In this paper we investigate the loading and unloading behavior of soft solids in adhesive contact with randomly rough profiles. The roughness is assumed to be described by a self-affine fractal on a limited range of wave-vectors. A spectral method is exploited to generate such randomly rough surfaces. The results are statistically averaged, and the calculated contact area and applied load are shown as a function of the penetration, for loading and unloading conditions. We found that the combination of adhesion forces and roughness leads to a hysteresis loading-unloading loop. This shows that energy can be lost simply as a consequence of roughness and van der Waals forces, as in this case a large number of local energy minima exist and the system may be trapped in metastable states. We numerically quantify the hysteretic loss and assess the influence of the surface statistical properties and the energy of adhesion on the hysteresis process.

In this work, Discrete Elements Method simulations are carried out to investigate the effective stiffness of an assembly of frictional, elastic spheres under anisotropic loading. Strain probes, following both forward and backward paths, are performed at several anisotropic levels and the corresponding stress is measured. For very small strain perturbations, we retrieve the linear elastic regime where the same response is measured when incremental loading and unloading are applied. Differently, for a greater magnitude of the incremental strain a different stress is measured, depending on the direction of the perturbation. In the case of unloading probes, the behavior stays elastic until non-linearity is reached.Under forward perturbations, the aggregate shows an intermediate inelastic stiffness, in which the main contribution comes from the normal contact forces. That is, when forward incremental probes are applied the behavior of anisotropic aggregates is an incremental frictionless behavior. In this regime we show that contacts roll or slide so the incremental tangential contact forces are zero. Graphical Abstract

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International audienceWe consider a random aggregate of identical, frictionless spheres whose contact is maintained by an applied pressure. The aggregate is then subjected to an axial compression at fixed pressure. We show that the incremental elastic response of the resulting transversely isotropic material is characterized by six rather than by five independent coefficients and that the stiffness tensor does not have the major symmetry. This is because we permit deviations from an affine deformation that are determined by local equilibrium, when anisotropy is present. Discrete element numerical simulations confirm these findings

In the context of the classical Biot theory for acoustic waves in a fully saturated granular material, we improve upon the constitutive relation of the solid phase by means of micro-mechanical modeling. This is needed to explain discrepancies on the dependency of the frequency with the sound speed attenuation and dispersion between present models and experiment. The micro-mechanical provides a more detailed description of the interaction between the particles and water and gives an expression for the stress of the entire aggregate based upon micro mechanical parameters such as coordination number (average number of contacts per particle), porosity, material properties. The aggregate is modeled as a collection of particles that are stiffer than the water; so in the particle fluid interaction, idealized by a Standard Linear Solid model, only the compressibility of the water is taken in account. The possibility to include a deviation of the particle motion from the classical affine deformation is explored. Predictions of the sound speed attenuation and dispersion are provided in the context of a uniaxial deformation.