81 research outputs found
Stiff Polymers, Foams and Fiber Networks
We study the elasticity of fibrous materials composed of generalized stiff
polymers. It is shown that in contrast to cellular foam-like structures affine
strain fields are generically unstable. Instead, a subtle interplay between the
architecture of the network and the elastic properties of its building blocks
leads to intriguing mechanical properties with intermediate asymptotic scaling
regimes. We present exhaustive numerical studies based on a finite element
method complemented by scaling arguments.Comment: 4 pages, 5 figure
Nonaffine rubber elasticity for stiff polymer networks
We present a theory for the elasticity of cross-linked stiff polymer
networks. Stiff polymers, unlike their flexible counterparts, are highly
anisotropic elastic objects. Similar to mechanical beams stiff polymers easily
deform in bending, while they are much stiffer with respect to tensile forces
(``stretching''). Unlike in previous approaches, where network elasticity is
derived from the stretching mode, our theory properly accounts for the soft
bending response. A self-consistent effective medium approach is used to
calculate the macroscopic elastic moduli starting from a microscopic
characterization of the deformation field in terms of ``floppy modes'' --
low-energy bending excitations that retain a high degree of non-affinity. The
length-scale characterizing the emergent non-affinity is given by the ``fiber
length'' , defined as the scale over which the polymers remain straight.
The calculated scaling properties for the shear modulus are in excellent
agreement with the results of recent simulations obtained in two-dimensional
model networks. Furthermore, our theory can be applied to rationalize bulk
rheological data in reconstituted actin networks.Comment: 12 pages, 10 figures, revised Section II
Shear-Induced Stress Relaxation in a Two-Dimensional Wet Foam
We report on experimental measurements of the flow behavior of a wet,
two-dimensional foam under conditions of slow, steady shear. The initial
response of the foam is elastic. Above the yield strain, the foam begins to
flow. The flow consists of irregular intervals of elastic stretch followed by
sudden reductions of the stress, i.e. stress drops. We report on the
distribution of the stress drops as a function of the applied shear rate. We
also comment on our results in the context of various two-dimensional models of
foams
A Model for the Elasticity of Compressed Emulsions
We present a new model to describe the unusual elastic properties of
compressed emulsions. The response of a single droplet under compression is
investigated numerically for different Wigner-Seitz cells. The response is
softer than harmonic, and depends on the coordination number of the droplet.
Using these results, we propose a new effective inter-droplet potential which
is used to determine the elastic response of a monodisperse collection of
disordered droplets as a function of volume fraction. Our results are in
excellent agreement with recent experiments. This suggests that anharmonicity,
together with disorder, are responsible for the quasi-linear increase of
and observed at .Comment: RevTeX with psfig-included figures and a galley macr
Numerical observation of non-axisymmetric vesicles in fluid membranes
By means of Surface Evolver (Exp. Math,1,141 1992), a software package of
brute-force energy minimization over a triangulated surface developed by the
geometry center of University of Minnesota, we have numerically searched the
non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy
model. We show for the first time there are abundant mechanically stable
non-axisymmetric vesicles in SC model, including regular ones with intrinsic
geometric symmetry and complex irregular ones. We report in this paper several
interesting shapes including a corniculate shape with six corns, a
quadri-concave shape, a shape resembling sickle cells, and a shape resembling
acanthocytes. As far as we know, these shapes have not been theoretically
obtained by any curvature model before. In addition, the role of the
spontaneous curvature in the formation of irregular crenated vesicles has been
studied. The results shows a positive spontaneous curvature may be a necessary
condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques
Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
We analyze in details the atomistic response of a model amorphous material
submitted to plastic shear in the athermal, quasistatic limit. After a linear
stress-strain behavior, the system undergoes a noisy plastic flow. We show that
the plastic flow is spatially heterogeneous. Two kinds of plastic events occur
in the system: quadrupolar localized rearrangements, and shear bands. The
analysis of the individual motion of a particle shows also two regimes: a
hyper-diffusive regime followed by a diffusive regime, even at zero
temperature
Rheological constitutive equation for model of soft glassy materials
We solve exactly and describe in detail a simplified scalar model for the low
frequency shear rheology of foams, emulsions, slurries, etc. [P. Sollich, F.
Lequeux, P. Hebraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)]. The model
attributes similarities in the rheology of such ``soft glassy materials'' to
the shared features of structural disorder and metastability. By focusing on
the dynamics of mesoscopic elements, it retains a generic character.
Interactions are represented by a mean-field noise temperature x, with a glass
transition occurring at x=1 (in appropriate units). The exact solution of the
model takes the form of a constitutive equation relating stress to strain
history, from which all rheological properties can be derived. For the linear
response, we find that both the storage modulus G' and the loss modulus G''
vary with frequency as \omega^{x-1} for 1<x<2, becoming flat near the glass
transition. In the glass phase, aging of the moduli is predicted. The steady
shear flow curves show power law fluid behavior for x<2, with a nonzero yield
stress in the glass phase; the Cox-Merz rule does not hold in this
non-Newtonian regime. Single and double step strains further probe the
nonlinear behavior of the model, which is not well represented by the BKZ
relation. Finally, we consider measurements of G' and G'' at finite strain
amplitude \gamma. Near the glass transition, G'' exhibits a maximum as \gamma
is increased in a strain sweep. Its value can be strongly overestimated due to
nonlinear effects, which can be present even when the stress response is very
nearly harmonic. The largest strain \gamma_c at which measurements still probe
the linear response is predicted to be roughly frequency-independent.Comment: 24 pages, REVTeX, uses multicol, epsf and amssymp; 20 postscript
figures (included). Minor changes to text (relation to mode coupling theory,
update on recent foam simulations etc.) and figures (emphasis on low
frequency regime); typos corrected and reference added. Version to appear in
Physical Review
Deformation of Small Compressed Droplets
We investigate the elastic properties of small droplets under compression.
The compression of a bubble by two parallel plates is solved exactly and it is
shown that a lowest-order expansion of the solution reduces to a form similar
to that obtained by Morse and Witten. Other systems are studied numerically and
results for configurations involving between 2 and 20 compressing planes are
presented. It is found that the response to compression depends on the number
of planes. The shear modulus is also calculated for common lattices and the
stability crossover between f.c.c.\ and b.c.c.\ is discussed.Comment: RevTeX with psfig-included figures and a galley macr
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