Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability
Aditi Chakrabarti, Serge Mora, Franck Richard, Ty Phou, Jean-Marc Fromental, Yves Pomeau, Basile Audoly
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.
Parallel implicit contact algorithm for soft particle systems
This paper presents a numerical technique to model soft particle materials in which the particles can undergo large deformations. It combines an implicit finite strain formalism of the Material Point Method and the Contact Dynamics method. In this framework, the large deformations of individual particles as well as their collective interactions are treated consistently. In order to reduce the computational cost, this method is parallelised using the Message Passing Interface (MPI) strategy. Using this approach, we investigate the uniaxial compaction of 2D packings composed of particles governed by a Neo-Hookean material behaviour. We consider compressibility rates ranging from fully compressible to incompressible particles. The packing deformation mechanism is a combination of both particle rearrangements and large deformations, and leads to high packing fractions beyond the jamming state. We show that the packing strength declines when the particle compressibility decreases, and the packing can deform considerably. We also discuss the evolution of the connectivity of the particles and particle deformation distributions in the packing.
Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses
Franck Richard, Aditi Chakrabarti, Basile Audoly, Yves Pomeau, Serge Mora
An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.
Multiscale modeling for bioresources and bioproducts
Marc Barnabe, Nicolas Blanc, Thomas Chabin, J-Y Delenne, A Duri, Xavier Frank, Virginie Hugouvieux, Evelyne Lutton, Frederic Mabille, Saeid Nezamabadi, Nathalie Perrot, Farhang Radjai, Thierry Ruiz, Alberto Tonda
Designing and processing complex matter and materials are key objectives of bioresource and bioproduct research. Modeling approaches targeting such systems have to account for their two main sources of complexity: their intrinsic multi-scale nature; and the variability and heterogeneity inherent to all living systems. Here we provide insight into methods developed at the Food & Bioproduct Engineering division (CEPIA) of the French National Institute of Agricultural Research (INRA). This brief survey focuses on innovative research lines that tackle complexity by mobilizing different approaches with complementary objectives. On one hand cognitive approaches aim to uncover the basic mechanisms and laws underlying the emerging collective properties and macroscopic behavior of soft-matter and granular systems, using numerical and experimental methods borrowed from physics and mechanics. The corresponding case studies are dedicated to the structuring and phase behavior of biopolymers, powders and granular materials, and to the evolution of these structures caused by external constraints. On the other hand machine learning approaches can deal with process optimizations and outcome predictions by extracting useful information and correlations from huge datasets built from experiments at different length scales and in heterogeneous conditions. These predictive methods are illustrated in the context of cheese ripening, grape maturity prediction and bacterial production.
Souple et solide: comment la matière élastique se déforme-t-elle?
Serge Mora, Yves Pomeau
Les solides mous, tels que la “jelly” de la cuisine anglo-américaine, peuvent supporter de grandes, voire de très grandes déformations. Ils permettent ainsi d’étudier le comportement de la matière élastique soumise à de fortes sollicitations mécaniques.Nous donnons ici un aperçu de phénomènes originaux rencontrés lorsque ces solides sont placés dans des conditions mettant en évidence leur extraordinaire souplesse : cylindres instables, émoussement des arêtes, instabilité de Rayleigh-Taylor, flottabilité élastique.