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The present manuscript is devoted to two works related to the spontaneous formation of patterns in Nature: venation in leaves and evolution of embryos. Morphogenetic processes and growth-induced instability phenomena are modelled through analogue experiments. The organization of veins in leaves is similar to what is expected from growth in a tensorial stress field that governs the formation of fractures, while the change in the shape of embryos is related to the deformation of a shell-like membrane whose properties evolve with time. The approaches resulting from analogue experiments is a way to explore specific properties of the media at a macroscopic scale. Thus the manuscript aims to focus on the analogue experiments, their adaptability to reproduce specific patterns and the relation between both growth-induced instability and mechanical behaviour of the matter. [ABSTRACT FROM AUTHOR]

Abstract: In this Note, the phenomenon of cumulative slip of solids under cyclic loads is considered. The topic concerns with the relative displacements of two solids maintained in contact by friction. This problem of the daily-life mechanics can be compared to the shakedown of elastic plastic solids under cyclic loads. A transcription of the plastic shakedown theorems is given here for the problem of frictional contact. The statement of Melan theorem is first given for the cumulative-slip problem under some restrictive assumptions. It suggests again the introduction of a safety coefficient with respect to slips. The safety coefficient can be computed from two static and kinematic approaches in min–max duality and leads again to Koiter theorem. As in plasticity, these results are available only for associated laws and do not hold for Coulomb law of friction, except in some very particular situations. These results can be understood mathematically as a particular case of shakedown theorems in plasticity, when the plastic strain is localized on a surface. For Coulomb friction, numerical simulations by direct step-by-step calculations show that the asymptotic behaviour of the response with or without slip-shakedown could be obtained very quickly after some cycles. To cite this article: N. Antoni, Q.-S. Nguyen, C. R. Mecanique 336 (2008). [Copyright &y& Elsevier]

Local buckling of steel structural members has to be well understood in order to design accurately steel structures in seismic areas. Induced softening moment-curvature law leads to a well known ill-posedness elastoplastic evolution problem. Localization is chosen to be controlled with a gradient plasticity approach. The concept of cross-section behavioural classes, classically adopted in modern rule design, should be substituted by the concept of member behavioural classes. To cite this article: N. Challamel, C. R. Mecanique 331 (2003). [Copyright &y& Elsevier]