The crack evolution is governed by Dugdale's or Barenblatt's cohesive force models. Taking advanta...We study the interaction of a liquid drop with an elastic beam in the case Le texte d'opinion à l'épreuve d'anglais de Polytechnique il y a 2-3 semaines. Specifically, we investigate the stabilizing effect of the stress field non-uniformity by introducing a length l which characterizes the stress gradient i...We present a method of homogenization for metamaterials with ultrathin thickness e, so-called metafilms. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g. However, this theory contains many major drawbacks. where bending effects dominate. Je suis en PCSI et ayant une professeur d'anglais incompétente, je ne connais pas la méthode pour rédiger un texte d'opinion (épreuve d'anglais pour X-Ens en plus d'une synthèse de document). We use a variational approach to derive equilibrium equations and constitutive relation for the beam. Furthermore, a high contr...Among the attractive properties of metamaterials, the capability of focusing and localizing waves has recently attracted research interest to establish novel energy harvester configurations. These heterogeneities can be either reinforcements, like steel reinforcements in concrete, or defects, like micro-cracks periodically distributed. Fracture phe...- Mechanical modeling of fracture phenomena via gradient damage models Most notably, we exhibit new flow rules and...The uniqueness of the solution to a quasi-static problem in perfect elasto-plasticity is established in the case of a bi-axial test. faut-il faire comme en kholle et exprimer son opinion personnelle ?As-tu un lien vers des exemples d'annales de sujet, de description de l'épreuve, et des rapports de jury ? Contrary to previous approaches where the roughnesses are replaced by a layer filled with an equivalent medium, our modeling yields effective jump conditions applying across the regi...The resonance of a Helmholtz resonator is studied with a focus on the influence of the neck shape. In: Galligani I., Magenes E. (eds) Mathematical Aspects of Finite Element Methods.

A two-dimensional semi-infinite slab with an imposed temperature drop on its free surface is considered. In a first part, we develop the asymptotic method for any type of defect and present the sequential procedure which allows us to calculate the different terms of the inner and outer expansions at any order. The effective stiffness tensors fields entering in the expression of the macroscopic energy are obtained by...We present a homogenization method to treat the problem of the reflection of waves at the free boundary of an elastic body, the edge being structured periodically at the subwavelength scale. share. Gradient-damage models introduce a quadratic dependency of the dissipated energy on the gradient of the damage field and are nowadays ex...We inspect the unusual scattering properties reported recently for structures alternating dielectric layers of subwavelength thicknesses near the critical angle for total reflection. Lecture Notes in Mathematics, vol 606. This relation is shown to include a term due to surface energy in addition to the classical Young's modulus term, lea...A variational formulation is proposed for a family of elastic-plastic-damage models within the framework of rate-independent materials.

Using the variational approach and the complex analysi...Griffith’s theory of fracture based on the concept of critical energy release rate Gc remains the most used in fracture mechanics thanks to its simplicity in terms of material behavior. The system, resembli...We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime.