Local structure controls the nonaffine shear and bulk moduli of disordered solids.
ABSTRACT: Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.
Project description:We describe here experiments on the mechanics of hydrogel particle packings from the Behringer lab, performed between 2012 and 2015. These experiments quantify the evolution of all contact forces inside soft particle packings exposed to compression, shear, and the intrusion of a large intruder. The experimental set-ups and processes are presented and the data are concomitantly published in a repository (Barés et al. in Dryad, Dataset 10.5061/dryad.6djh9w0x8, 2019).
Project description:Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction.
Project description:Gels formed by semiflexible filaments such as most biopolymers exhibit non-linear behavior in their response to shear deformation, e.g., with a pronounced strain stiffening and negative normal stress. These negative normal stresses suggest that networks would collapse axially when subject to shear stress. This coupling of axial and shear deformations can have particularly important consequences for extracellular matrices and collagenous tissues. Although measurements of uniaxial moduli have been made on biopolymer gels, these have not directly been related to the shear response. Here, we report measurements and simulations of axial and shear stresses exerted by a range of hydrogels subjected to simultaneous uniaxial and shear strains. These studies show that, in contrast to volume-conserving linearly elastic hydrogels, the Young's moduli of networks formed by the biopolymers are not proportional to their shear moduli and both shear and uniaxial moduli are strongly affected by even modest degrees of uniaxial strain.
Project description:The local elasticity of glasses is known to be inhomogeneous on a microscopic scale compared to that of crystalline materials. Their vibrational spectrum strongly deviates from that expected from Debye's elasticity theory: The density of states deviates from Debye's law, the sound velocity shows a negative dispersion in the boson-peak frequency regime and there is a strong increase of the sound attenuation near the boson-peak frequency. By comparing a mean-field theory of shear-elastic heterogeneity with a large-scale simulation of a soft-sphere glass we demonstrate that the observed anomalies in glasses are caused by elastic heterogeneity. By observing that the macroscopic bulk modulus is frequency independent we show that the boson-peak-related vibrational anomalies are predominantly due to the spatially fluctuating microscopic shear stresses. It is demonstrated that the boson-peak arises from the steep increase of the sound attenuation at a frequency which marks the transition from wave-like excitations to disorder-dominated ones.
Project description:Understanding of the conformational ensemble of flexible polyelectrolytes, such as single-stranded nucleic acids (ssNAs), is complicated by the interplay of chain backbone entropy and salt-dependent electrostatic repulsions. Molecular elasticity measurements are sensitive probes of the statistical conformation of polymers and have elucidated ssNA conformation at low force, where electrostatic repulsion leads to a strong excluded volume effect, and at high force, where details of the backbone structure become important. Here, we report measurements of ssDNA and ssRNA elasticity in the intermediate-force regime, corresponding to 5- to 100-pN forces and 50-85% extension. These data are explained by a modified wormlike chain model incorporating an internal electrostatic tension. Fits to the elastic data show that the internal tension decreases with salt, from [Formula: see text]5 pN under 5 mM ionic strength to near zero at 1 M. This decrease is quantitatively described by an analytical model of electrostatic screening that ascribes to the polymer an effective charge density that is independent of force and salt. Our results thus connect microscopic chain physics to elasticity and structure at intermediate scales and provide a framework for understanding flexible polyelectrolyte elasticity across a broad range of relative extensions.
Project description:Viscoelastic fluids exhibit rheological nonlinearity at a high shear rate. Although typical nonlinear effects, shear thinning and shear thickening, have been usually understood by variation of intrinsic quantities such as viscosity, one still requires a better understanding of the microscopic origins, currently under debate, especially on the shear-thickening mechanism. We present accurate measurements of shear stress in the bound hydration water layer using noncontact dynamic force microscopy. We find shear thickening occurs above ? 10(6) s(-1) shear rate beyond 0.3-nm layer thickness, which is attributed to the nonviscous, elasticity-associated fluidic instability via fluctuation correlation. Such a nonlinear fluidic transition is observed due to the long relaxation time (? 10(-6) s) of water available in the nanoconfined hydration layer, which indicates the onset of elastic turbulence at nanoscale, elucidating the interplay between relaxation and shear motion, which also indicates the onset of elastic turbulence at nanoscale above a universal shear velocity of ? 1 mm/s. This extensive layer-by-layer control paves the way for fundamental studies of nonlinear nanorheology and nanoscale hydrodynamics, as well as provides novel insights on viscoelastic dynamics of interfacial water.
Project description:Rejuvenation of metallic glasses, bringing them to higher-energy states, is of interest in improving their plasticity. The mechanisms of rejuvenation are poorly understood, and its limits remain unexplored. We use constrained loading in compression to impose substantial plastic flow on a zirconium-based bulk metallic glass. The maximum measured effects are that the hardness of the glass decreases by 36%, and its excess enthalpy (above the relaxed state) increases to 41% of the enthalpy of melting. Comparably high degrees of rejuvenation have been reported only on microscopic scales at the centre of shear bands confined to low volume fractions. This extreme rejuvenation of a bulk glass gives a state equivalent to that obtainable by quenching the liquid at ~1010?K?s-1, many orders of magnitude faster than is possible for bulk specimens. The contrast with earlier results showing relaxation in similar tests under tension emphasizes the importance of hydrostatic stress.
Project description:We report on a quantitative optical elastographic method based on shear wave imaging optical coherence tomography (SWI-OCT) for biomechanical characterization of cardiac muscle through noncontact elasticity measurement. The SWI-OCT system employs a focused air-puff device for localized loading of the cardiac muscle and utilizes phase-sensitive OCT to monitor the induced tissue deformation. Phase information from the optical interferometry is used to reconstruct 2-D depth-resolved shear wave propagation inside the muscle tissue. Cross-correlation of the displacement profiles at various spatial locations in the propagation direction is applied to measure the group velocity of the shear waves, based on which the Young's modulus of tissue is quantified. The quantitative feature and measurement accuracy of this method is demonstrated from the experiments on tissue-mimicking phantoms with the verification using uniaxial compression test. The experiments are performed on ex vivo cardiac muscle tissue from mice with normal and genetically altered myocardium. Our results indicate this optical elastographic technique is useful as a noncontact tool to assist the cardiac muscle studies.
Project description:Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic model of solid flow that incorporates a local Mohr-Coulomb failure criterion. This differs from the interpretation of Le Bouil et al., which is based on purely elastic considerations ignoring the potential role of local friction on deformation patterns. We show that the angle observed in the microscopic correlations can be understood by combining the elastic interactions associated with Eshelby transformation with the local failure criterion. At large strains, we also induce permanent shear bands at an angle that is different from the one observed in the correlation pattern. We interpret this angle as the one that leads to the maximal instability of slip lines.
Project description:Self-organization, and transitions from reversible to irreversible behavior, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behavior is related to yielding of amorphous solids, jamming, memory formation, etc. How these phenomena are related to each other has not, however, been much studied. In order to obtain a unified view of the different regimes of behavior, and transitions between them, we investigate computationally the response of soft-sphere assemblies to athermal cyclic-shear deformation over a wide range of densities and amplitudes of shear deformation. Cyclic-shear deformation induces transitions from reversible to irreversible behavior in both unjammed and jammed soft-sphere packings. Well above the minimum isotropic jamming density ([Formula: see text]), this transition corresponds to yielding. In the vicinity of the jamming point, up to a higher-density limit, we designate [Formula: see text], an unjammed phase emerges between a localized, absorbing phase and a diffusive, irreversible, phase. The emergence of the unjammed phase signals the shifting of the jamming point to higher densities as a result of annealing and opens a window where shear jamming becomes possible for frictionless packings. Below [Formula: see text], two distinct localized states, termed point- and loop-reversible, are observed. We characterize in detail the different regimes and transitions between them and obtain a unified density-shear amplitude phase diagram.