85 research outputs found
Force distributions and force chains in random stiff fiber networks
We study the elasticity of random stiff fiber networks. The elastic response
of the fibers is characterized by a central force stretching stiffness as well
as a bending stiffness that acts transverse to the fiber contour. Previous
studies have shown that this model displays an anomalous elastic regime where
the stretching mode is fully frozen out and the elastic energy is completely
dominated by the bending mode. We demonstrate by simulations and scaling
arguments that, in contrast to the bending dominated \emph{elastic energy}, the
equally important \emph{elastic forces} are to a large extent stretching
dominated. By characterizing these forces on microscopic, mesoscopic and
macroscopic scales we find two mechanisms of how forces are transmitted in the
network. While forces smaller than a threshold are effectively balanced
by a homogeneous background medium, forces larger than are found to be
heterogeneously distributed throughout the sample, giving rise to highly
localized force-chains known from granular media.Comment: 7 pages, 7 figures, final version as publishe
Floppy modes and non-affine deformations in random fiber networks
We study the elasticity of random fiber networks. Starting from a microscopic
picture of the non-affine deformation fields we calculate the macroscopic
elastic moduli both in a scaling theory and a self-consistent effective medium
theory. By relating non-affinity to the low-energy excitations of the network
(``floppy-modes'') we achieve a detailed characterization of the non-affine
deformations present in fibrous networks.Comment: 4 pages, 2 figures, new figure
Mechanics of bundled semiflexible polymer networks
While actin bundles are used by living cells for structural fortification,
the microscopic origin of the elasticity of bundled networks is not understood.
Here, we show that above a critical concentration of the actin binding protein
fascin, a solution of actin filaments organizes into a pure network of bundles.
While the elasticity of weakly crosslinked networks is dominated by the affine
deformation of tubes, the network of bundles can be fully understood in terms
of non-affine bending undulations.Comment: 5 pages, 3 figures, final version as publishe
Rheology and dynamical heterogeneity in frictionless beads at jamming density
We investigate the rheological properties of an assembly of inelastic (but
frictionless) particles close to the jamming density using numerical
simulation, in which uniform steady states with a constant shear rate
is realized. The system behaves as a power-law fluid and the
relevant exponents are estimated; e.g., the shear stress is proportional to
, where . It is also found that
the relaxation time and the correlation length of the velocity
increase obeying power laws: and
, where and
Semiflexible Filamentous Composites
Inspired by the ubiquity of composite filamentous networks in nature we
investigate models of biopolymer networks that consist of interconnected floppy
and stiff filaments. Numerical simulations carried out in three dimensions
allow us to explore the microscopic partitioning of stresses and strains
between the stiff and floppy fractions c_s and c_f, and reveal a non-trivial
relationship between the mechanical behavior and the relative fraction of stiff
polymer: when there are few stiff polymers, non-percolated stiff ``inclusions``
are protected from large deformations by an encompassing floppy matrix, while
at higher fractions of stiff material the stiff network is independently
percolated and dominates the mechanical response.Comment: Phys. Rev. Lett, to appear (4 pages, 2 figures
Size-dependent rheology of type-I collagen networks
We investigate the system size dependent rheological response of branched
type I collagen gels. When subjected to a shear strain, the highly
interconnected mesh dynamically reorients, resulting in overall stiffening of
the network. When a continuous shear strain is applied to a collagen network,
we observe that the local apparent modulus, in the strain-stiffening regime, is
strongly dependent on the gel thickness. In addition, we demonstrate that the
overall network failure is determined by the ratio of the gel thickness to the
mesh size. These findings have broad implications for cell-matrix interactions,
the interpretation of rheological tissue data, and the engineering of
biomimetic scaffolds.Comment: 3 pages, 4 figures, to appear in Biophysical Journal Letters,
September 201
Statics and Dynamics of the Wormlike Bundle Model
Bundles of filamentous polymers are primary structural components of a broad
range of cytoskeletal structures, and their mechanical properties play key
roles in cellular functions ranging from locomotion to mechanotransduction and
fertilization. We give a detailed derivation of a wormlike bundle model as a
generic description for the statics and dynamics of polymer bundles consisting
of semiflexible polymers interconnected by crosslinking agents. The elastic
degrees of freedom include bending as well as twist deformations of the
filaments and shear deformation of the crosslinks. We show that a competition
between the elastic properties of the filaments and those of the crosslinks
leads to renormalized effective bend and twist rigidities that become
mode-number dependent. The strength and character of this dependence is found
to vary with bundle architecture, such as the arrangement of filaments in the
cross section and pretwist. We discuss two paradigmatic cases of bundle
architecture, a uniform arrangement of filaments as found in F-actin bundles
and a shell-like architecture as characteristic for microtubules. Each
architecture is found to have its own universal ratio of maximal to minimal
bending rigidity, independent of the specific type of crosslink induced
filament coupling; our predictions are in reasonable agreement with available
experimental data for microtubules. Moreover, we analyze the predictions of the
wormlike bundle model for experimental observables such as the tangent-tangent
correlation function and dynamic response and correlation functions. Finally,
we analyze the effect of pretwist (helicity) on the mechanical properties of
bundles. We predict that microtubules with different number of protofilaments
should have distinct variations in their effective bending rigidity
Probing Internal Stress and Crystallinity in Wet Foam via Raman Spectroscopy
In this article, we correlate the internal stress and the characteristics of
a vibrational mode in wet foam. Using microscope images, we estimate the
average size of the bubbles in wet foam, at specific time intervals, over a
duration of twenty four hours. Raman spectra are also recorded at the same time
intervals, over the same time frame. We show that the internal stress,
originated from the macroscopic structural change of foam with ageing, can be
related to the observed Raman shift of the low frequency methylene rocking mode
of the constituent surfactant molecules in foam. In this report we also show
the capability of the Raman spectroscopy to reveal the crystallinity in foamy
materials, when studied for a longer period of time.Comment: 16 pages, 7 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
- …