles through the pores of a packing of large
grains is one of the best known mechanisms of segregation in granular materials.
We report on an experimental study carried out in a porous medium modelled
by a random close packing of beads where a little particle can flow into
the medium. The geometrical parameters of the problem are: r, the radius
of the flowing bead; R, the radius of the porous medium beads (particulate
percolation is possile only if r/R < 0.1547, the apollonian ratio).
The bead attains a steady state after travelling a short distance. The
behaviour was found to be diffusive. The relation between the geometrical
parameters of the system and diffusion in transverse and parallel directions
(to the bead velocity direction) is investigated. An acoustic technique
was used for studying the number of collisions of the flowing bead during
its trajectory. These results give complementary information about the
typical diffusion length.
Stretching of linear polymers in high-gradient longitudinal flows
occurs as a single-molecule phase transition. The nature of this
effect and its relevance to the flow of polymeric solutions in porous
media have been a subject of extensive experimental and theoretical
investigations for more than two decades. We argue that the specifics
of the coil-stretch transition in branched polymers is determined by
the hydrodynamic interaction between different branches. For a star
polymer consisting of f identical branches, we predict a stepwise
uncoiling of the macromolecule with the increase in the flow gradient
through a cascade of transitions. The first of them involves
stretching of only one pair of branches, the other branches being
still in the coiled state. This effect has a direct bearing on the
permeation of branched polymers through nanopores as discussed by
Brochard and de Gennes.
Fresh water sources issuing in the littoral are becoming increasingly
needed. Their presence in the sea makes their expoitation difficult. Their
output is not well understood as they occur under complex flow conditions
especially in land. These conditions are the karstic carbonate mass on one
hand and and the fractured terrain on the other. The purpose of the study
is to reveal and try to simplify this complexity through advanced sensing
techniques. This may help contribute to better understand the flow water
regime.
The sensing techniques used are the recent satellite optical imagery
which delineates surface fractures, airborne infrared scaning (in 1972
and in 1997) which differentiates water temperature anomalies, and noting
the ground geophysical study results of 1972 reflecting on subsurface
structures.
Analysis of fracture patterns from satellite imagery reveals oriented sets
that seem to enhance preferential flow directions. They connect geologically
with the submarine springs. However, the karstic nature, the subsurface
lithology, and active stress regime are constraining the water flow.
Furthermore, the fracture system also allows water flow in the reverse
direction, i.e. sat-water intrusion into the fresh water of the land mass.
The current study gives examples of ice drift and deformation in
the Kara Sea based on a time series of ERS-1 SAR images covering
the same area (100 times 100 km2) in the middle of the Kara Sea
each 3 day during the period 1 January - 29 March 1994. The study
indicates that forces from the shore-line through the ice can be
significant for ice drift in the whole Kara Sea during the winter.
There are events where the ice seems to be anchored to the shore-line
during 3 days. Size distributions of ice floes ("rigid areas")
lasting more than 3 days, show large variations during the observation
time period. The current work includes to develop conceptual models
for deformation patterns and its temporal variation.
Dragontooth and Sharkskin surface fracturing during extrusion of clay
were observed in our experiments for several die designs and materials.
We show that low friction and slip at the die wall aid to get extrusion
of clay without the fracture. Lubrication of the die wall by concentrated
salts’ solutions drive water out of clay (osmoses) and diminish friction.
We propose a die geometry solution to flow defects and a process for reducing
surface fracture problems in addition. Specially configured insertions
(flow body) into the die mouth were used for producing a clay column with
thin opening and without flow fracture. We present a set of photos to demonstrate
the process. Results of our research could improve quality of clay bricks
and some products from plastic materials.
Silo design (outlet angle and diameter) is based on shear tests on samples
of the powder to be stored, in order to know its mechanical strengh and
flow properties. The shear resistance of a fine non-cohesive powder has
been investigated using a ring shear tester. A stick-slip instability is
observed above a threshold in shear velocity or normal load. Two types of
oscillations are observed (small ones without dilatancy and bigger ones
associated with a dilatation phenomenon). For fine cohesive powders, the
observation of these instabilities should help us to measure the kinetics
of lumping.
Theoretically, there is an upper limit for the velocity with which
cracks can propagate in a solid. This limit is a function of the ratio of
Young's modulus to the density of the solid. However, experimentally such
limiting velocities are rarely achieved and it is thought that this is
because a fast propagating crack bifurcates before it is able to reach the
predicted value. The process of bifurcation is highly dissipative and
therefore not enough energy is available for continuing to accelerate the
crack velocity in an epoxy amorphous polymer. Two sets of experiments are
conducted. In the first one, the crack is driven by detonating a small
amount of a primary explosive charge in a pre-existing notch in which
photos are taken at a rate of 3 s/frame. Circular polarizors are used in
some of these tests to determine the distribution of the stress fields
around the crack tip. In the other set of experiments, the crack is
produced by the impact of a Rockwell or ball indenter on cubic samples and
photos are taken at a rate of 5 - 10 s/frame. In all experiments,
post-mortem examination of the fractured fragments is done where the aim is
to find whether there exists a unique correlation between the crack speed
and the surface morphology. More elaboration on the fracture surface
topography and the velocities registered will be given during the talk.
Under a slow drive, a system may spontaneously evolve to a scale free
critical state, starting from any arbitrary initial condition - is the
basic concept of Self-Organized Criticality (SOC). Avalanches on the surface
of a sandpile do not show strong support to the suggestion that a sandpile
may be an exmaple of SOC. Therefore we aim to study the avalanches in the
interior of a granular heap. Our system is a granular material kept at
rest inside a bin. System is disturbed by taking out grains one after another.
Every such disturbance creates an avalanche of grain displacements in the
heap. The spatial size and duration of these avalanches are observed to
be power law distributed. In a two dimentional model we see that there
may be at least two universality classes involved in this process depending
on if formation of `arches' is allowed or not.
We investigate two-phase flow in fracture joints both experimentally and by computer simulations. The experiments were performed using transparent fracture models made as castings of real granite fractures. The fracture joint is covered by a mono-layer of 1mm glass beads. The fact that the models are transparent makes it possible to visualize the displacement structures.
In the numerical simulations, we model the capillary threshold fluctuations by white noise with an additional term given by the vertical position of the fracture joint. As the fracture surface is self affine, the additional term introduces long range correlatons.
Both the structure and the dynamics of
the invasion fronts have been investigated numerically and experimentally,
and we present qualitative comparisons between the two.
We focus on the problem of stress fluctuations in a bidimensional
piling submitted to a compression. Measurements of the force
required by the system to be strained at a constant rate are
reported. This force is shown to exhibit sudden fluctuations
of large amplitude which strongly deviate from the mean value.
The mean value of the force is that expected from Continuum
Mechanics, in opposition to the fluctuation peaks which correspond
to a completely different process, namely the buckling of chains
of grains. We establish the scaling laws followed by the mean
force and by the fluctuations as a function of the grain diameter,
the grain mass, the aspect ratio and the container filling.
The regression law of the fluctuations with the system size
is determined and the passage to the Mohr-Coulomb plasticity
behavior in the limit of very large systems is observed.
A considerable part of natural oil and gas reservoirs belongs to fractured or fractured porous type. Numerous laboratory and field experiments evidence a strong dependence of effective characteristics of a fractured medium on its stress state and the filtrating fluid pressure. On a basis of a new nonlinear theory (Buyevich and Nustrov, 1993) nonisothermal filtration processes are investigated by using of analytic and computational methods. Within the framework of the theory the fracture porosity decreases according to elastic law, when the reservoir pressure falls down. It is possible that the complete closing of the fractures is realized. This conclusion was formulated by many authors on the basis of field observations analysis. Capabilities of the new model as compared with conventional approaches have been demonstrated in isothermal problems earlier. Self-similar nonisothermal regimes under the bringing into production of gas well and the injection of a hot fluid into formation are obtained. There exists the heat localization in the second case. Self-similar solutions are used as initial approaches in computational modelling of heat transfer processes in fractured porous collectors.
[1] Buyevich, Yu.A. and Nustrov, V.S., Non-Linear Flow in
Fractured Porous Media, Transport in Porous Media, 12, 1 (1993).
The concept of arching is often used as the deviation of forces from
straight propagation due to the presence of micro-vaults inside a granular
packing. These nonlocal micro-structures are sometimes regarded as the
main ingredient of the texture of granular systems. However, using numerical
simulations of quasi-statically driven assemblies of particles in 2 and
3 dimensions, we observed no arching in this sense. We show that it is
possible to give a rigorous definition of arching by taking into account
both the fabric tensor, as a measure of the anisotropy of texture, and
the contact forces inside a granular medium. We illustrate this definition
through several examples of simple textures, and we discuss in more detail
the influence of wall friction and gravity-induced stress gradients on
arching and on the transmission of forces.
Experimental works and theoretical results concerning grain flows are
reviewed. The three different flow regimes are addressed : first, the slow
deformation regime, which is mainly driven by friction forces and
steric hindrance, next the rapid flows, which are governed by inelastic
collisions, and lastly the regime of intermittent avalanches.
The roughness of crack surfaces exhibits scaling invariances. A permanent
regime can be distinguished and caracterized with self-affine fractals.
The roughness exponent seems robust over different materials and fracture
modes. However exceptions exist. The transient regime corresponds to the
development of the roughness. Two frameworks for the roughness growth can
be proposed : Family-Viscek and anomalous scaling. Some physical consequences
of the geometrical description of the crack roughness will be discussed.
We present a method for determining Hurst exponents based on wavelets. We test it out on synthetic data, fracture surfaces, financial data and well logs. The results are compared to those obtained with Fourier analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when only one or a few samples are available, the wavelet method outperforms the Fourier method by a large margin [1]. We also discuss wavelet analysis of multiaffine surfaces, and the inverse problem: How to generate tailored multiaffine surfaces.
[1] I. Simonsen, A. Hansen and O. M. Nes, Cond-mat
9707153.
2National Center for Remote Sensing, National Council for Scientific Research, Beirut, Lebanon
Earthquakes, which are a common feature in Lebanon, are the cause of severe damage to human beings and property. Lebanon occupies a stretch of around 225 Km of the most active teconic feature of the Arabian Plate boundary, known as the Yammouneh fault. It is of great importance to delineate accurately the seismic source zones that are characterized by low, moderate, an high seismicity depending on the type of faults present. The land mass in Lebanon is a combination of complex fractured zones that can produce deformation of the topography and morphology of the country if triggered by moderate > 5.0 to high magnitude > 6.9 earthquakes on the Richter scale. Preliminary studies on lineament density as obtained from satellite imagery, reveal a range of 25-50/100 km$^2$is very to extremely dense. In fact the propagation of tremors and movements through the fractured mass from past seismic events, have led to increase their adverse effects. Landslides, depressions, pull-apart basins, upifts, etc can be seen all over the land, andare the result of such seismic events. It is crucial to control these effects as they impact the environment and quality of living. A rather serious and additional concern are the tremors caused by illegal use of explosives during some quarrying operations. It is noticed that, other things being equal, settlements close to such quarries and lying in denser fractured terrain are more heavily affected. Thus, both natural and man-made tremors of seismic events are available causing geo-environmental hazzards in a fragile fractured land mass. The implications from the previous picture are very imposing. Some control, monitoring, or emergency measures etcmust be put in effect. Studies required to contribute to that should include the following:
a) land mass fractured classification
b) a fracture activity or ``movement'' classification and monitoring
c) a better understanding of the nature of wave propagtion in the
fractured mass with a heterogeneous medium.
A simple model is proposed which simulates the growth process of porous sedimentary rocks, and reproduces some of the characteristic features of the pore space of real rocks. We generate the structure by a ballistic deposition of particles with a bimodal size distribution. The pore structure generated in three dimensions has a low percolation threshold of .08 in the direction of growth. A fractal nature is found for certain length scales. We calculate the variation of porosity and specific surface area on varying the size distribution. these results are used to estimate the permeability and the electrical conductivity of brine filled sedimentary rocks.
Dispersion of colloidal particles in a liquid leads to the formation
of complex fluids which are most often non-Newtonian and viscoelastic.
At high enough volume fraction, elastic gels are obtained. When larger
particles are used, almost ideally plastic pastes may be obtained. Each
of these systems exhibit peculiar flow or fracture behaviors which allows
for a rich variety of patterns, including viscous fingers (in non-Newtonian
fluids), viscoelastic fracturing patterns (in gels) and rough fracture
surfaces (in pastes). In spite of considerable differences in time scales
and material properties, the underlying physics of soft matter fracture
is surprisingly similar to that of hard disordered matter.
We investigate experimentally the flow of grains from a sealed
container through an elongated outlet. We measure the related
air pressure variations and the grain flux simultaneously. The results
depend sensitively on the grain size. Generally the dynamics are found
to behave like a relaxation oscillator with one slow and one fast
time scale. The slow time scale is related to an upward propagating
air/grain interface while the air pressure is relaxing, whereas the
fast time scale is related to the collapse of the interface. Using
image analysis we track the interface. This also renders visible an
air-bubble at the bottom of the resevoir.