26 research outputs found
Homogenenized interface model describing defects periodically distributed on a surface
Titre du résumé français joint : Modèle d'interface homogénéisée décrivant des défauts périodiquement répartis sur une surfaceNational audienceWe undertake the homogenization of a three-dimensional elastic medium, which contains heterogeneities localized on a surface. These can be either reinforcements, like steel reinforcements in concrete, or defects, like microcracks periodically distributed. We propose a simple model describing the effective behaviour of these heterogeneities. This model, formulated in an energetic framework, com- bines an elastic interface behaviour with that of a membrane. Its interest is discussed through several applications.See http://hal.archives-ouvertes.fr/docs/00/59/28/84/ANNEX/r_O1H9ABAW.pd
A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations
International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model
Linear Models for Composite Thin-Walled Beams by -Convergence. Part I: Open Cross Sections
Homogenization with an oscillating drift: from L 2-bounded to unbounded drifts, 2D compactness results, and 3D nonlocal effects
King post truss as a motif for internal structure of (meta)material with controlled elastic properties
Virtual spring damper method for nonholonomic robotic swarm self-organization and leader following
Higher Gradient Theories and Their Foundations
International audienceContinuum mechanics always supplies approximate models for physical systems, in which a more fundamental (possibly discrete or inhomogeneous) microstructure may be somehow neglected. Indeed, Cauchy (or Cauchy-Navier) continuum theory describes efficiently, at a macroscopic level, the behavior of a mechanical system only when the inhomogeneities which the model does not take into account have a characteristic length scale much smaller than the macroscale where phenomena are observed.Therefore, it is now widely accepted that in some circumstances, it is necessary to add to the placement field some extra kinematical fields, to take into account, at a macroscopic level, some aspects of the mechanical behavior of materials having complex microscopic..