International audienceThis paper presents a numerical technique to deal with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and/or microscopic scales. We limit ourselves to elastic materials but geometrical nonlinearity is taken into account at both scales. The proposed approach combines the multilevel finite element analysis (FE2) and the asymptotic method (ANM). In that framework, the unknown nonlinear constitutive relationship at the macroscale is found by solving a local finite element problem at the microscale. In contrast with FE2, the use of the asymptotic development allows to transform the nonlinear microscopic problems into a sequence of linear problems. Thus, a direct analogy with classical linear homogenization can be made to construct a localisation tensor at each step of the asymptotic development, and an explicit macroscopic constitutive relationship can be constructed at each step. Furthermore, the salient features of the ANM allow treating instabilities and limit points in a very simple way at both scales. The method is tested and illustrated through numerical examples involving local instabilities which have ignificant influence on the macroscopic behavior

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Using the contact dymanics method together with the finite element method, we simulate the uniaxial compression of assemblies of elastic cylinders. The numerical model accounts for finite deformations of the particles through the neo-Hookean constitutive equation and solid friction between the particles. A quantitative comparison with experiments carried out with centimetric rubberlike cylinders, with local deformations of the particles determined by image correlation, is proposed. We show that the simulations accurately capture the details of both the microstructure and the macroscopic behavior of the real granular system, demonstrating the relevancy of the numerical approach.

International audienceSoft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction

We introduce a novel numerical approach for the simulation of soft particles interacting via frictional contacts. This approach is based on an implicit formulation of the Material Point Method, allowing for large particle deformations, combined with the Contact Dynamics method for the treatment of unilateral frictional contacts between particles. This approach is both precise due to the treatment of contacts with no regularization and artificial damping parameters, and robust due to implicit time integration of both bulk degrees of freedom and relative contact velocities at the nodes representing the contact points. By construction, our algorithm is capable of handling arbitrary particle shapes and deformations. We illustrate this approach by two simple 2D examples: a Hertz contact and a rolling particle on an inclined plane. We also investigate the compaction of a packing of circular particles up to a solid fraction well above the jamming limit of hard particles. We find that, for the same level of deformation, the solid fraction in a packing of frictional particles is above that of a packing of frictionless particles as a result of larger particle shape change

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.

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The uni-axial compaction of granular materials made of elastic neo-Hookean particles is investigated in the quasi-static regime.