5 research outputs found
Rigidity and auxeticity transitions in networks with strong bond-bending interactions
A widely-studied model for gels or biopolymeric fibrous materials are
networks with central force interactions, such as Hookean springs. Less
commonly studied are materials whose mechanics are dominated by non-central
force interactions such as bond-bending potentials. Inspired by recent
experimental advancements in designing colloidal gels with tunable
interactions, we study the micro- and macroscopic elasticity of two-dimensional
planar graphs with strong bond bending potentials, in addition to weak central
forces. We introduce a theoretical framework that allows us to directly
investigate the limit in which the ratio of characteristic central-force to
bending stiffnesses vanishes. In this limit we show that a generic isostatic
point exists at , coinciding with the isostatic point of frames with
central force interactions in two dimensions. We further demonstrate the
emergence of a stiffening transition when the coordination is increased towards
the isostatic point, which shares similarities with the strain-induced
stiffening transition observed in biopolymeric fibrous materials, and coincides
with an auxeticity transition above which the material's Poisson's ratio
approaches -1 when bond-bending interactions dominate.Comment: 11 pages, 8 figure
Micromechanical theory of strain-stiffening of biopolymer networks
Filamentous bio-materials such as fibrin or collagen networks exhibit an
enormous stiffening of their elastic moduli upon large deformations. This
pronounced nonlinear behavior stems from a significant separation between the
stiffnesses scales associated with bending vs. stretching the material's
constituent elements. Here we study a simple model of such materials - floppy
networks of hinged rigid bars embedded in an elastic matrix - in which the
effective ratio of bending to stretching stiffnesses vanishes identically. We
introduce a theoretical framework and build upon it to construct a numerical
method with which the model's micro- and macro-mechanics can be carefully
studied. Our model, numerical method and theoretical framework allow us to
robustly observe and fully understand the critical properties of the athermal
strain-stiffening transition that underlies the nonlinear mechanical response
of a broad class of biomaterials
On-site residence time in a driven diffusive system: violation and recovery of mean-field
We investigate simple one-dimensional driven diffusive systems with open
boundaries. We are interested in the average on-site residence time defined as
the time a particle spends on a given site before moving on to the next site.
Using mean-field theory, we obtain an analytical expression for the on-site
residence times. By comparing the analytic predictions with numerics, we
demonstrate that the mean-field significantly underestimates the residence time
due to the neglect of time correlations in the local density of particles. The
temporal correlations are particularly long-lived near the average shock
position, where the density changes abruptly from low to high. By using Domain
wall theory (DWT), we obtain highly accurate estimates of the residence time
for different boundary conditions. We apply our analytical approach to
residence times in a totally asymmetric exclusion process (TASEP), TASEP
coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually
interactive LK (TASEP + MILK). The high accuracy of our predictions is verified
by comparing these with detailed Monte Carlo simulations
Rigidity and auxeticity transitions in networks with strong bond-bending interactions
A widely studied model for gels or biopolymeric fibrous materials are networks with central force interactions, such as Hookean springs. Less commonly studied are materials whose mechanics are dominated by non-central force interactions such as bond-bending potentials. Inspired by recent experimental advancements in designing colloidal gels with tunable interactions, we study the micro- and macroscopic elasticity of two-dimensional planar graphs with strong bond-bending potentials, in addition to weak central forces. We introduce a theoretical framework that allows us to directly investigate the limit in which the ratio of characteristic central-force to bending stiffnesses vanishes. In this limit we show that a generic isostatic point exists at , coinciding with the isostatic point of frames with central-force interactions in two dimensions. We further demonstrate the emergence of a stiffening transition when the coordination is increased towards the isostatic point, which shares similarities with the strain-induced stiffening transition observed in biopolymeric fibrous materials, and coincides with an auxeticity transition above which the material’s Poisson’s ratio approaches -1 when bond-bending interactions dominate
The Role of Network Architecture in Collagen Mechanics
Collagen forms fibrous networks that reinforce tissues and provide an extracellular matrix for cells. These networks exhibit remarkable strain-stiffening properties that tailor the mechanical functions of tissues and regulate cell behavior. Recent models explain this nonlinear behavior as an intrinsic feature of disordered networks of stiff fibers. Here, we experimentally validate this theoretical framework by measuring the elastic properties of collagen networks over a wide range of self-assembly conditions. We show that the model allows us to quantitatively relate both the linear and nonlinear elastic behavior of collagen networks to their underlying architecture. Specifically, we identify the local coordination number (or connectivity) 〈z〉 as a key architectural parameter that governs the elastic response of collagen. The network elastic response reveals that 〈z〉 decreases from 3.5 to 3 as the polymerization temperature is raised from 26 to 37°C while being weakly dependent on concentration. We furthermore infer a Young's modulus of 1.1 MPa for the collagen fibrils from the linear modulus. Scanning electron microscopy confirms that 〈z〉 is between three and four but is unable to detect the subtle changes in 〈z〉 with polymerization conditions that rheology is sensitive to. Finally, we show that, consistent with the model, the initial stress-stiffening response of collagen networks is controlled by the negative normal stress that builds up under shear. Our work provides a predictive framework to facilitate future studies of the regulatory effect of extracellular matrix molecules on collagen mechanics. Moreover, our findings can aid mechanobiological studies of wound healing, fibrosis, and cancer metastasis, which require collagen matrices with tunable mechanical properties