1The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the cutting/slicing and eating characteristics of food gels 1 . It is also critical for their utilization in tissue engineering, for which mechanical protection of encapsulated components is needed 2,3 . Its dependence on loading rate 4 and, recently, on the density and strength of cross-links 3 has been investigated.But no attention was paid so far to solvent nor to environment effects. Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures. We show on this model system that: (i) increasing solvent viscosity slows down cracks; (ii) soaking with solvent increases markedly gel fragility; (iii) tuning the viscosity of the (miscible) environmental liquid affects crack propagation via diffusive invasion of the crack tip vicinity. The results point toward the fact that fracture occurs by viscoplastic chain pull-out. This mechanism, as well as the related phenomenology, should be common to all reversibly cross-linked (physical) gels.Gelatin gels are constituted of denatured (coil) collagen chains, held together by crosslinks made of segments of three-stranded helices stabilized by hydrogen bonds 5 . This network, swollen by the aqueous solvent, which controls its (undrained) bulk modulus, is responsible for the finite shear modulus µ, of order a few kPa. Hence, hydrogels can be considered incompressible. One estimates average mesh sizes ξ ∼ (kT /µ) 1/3 of order 10 nm, i.e. coil segments involving a few 100 units (residues) 6 . Moreover, in the presence of pressure gradients, the solvent diffuses through the network. This poroelastic behaviour 7,8 controls e.g. slow solvent draining in or out of the gel under applied stresses.They are thermoreversible, i.e., in contrast with chemical, covalently cross-linked gels, their network "melts" close above room temperature. This behavior, assignable to their small cross-link binding energy, leads to the well studied 5 slow aging (strengthening) of µ, and to their noticeable creep under moderate stresses 9 . When stretched at constant strain rate, gelatin gels ultimately fail at a strain ∼ 1 which, though rather poorly reproducible, is clearly rate-dependent 4 . In order to get insight into the nature of the dissipative processes at play, one needs to investigate the propagation of cracks independently from their (stochastic) nucleation 10 . Here we study the fracture energy G(V ) needed to propagate a crack at constant velocity V in notched long thin plates (see Fig. 1) of gels differing by the glycerol content of their aqueous solvent.

International audienceThe rate dependence of fracture has been studied in a series of physically associating triblock copolymer gels that have a well-defined molecular structure. Compressive experiments were performed to develop a strain energy function that accurately captures the strain hardening behavior of these materials. This same strain energy function was utilized in a finite element model of the crack tip stresses, which become highly anisotropic at stress values below the failure strength of the gels. The rate dependence of the energy release rate, G, is independent of the gel concentration when G is normalized by the small strain Young's modulus, E. The gels exhibit a transition from rough, slow crack propagation to smooth, fast crack propagation for a well-defined value of the characteristic length, G/E

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. On the sensor side, without a reference beam, the CCD camera provides only intensity measurements. Within this framework, this paper shows that the TM can still be retrieved, through signal processing techniques of phase retrieval. This is experimentally validated on three criteria : quality of prediction, distribution of singular values, and quality of focusing.

We present an extensive experimental study of mode-I, steady, slow crack dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic stiffness to gel composition and history we confirm and extend the model for fracture of physical hydrogels which we proposed in a previous paper (Nature Mater. 5, 552 (2006)), which attributes decohesion to the viscoplastic pull-out of the network-constituting chains. So, we propose that, in contrast with chemically cross-linked ones, reversible gels fracture without chain scission.

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The adhesive properties of a material can be greatly affected simply by wrinkling its surface. We show the importance of selecting the wrinkle feature sizes (amplitude, b; and wavelength, λ) that complement the material-defined length scale related to the adhesion energy and modulus. A rigid circular cylindrical punch patterned with aligned wrinkles ranging in amplitude from 0.5 to 5.0 μm with a fixed aspect ratio of 0.1 is used to characterize the adhesion of elastic films of smooth poly(dimethyl siloxane) (PDMS). The cross-linker concentration used to form the PDMS layers is varied to determine the impact of material properties on wrinkled surface adhesion. The elastic films have an average thickness of 240 μm and the average probe radius is 1 mm, leading to a confined contact scenario. The separation stress and work of debonding are presented for each cross-linker concentration with testing rates ranging over 3 orders of magnitude. For stiffer films (10 wt % cross-linker, E' ≈ 3.00 MPa), small wrinkles (b ≈ 0.5 μm) increase the separation stress by nearly 200% relative to a smooth interface whereas large wrinkles (b ≈ 5.0 μm) are shown to reduce adhesion significantly. A substantial increase in the debonding energy is also observed for these small-amplitude wrinkles contacting stiff materials. No discernible impact of wrinkled surface topography on the adhesion of softer (2 and 4 wt % cross-linker, 0.05 MPa < E' < 0.30 MPa) films is measured.

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasi-static crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at V -independent symmetry-preserving angles, (ii) a sub-critical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities.Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger that low strain moduli.PACS numbers: 62.20. Mk, 83.80.Kn Over the past two decades, considerable effort has been devoted to characterizing and understanding the statistical properties of the roughness of fracture surfaces in linear elastic disordered materials. Investigation of a wide variety of systems, ranging from brittle silica glass to ductile metallic alloys, has revealed the ubiquity of wide roughness spectra exhibiting self-affine characteristics on sizeable wavelength ranges. On the basis of analysis of height-height correlation functions in a single direction, E. Bouchaud et al.[1] first conjectured a fully universal behavior summed up into a single Hurst exponent. The discrepancies between the predictions of various subsequent theoretical models have pointed toward the importance of also investigating possible anisotropies of the scaling properties [2]. Work along this line indeed reveals different scaling exponents along the crack propagation direction and the (orthogonal) crack front one. From this, Ponson et al. [3] conclude that the self-affinity of the roughness is described by a Family-Vicsek scaling, hence by a set of two exponents. Within their new analysis, full universality is no longer the case since they evidence the existence of at least two classes of materials.However, on the basis of their theoretical work, Bouchbinder et al. [4] have recently raised several new issues. In particular, they point to the necessity of a full 2D analysis of the correlations and find, when reexamining some experimental data, that a host of up to now unidentified exponents appear. They insist on the need to focus on the effects of departures from linear elasticity in the fracture process.In this spirit we report here on the nature of surface morphologies resulting from the fracture of gelatin, a highly compliant thermally reversible hydrogel, in the strongly subsonic regime. We show that these surfaces present very striking anisotropic features. Namely, the rms roughness R(θ), measured along a direction at angle θ from the propagation one Ox, exhibits two symmetrypreserving maxima for θ = ±θ m . For gels with a fixed gelatin concentration, this "magic angle" θ m is constant over more than one decade of both crack velocity V and solvent viscosity η. Moreover, below a critical, η-dependent, velocity V c a new regime develops, characterized by a cross-hatched (CH) mo...