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International audience; Deformation fields at the surface of diametrically squeezed shallow cylinders in the large deformation regime are measured experimentally and numerically for different material behaviour in the large deformation regime. By means of a digital image correlation method optimized for large displacements, strain fields are measured and compared with finite element simulations. Assuming a neo-Hookean behaviour for cylinders made of rubber silicone, the strain field is found to be in quantitative agreement with non-linear finite element simulations up to the highest deformations reached in our experiments (15%). For materials that follow an elastoplastic constitutive law, agreement is lost after few percents of deformation and location of the strain field differences are identified up to strains as high as 30%. Strain field evolution is also measured for solid foam cylinders up to 60% of global deformation strain. This method that can be applied to a broad variety of materials, even in the occurrence of large deformations, provides a way to study quantitatively local features of the mechanical contact.

International audience; Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacry-lamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and surface energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which surface energy and surface tension coincide for amorphous polymer gels.

International audience; Bifurcations in the equilibrium shape of a thick elastic layer attached to a circular rigid cylinder rotating about its axis are investigated analytically and numerically. The centrifugal force breaks the symmetry of the system leading to deformations invariant along the axis as the result of an instability. The instability threshold depends at linear order on the relative thickness of the compliant layer, and on a dimensionless control parameter based on the elastic modulus, the angular velocity and the outer radius. A weakly non linear analysis, carried out for layers following the Mooney-Rivlin constitutive law, points out the discon-tinuous (sub-critical) features of the bifurcation, except for relative thickness laying in a very narrow range in which the bifurcation is super-critical. Numerical simulations in the fully post-buckled regime yield the absolute instability threshold, and the order in the rotational symmetry of the developed equilibrium shape.

International audience; Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.

Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to $1$. Inspired by the contact mechanics in the Hertz's limit, we show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.

International audience; Soft granular materials are assemblies of highly deformable grains interacting via surface forces. The large grain deformations of these materials differ them from hard granular systems, in which, their behaviors are essentially governed by grain rearrangements. In this paper, we study the uniaxial compression of soft granular materials using a numerical approach based on the Material Point Method allowing for large grain deformations, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains. Considering the neo-Hookean and elasto-plastic grains, the compaction of 2D soft granular packings is analyzed. We focus essentially on the evolution of the packing vertical stress as a function of the packing fraction and the predictive models are proposed.

We investigate the nucleation and propagation of cracks in self-assembled viscoelastic fluids, which are made of surfactant micelles reversibly linked by telechelic polymers. The morphology of the micelles can be continuously tuned, from spherical to rod-like to wormlike, thus producing transient double networks when the micelles are sufficiently long and entangled, and transient single networks otherwise. For a single network, we show that cracks nucleate when the sample deformation rate involved is comparable to the relaxation time scale of the network. For a double network, by contrast, significant rearrangements of the micelles occur as a crack nucleates and propagates. We show that birefringence develops at the crack tip over a finite length, $\xi$, which corresponds to the length scale over which micelles alignment occur. We find that $\xi$ is larger for slower cracks, suggesting an increase of ductility., Comment: 10 pages, 4 figures

International audience; We investigate the non-linear buckling patterns produced by the elastic Rayleigh-Taylor instability in a hyper-elastic slab hanging below a rigid horizontal plane, using a combination of experiments, weakly non-linear expansions and numerical simulations. Our experiments reveal the formation of hexagonal patterns through a discontinuous transition. As the unbuckled state is transversely isotropic, a continuum of linear modes become critical at the first bifurcation load: the critical wavevectors form a circle contained in a horizontal plane. Using a weakly non-linear post-bifurcation expansion, we investigate how these linear modes cooperate to produce buckling patterns: by a mechanism documented in other transversely isotropic structures, three-modes coupling make the unbuckled configuration unstable with respect to hexagonal patterns by a transcritical bifurcation. Stripe and square patterns are solutions of the post-bifurcation expansion as well but they are unstable near the threshold. These analytical results are confirmed and complemented by numerical simulations.

International audience; Most of the 2D studies on granular materials consider an assembly of cylindrical particles in the small deformation regime. Investigating the range of validity of the small deformation hypothesis is therefore of crucial importance in order to determine the quantitative relevance of the predictions emerging from these 2D studies. We introduce here a novel experimental setup based on high resolution imaging and image correlation, and capable of measuring the strain field inside the particles with a cutting edge accuracy. We measure the strain field inside a unique circular cylindrical elastic particle undergoing an uniaxial compression. The significant deviations arising from the comparison with the predictions of the small deformation limit predicted by the Hertz's theory, and numerical simulations, give insight to improve the modeling of 2D granular materials.

International audience; This paper concerns modeling of soft granular materials in which the grains are highly deformable. In order to simulate these materials, an approach based on an implicit formulation of the Material Point Method in the context of the finite strain theory, allowing for large deformations of grains, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains, is proposed. In this context, the Mooney-Rivlin constitutive relationship is applied with two different set of elastic parameters. Considering these two material behaviors, a uniaxial compression of 2D soft granular packings is analyzed. The stress-strain relation and the evolution of the packing fraction as well as of the connectivity of the grains are discussed.

International audience; Interfacial tension between immiscible phases is a well-known phenomenon, which manifests itself in everyday life, from the shape of droplets and foam bubbles to the capillary rise of sap in plants or the locomotion of insects on a water surface. More than a century ago, Korteweg generalized this notion by arguing that stresses at the interface between two miscible fluids act transiently as an effective, nonequilibrium interfacial tension, before homogenization is eventually reached. In spite of its relevance in fields as diverse as geosciences, polymer physics, multiphase flows, and fluid removal, experiments and theoretical works on the interfacial tension of miscible systems are still scarce, and mostly restricted to molecular fluids. This leaves crucial questions unanswered, concerning the very existence of the effective interfacial tension, its stabilizing or destabilizing character, and its dependence on the fluid's composition and concentration gradients. We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg's predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface. We introduce a simple yet general model that rationalizes nonequilibrium interfacial stresses to arbitrary mixtures, beyond Korteweg's small gradient regime, and show that the model captures remarkably well both our new measurements and literature data on molecular and polymer fluids. Finally, we briefly discuss the relevance of our model to a variety of interface-driven problems, from phase separation to fracture, which are not adequately captured by current approaches based on the assumption of small gradients.

Extra-large deformations in ultra-soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius $a$ in an incompressible ultra-soft elastic medium. We find a scaling law for the penetration depth ($\delta$) of the bead inside the softest gels as $\delta \sim a^{3/2}$. While this result is inconsistent with an ideal neo-Hookean model of elastic deformation, according to which the displacement fields must diverge, it is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly non-linear materials.

We explore the influence of particle softness and internal structure on both the bulk and interfacial rheological properties of colloidal suspensions. We probe bulk stresses by conventional rheology, by measuring the flow curves, shear stress vs strain rate, for suspensions of soft, deformable microgel particles and suspensions of near hard-sphere-like silica particles. A similar behavior is seen for both kind of particles in suspensions at concentrations up to the random close packing volume fraction, in agreement with recent theoretical predictions for sub-micron colloids. Transient interfacial stresses are measured by analyzing the patterns formed by the interface between the suspensions and their own solvent, due to a generalized Saffman-Taylor hydrodynamic instability. At odd with the bulk behavior, we find that microgels and hard particle suspensions exhibit vastly different interfacial stress properties. We propose that this surprising behavior results mainly from the difference in particle internal structure (polymeric network for microgels vs compact solid for the silica particles), rather than softness alone., Comment: 20 pages, 8 figures

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other.

We present a comprehensive review of the current state of fracture phenomena in transient networks, a wide class of viscoelastic fluids. We will first define what is a fracture in a complex fluid, and recall the main structural and rheological properties of transient networks. Secondly, we review experimental reports on fractures of transient networks in several configurations: shear-induced fractures, fractures in Hele-Shaw cells and fracture in extensional geometries (filament stretching rheometry and pendant drop experiments), including fracture propagation. The tentative extension of the concepts of brittleness and ductility to the fracture mechanisms in transient networks is also discussed. Finally, the different and apparently contradictory theoretical approaches developed to interpret fracture nucleation will be addressed and confronted to experimental results. Rationalized criteria to discriminate the relevance of these different models will be proposed., Review; Rheologica Acta 2013 published on line

Fracture processes are ubiquitous in soft materials, even in complex fluids, subjected to stresses. To investigate these processes in a simple geometry, we use a model self-assembled transient gel and study the instability patterns obtained in a radial Hele-Shaw cell when a low viscosity oil pushes the more viscous transient gel. Thanks to an analysis of the morphology of the patterns, we find a discontinuous transition between the standard Saffman-Taylor fingering instability and a fracturing instability as the oil injection rate increases. Our data suggest that the flow properties of the gel ahead of the finger tip controls the transition towards fracturing. By analyzing the displacement field of the gel in the vicinity of the fingers and cracks, we show that in the fingering regime, the oil gently pushes the gel, whereas in the fracturing regime, the crack tears apart the gel, resulting in a strong drop of the gel velocity ahead of the crack tip as compared to the tip velocity. We find a unique behavior for the whole displacement field of a gel around a crack, which is drastically different from that around a finger, and reveals the solid-like behavior of the gel at short time. Our experiments and analysis provide quantitative yet simple tools to unambiguously discriminate a finger from a crack in a visco-elastic material., Comment: to appear in Soft Matter

International audience; The rheological properties of associative polymers (APs) are modified by the presence of surfactants, but little is known about the influence of surfactants on the structure of selfassociated aggregates in aqueous media. Using small-angle neutron scattering (SANS), the structure of self-assembled aggregates of a series in concentration of telechelic poly(ethylene oxide) (M ≈ 20 000 g mol 1) end-capped by hydrocarbon or of fluorocarbon groups in the presence of a fixed amount of sodium dodecyl sulfate (SDS) or lithium perfluorooctyl sulfonate (LiFOS) is investigated. In all systems studied, surfactants and telechelic polymers form mixed aggregates. Their aggregation numbers are reduced and evolve with the concentration of each component. For example, with SDS at 8 mM, the mixed aggregates are composed of 1 AP and 15 SDS or 9 APs and 45 SDS molecules for 1 or 3 wt % of polymer, respectively. The addition of a surfactant enhances the number density of aggregates, which causes the increase of the gel viscosity.

International audience; We report on a small angle neutron scattering (SANS) study of self-organization of a novel triblock copolymer containing a crystalline poly(ethylene terephthalate) oligomer, a rubbery poly(lauryl acrylate) midblock, and a polyelectrolyte block (quaternized poly(2-(dimethylamino)ethyl methacrylate)) of various length. The rheology of the solutions showed a transition from Newtonian flow at low concentrations, to shear-thinning at intermediate concentrations, and finally a yield behavior at high concentrations. The microstructure of the samples investigated by SANS was found to evolve strongly with the polyelectrolyte block length. The data were analyzed in terms of aggregation numbers, radius of gyration, and aggregate hydration. Complete modeling of the intensity curves was achieved by an inversion method extracting an average aggregate radial volume fraction profile. In both rheology and microstructure, a surprising strong impact of the small PET block was observed.

Using a uniaxial deformation setup, we show that the free surface of an homogeneous elastic material is unstable under compression: parallel grooves nucleate orthogonally to the direction of compression when a characteristic stretch ratio a* is reached. We measure experimentally the variation of a* as well as the wavelength of the grooves as a function of the thickness h(0) of the material. All data collapse on single curves when normalizing h(0) by a characteristic length which is the ratio of the surface tension to the shear modulus of the material. This length scale acts as a regularization parameter for the system. We introduce a theoretical model that captures well the features of the instability. The observed nucleation-like process for the grooves development suggests that the instability is subcritical.

International audience; We introduce a model describing failure in transient networks. The two main ingredients are (i) the lifetime of a non connecting bond is far smaller than that of an active bond, (ii) the lifetime of an active bond is a decreasing function of the force carried by this bond. We show that these assumptions are sufficient to predict a failure threshold. Below this threshold the bonds distribution is driven by a diffusion equation. The bonds are redistributed homogeneously in the sample, leading to its self-adhesive feature. Beyond this threshold, the diffusion coefficient is negative, causing a catastrophic amplification of any heterogeneity. The final stage is the fracture. Finally, we give an interpretation of delayed fractures for these kinds of materials.

International audience; The interactions, in aqueous medium, between hydrophobically end-capped poly(ethylene oxide) (PEO) and sodium dodecyl sulfate (SDS) have been investigated by means of tensiometry, 13C NMR spectroscopy and small-angle neutron scattering (SANS). Besides the association of SDS with the ethylene oxide backbone of associative polymer (AP), revealed by 13C NMR, SDS interacts with hydrophobic endcaps leading to the formation of mixed aggregates. At low SDS concentration, the formation of flowerlike mixed aggregates is governed by AP. Despite the poor affinity between hydrocarbon and fluorocarbon chains, uncooperative binding was detected between SDS and fluorinated AP end groups. With a further increase of SDS concentration, the critical aggregation concentration (cac) marks the onset of SDS cooperative binding with AP end-caps. This process driven by SDS leads to the formation of micellar aggregates with a necklacelike structure. Due to the SDS/AP complex formation, the surfactant aggregation number determined by SANS is lower than that observed in pure water.

International audience; Model self-assembled networks of telechelic polymer C18-PEO(35k)-C18 in water have been studied. The rheology of such transient networks has been investigated as a function of polymer concentration, and a typical percolation law has been observed. The network structure has been characterised by Small Angle Neutron Scattering in D2O, where the interactions between micelles formed by the hydrophobic C18-stickers of the polymer give rise to a peak in the scattered intensity. These model networks have then been used as a matrix for the incorporation of silica nanoparticles (R=10nm), and we have checked individual dispersion by scattering using contrast variation. The rheological response of the networks is considerably modified by the presence of the silica nanoparticles, and in particular an interesting dependence of the relaxation time on silica concentration has been found. The analogy in reinforcement behaviour of such a self-assembled, viscoelastic, and aqueous system with model experiments of elastomers filled with nanoparticles is discussed by comparison to a silica-latex system.

The elastic properties of organic–inorganic two-dimensional crystals floating at the water surface have been fully characterized by grazing incidence X-ray diffuse scattering and high-resolution diffraction. We show that the strong interaction between the organic molecules and the inorganic divalent cations is enough for these nm thick crystals to behave like true solids, with a residual tension of 1 × 10−4–10−3N m−1. Their bending rigidity is renormalized as κ(q) ∝ q−ηk with ηk = 0.25 ± 0.07 and a microscopic value ≈ 100 kBT at q = 1 × 109 m−1. The in-plane elastic constants behave like qηu with ηu = 1.41 ± 0.2, obeying the scaling relation ηu = 2 − 2ηk. These results are consistent with a long-range phonon-mediated interaction between out-of-plane fluctuations but the values of the exponents differ from those generally obtained in numerical simulations.

We show that a large class of viscoelastic fluids, i.e., transient networks, are brittle according to the Griffith's theory of solid fracture. However, contrary to solids, cracks are intrinsic to the material arising from the equilibrium nature of the fluid microstructure. The brittleness of these fluids comes from thermal fluctuations of bonds distribution. In this approach, the rupture stress is predicted to be on the order of the Young modulus, in very good agreement with experimental values.

International audience; A method was developed to prepare asymmetric end-capped poly(ethylene oxide)s (PEOs), containing an alkyl group on one chain end and a perfluoroalkyl group on the other one (C18H37-PEO-C2H4-C8F17 and C18H37-PEO-C10H20-C8F17). These new telechelic associative polymers (APs) were synthesized by anionic polymerization of ethylene oxide initiated by an alkoxide (C18H37-O-K+) followed by esterification. The rheological behavior of asymmetric and analogous symmetric APs in aqueous solutions has been investigated as a function of polymer concentration (C), hydrophobic end-cap and surfactant used to homogenize the system: sodium dodecyl sulfate (SDS) or lithium perfluorooctyl sulfonate (LiFOS). A steep increase of the static viscosity η, attributed to the formation of a multiconnected network, is observed for C ≈ 1 wt %. Semidilute solutions present a Maxwellian rheological behavior with only one relaxation time τ associated with the least hydrophobic end group. The viscoelastic response is modified by the interactions between hydrophobic end groups and surfactant inside mixed aggregates.

International audience; We show that two types of complex fluids belonging to the same class of soft materials (transient networks), and having the same linear rheological properties (Maxwell fluids) exhibit two distinct fracture behaviors as solids do. We have designed a third experimental system that captures the distinct features of both former ones. We show that it could be a good candidate to investigate the brittle-ductile transition in complex fluids.

A single lipid molecular bilayer of 17 or 18 carbon chain phosphocholines, floating in water near a flat wall, is prepared in the bilayer gel phase and then heated to the fluid phase. Its structure (electron density profile) and height fluctuations are determined by using x-ray reflectivity and nonspecular scattering. By fitting the off-specular signal to that calculated for a two-dimensional membrane using a Helfrich Hamiltonian, we determine the three main physical quantities that govern the bilayer height fluctuations: The wall attraction potential is unexpectedly low; the surface tension, roughly independent on chain length and temperature, is moderate (≈5 × 10 –4 J·m –2 ) but large enough to dominate the intermediate range of the fluctuation spectrum; and the bending modulus abruptly decreases by an order-of-magnitude from 10 –18 J to 10 –19 J at the bilayer gel-to-fluid transition.