Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X42: Topology, Geometry, and Physics of Elastic NetworksInvited
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Sponsoring Units: GSNP DPOLY GSNP Chair: Eleni Katifori, University of Pennsylvania Room: LACC 502B |
Friday, March 9, 2018 8:00AM - 8:36AM |
X42.00001: Structure function properties of cytoskeletal and extracellular networks: Mechanics and crack propagation Invited Speaker: Moumita Das Living cells and tissues are highly mechanically sensitive and active. Mechanical stimuli influence the shape, motility, and functions of cells, modulate the behavior of tissues, and play a key role in several diseases. In this talk I will discuss the structure function properties of biopolymer networks in cells and tissues that arise due to the interplay of their mechanical and statistical mechanical properties. I will start with articular cartilage (AC), a soft tissue mainly made of network like extra-cellular matrix. AC covers the ends of long mammalian bones, serving to minimize friction and distribute mechanical loads in joints. It is a remarkable tissue: it can support loads exceeding ten times our body weight and bear 60+ years of daily mechanical loading despite having minimal regenerative capacity. I will discuss the physical principles underlying this exceptional mechanical response and crack resistance in AC, and compare our theoretical predictions with experimental results. The second focus of my talk consists of the dynamic mechanical response of actin networks. Actin is a key component of the cytoskeleton essential to cell growth, division, shape change, and motility. To enable this wide range of mechanical processes and properties, networks of actin filaments continuously disassemble and reassemble via active de/re-polymerization. I will discuss how de/re-polymerization kinetics of individual actin filaments translate to experimentally observed time-varying mechanical properties of dis/re-assembling networks. Understanding the mechanical structure function properties of these systems will provide insights into the dynamic response, toughness, and failure of biopolymer neworks in cells and tissues, tissue repair therapies, and design principles for soft robotics. |
Friday, March 9, 2018 8:36AM - 9:12AM |
X42.00002: Elastic networks with optimal mechanical properties Invited Speaker: Marc Durand Various elastic systems can be modeled as networks of interconnected beams. Examples include polymer gels, protein networks, crystal atomic lattices, granular materials, wood, and bones. On a length scale much larger than the typical beam length (“macroscopic” scale), such a network can be viewed as a continuous and homogeneous medium characterized by spatially constant elastic moduli. The relationship between the mechanical properties of elastic networks on a macroscopic level, and the details of their microstructures is the key to optimization and design of lightweight, strong, and tough materials. The continuum modelling of such discrete structures has a long history, going as back as the pioneering work of A. Cauchy and S. Poisson. The stiffness of such a system clearly depends on its density , defined as the volume of beams per unit volume of material. But for a given value of , it is also dramatically affected by the specific spatial arrangement of the elastic phase within the material. On dimensional grounds, the volumetric density of strain energy associated with a stretch-dominated deformation varies linearly with , while it scales as for the deformation of a three-dimensional network dominated by the beam bending mode [1]. Thus, for the low-density materials considered here ( ), a structure deforming primarily through the beam stretching mode is usually much stiffer. However, the constant of proportionality between and still varies significantly among stretched-dominated networks.\\ In this talk, I will present our numerical and theoretical investigations on the relation between the macroscopic mechanical response of a network under small strain condition and the details of its microstructure. I will stress that this relation is not straightforward. For instance, networks with identical node connectivity can have different stiffness. Conversely, networks with very different microstructures can present identical mechanical response. Moreover, contrary to a common belief, stiffness is not directly related to the triangulation of the mesh, and a fully triangulated network may have a lower stiffness than a network with few triangulated units. I will then show the existence of a class of isotropic networks which are stiffer than any other ones with the same symmetry, density and elastic phase [2, 3]. The elastic moduli of these optimal elastic networks can be calculated explicitly. They constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. I will establish a general set of criteria (which turn out to be necessary and sufficient conditions) that allow to identify these networks.\\ Relation between the mechanical and transport properties of these networks will also be discussed. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions. |
Friday, March 9, 2018 9:12AM - 9:48AM |
X42.00003: Cell contraction induces long-ranged stress stiffening in the extracellular matrix Invited Speaker: Pierre Ronceray Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells. |
Friday, March 9, 2018 9:48AM - 10:24AM |
X42.00004: Odd viscosity in chiral active materials Invited Speaker: Vincenzo Vitelli Chiral active materials are composed of self-spinning rotors that continuously inject energy and angular momentum at the microscale. Out-of-equilibrium materials with active-rotor constituents have been experimentally realized using nanoscale biomolecular motors, microscale active colloids, or macroscale driven chiral grains. Here, we show how such chiral active materials break both parity and time-reversal symmetries in their steady states, giving rise to a dissipationless linear-response coefficient called odd viscosity in the constitutive relations. This odd viscosity, analogous to the Hall viscosity of electron fluids, causes motion in a direction transverse to applied compression and allows the creation of crank-like active metamaterials. Our results suggest how an anomalous viscous response can be engineered in active metamaterials by controlling the dynamics of their constituents in the same spirit as an unusual elastic response can be engineered in passive metamaterials by controlling their architecture. |
Friday, March 9, 2018 10:24AM - 11:00AM |
X42.00005: Topology counts: Force distributions in random spring networks Invited Speaker: Andrew Sageman-Furnas Under large stresses, filamentous polymer networks often exhibit highly inhomogeneous force distributions. Forces propagate along nontrivial loops that make up a network's topology, where each nontrivial loop is a path that connects one boundary of the system to another. By introducing a toy model comprising ensembles of one-dimensional, periodic, linear spring networks, we demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks. In contrast to a mean-field approach, our graph-theoretic approach explicitly accounts for the full network topology and is in excellent agreement with numerical simulations. Our results are a first step towards understanding the concentration of forces along a few nontrivial loops, known as force chains, that has been observed in stressed 2D and 3D nonlinear networks. |
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