The goal of this study is to better understand the mathematical structure and ramifications of the secondorder homogenization of low-frequency wave motion in periodic solids. To this end, multiple-scales asymptotic approach is applied to the scalar wave equation (describing anti-plane shear motion) in one and two spatial dimensions. In contrast to previous studies where the second-order homogenization has lead to the introduction of a single fourth-order derivative in the governing equation, present investigation demonstrates that such (asymptotic) approach results in a family of field equations uniting spatial, temporal, and mixed fourth-order derivatives-that jointly control incipient wave dispersion. Given the consequent freedom in selecting the affiliated lengthscale parameters, the notion of an optimal asymptotic model is next considered in a onedimensional setting via its ability to capture the salient features of wave propagation within the first Brillouin zone, including the onset and magnitude of the phononic band gap. In the context of two-dimensional wave propagation, on the other hand, the asymptotic analysis is first established in a general setting, exposing the constant shear modulus as sufficient condition under which the second-order approximation of a bi-periodic elastic solid is both isotropic and limited to even-order derivatives. On adopting a chessboard-like periodic structure (with contrasts in both modulus and mass density) as a testbed for in-depth analytical treatment, it is next shown that the second-order approximation of germane wave motion is governed by a family fourthorder differential equations that: i) entail exclusively even-order derivatives and homogenization coefficients that depend explicitly on the contrast in mass density; ii) describe anisotropic wave dispersion characterized by the "sin 4 θ + cos 4 θ" term, and iii) include the asymptotic model for a square lattice of circular inclusions as degenerate case. For completeness, the analysis is illustrated by a set of numerical results highlighting the effects of periodic structure on the long-wavelength material response in terms of wave dispersion, phononic band gap, and second-order anisotropy.

The full 3‐D macroscopic mechanical behavior of snow is investigated by solving kinematically uniform boundary condition problems derived from homogenization theories over 3‐D images obtained by X‐ray tomography. Snow is modeled as a porous cohesive material, and its mechanical stiffness tensor is computed within the framework of the elastic behavior of ice. The size of the optimal representative elementary volume, expressed in terms of correlation lengths, is determined through a convergence analysis of the computed effective properties. A wide range of snow densities is explored, and power laws with high regression coefficients are proposed to link the Young's and shear moduli of snow to its density. The degree of anisotropy of these properties is quantified, and Poisson's ratios are also provided. Finally, the influence of the main types of metamorphism (isothermal, temperature gradient, and wet snow metamorphism) on the elastic properties of snow and on their anisotropy is reported.

Stress-oftening is one of the significant features experienced by cohesive-frictional granular materials subjected to deviatoric loading. This paper focuses on mesoscopic evolutions of the dense granular assembly during a typical drained biaxial test conducted by DEM, and proposes mesoscopically-based framework to interpret both hardening and softening mechanisms. In this context, force chains play a fundamental role as they form the strong contact phase in granular materials. Their geometrical and mechanical characteristics, as well as the surrounding structures, are defined and analyzed in terms of force chain bending evolution, local dilatancy, rotation and non coaxiality between the principal stress and the geometrical orientation of force chains. By distinguishing two zones inside and outside shear band, force chain rotations are shown to be of opposite sign, which may contribute to the observed macroscopic softening as one of the origin of the structural softening.

Summary Within the framework of the second‐order work theory, the onset of instabilities is explored numerically in loose granular materials through three‐dimensional DEM simulations. Stress controlled directional analysis are performed in Rendulic's plane, and a particular attention is paid to transient evolutions at the microscale. Thanks to a micromechanical analysis, the onset and development of transient mechanical instabilities is explored. It is shown that these instabilities result from the unjamming and bending of a few force chains associated with a local burst of kinetic energy. This burst of kinetic energy propagates to the whole sample and provokes a generalized unjamming of force chains. As force chains buckle, a phase transition from a quasi‐static to an inertial regime is observed. At the macroscopic scale, this results in a transient softening and a loss of controllability. After the collapse of existing force chains, the development of plastic strain is eventually stopped as new stable force chains are built.

Based on a discrete element method (DEM), this paper investigates the basic mechanisms and the associated scales related to grain detachment and grain transport processes at stake in widely graded poly-disperse assemblies of spheres subjected to internal fluid flows. From the identification of force chains, particles sensitive to grain detachment are identified. Based on the computation of autocorrelation lengths, a typical length scale associated with this phenomenon is then defined. From the characterization of the void space as a pore network, particles eligible for grain transport are identified among the detachable particles. Based on the definition of a mean travel distance, the typical length scale associated with grain transport is finally characterized. The comparison between the two length scales highlights a scale separation between grain detachment and grain transport.

Summary Internal erosion by suffusion can change dramatically the constitutive behavior of granular materials by modifying the fabric of granular materials. In this study, the effect of an internal fluid flow on granular materials is investigated at the material point scale using the numerical coupling between a discrete element method (DEM) and a pore‐scale finite volume (PFV) coupling scheme. The influence of the stress state and the hydraulic loading (direction and intensity) on the occurrence of grain transport in dense widely graded granular samples is thus investigated and interpreted in terms of micromechanics. In particular, it is shown that grain transport is increased when the macroscopic flow direction is aligned with the privileged force chain orientation. The stress‐induced microstructure modifications are shown to influence the transport distances by controlling the number of rattlers.

Recent researches on the behavior of gravelly sands advocate for the use of skeleton void ratio to characterize their density state. Skeleton void ratio corresponds to the void ratio of grains constituting the stress-bearing skeleton. However, such a void ratio relies on parameters difficult to determine in practice, such as the fraction of fine grains that take part actively in the load bearing skeleton. Also, it fails to consider the effect of Grain Size Distribution (GSD) of gravel and sand grains. Therefore, the skeleton void ratio index introduced by Chang et al (2015) is revisited to account for the effect of GSD of both gravel and sand grains. Two semi-empirical equations are developed in this paper to connect GSD parameters with skeleton void ratio parameters. The validity of the proposed equations has been checked for a particular class of gravelly sand materials. A series of specially-designed drained triaxial tests on gravelly sands were then conducted. Test results show that it is essential to consider the effect of GSD when using skeleton void ratio index. It also verifies the effectiveness and applicability of the proposed updated skeleton void ratio, which shows advantages in characterizing critical state lines of gravelly sands.

International audienceGranular materials react under external loading by self-organizing the topology of the grain assembly. Thus, quasi-linear grain patterns, known as force chains, develop within the assembly to carry the main part of the external loading. The stability of these grain patterns controls the strength of the material, under given loading conditions. This manuscript investigates the mechanical behavior of such grain columns and exhibits some instability modes that can occur even when the local behavior at the contact between grains is purely elastic. First, an analytical approach is developed, and the ability of a grain column to collapse is demonstrated. Then this result is confirmed from numerical simulations performed using a discrete element method