Asymptotic behavior of structures made of straight rods

This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single rod introduced in [6] and on the extension of this technique to a multi-structure. We characterize the asymptotic behavior of the infimum of the total elastic energy as the minimum of a limit functional for an energy of order $\delta^\beta$ ($2<\beta\le 4$)

Junction between a plate and a rod of comparable thickness in nonlinear elasticity. Part II

We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order $\delta$. We use the decomposition techniques obtained for the large deformations and the displacements in order to derive the limit energy as $\delta$ tends to 0.Comment: arXiv admin note: substantial text overlap with arXiv:1107.528

Interior error estimate for periodic homogenization

In a previous article about the homogenization of the classical problem of diff usion in a bounded domain with su ciently smooth boundary we proved that the error is of order $\epsilon^{1/2}$. Now, for an open set with su ciently smooth boundary $C^{1,1}$ and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in the error is of order $\epsilon$. If the open set $\Omega\subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates

Asymptotic behavior of a structure made by a plate and a straight rod

This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy leads to the Von-K\'arm\'an's equations (or the linear model for smaller forces) in the plate and to a one dimensional rod-model at the limit. The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction

Straight rod with different order of thickness

In this paper, we consider rods whose thickness vary linearly between \eps and \eps^2. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the displacement fields of the form $u=U\_e + \bar{u}$, where $U\_e$ stands for the translation-rotations of the cross-sections and $\bar{u}$ is related to their deformations. We establish a priori estimates. Passing to the limit in a fixed domain gives the problems satisfied by the bending, the stretching and the torsion limit fields which are ordinary differential equations depending on weights.Comment: in Asymptotic Analysis, IOS Press, 201

Homogenization via unfolding in periodic layer with contact

In this work we consider the elasticity problem for two domains separated by a heterogeneous layer. The layer has an $\varepsilon-$periodic structure, $\varepsilon\ll1$, including a multiple micro-contact between the structural components. The components are surrounded by cracks and can have rigid displacements. The contacts are described by the Signorini and Tresca-friction conditions. In order to obtain preliminary estimates modification of the Korn inequality for the $\varepsilon-$dependent periodic layer is performed. An asymptotic analysis with respect to $\varepsilon \to 0$ is provided and the limit problem is obtained, which consists of the elasticity problem together with the transmission condition across the interface. The periodic unfolding method is used to study the limit behavior.Comment: 20 pages, 1 figur

Triggering Soft Bombs at the LHC

Very high multiplicity, spherically-symmetric distributions of soft particles, with $p_T$ ~ few hundred MeV, may be a signature of strongly-coupled hidden valleys that exhibit long, efficient showering windows. With traditional triggers, such "soft bomb" events closely resemble pile-up and are therefore only recorded with minimum bias triggers at a very low efficiency. We demonstrate a proof-of-concept for a high-level triggering strategy that efficiently separates soft bombs from pile-up by searching for a "belt of fire": A high density band of hits on the innermost layer of the tracker. Seeding our proposed high-level trigger with existing jet, missing transverse energy or lepton hardware-level triggers, we show that net trigger efficiencies of order 10% are possible for bombs of mass several hundred GeV. We also consider the special case that soft bombs are the result of an exotic decay of the 125 GeV Higgs. The fiducial rate for "Higgs bombs" triggered in this manner is marginally higher than the rate achievable by triggering directly on a hard muon from associated Higgs production.Comment: 38 pages, 5 tables, 14 figure

Asymptotic behavior of structures made of curved rods

In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2δ when δ → 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on several decompositions of the structure displacements and on the passing to the limit in fixed domains. We show that any displacement of a structure is the sum of an elementary rods-structure displacement (e.r.s.d.) concerning the rods cross sections and a residual one related to the deformation of the cross-section. The e.r.s.d. coincide with rigid body displacements in the junctions. Any e.r.s.d. is given by two functions belonging to H1 (S;R3) where S is the skeleton structure (i.e. the set of the rods middle lines). One of this function U is the skeleton displacement, the other R gives the cross-sections rotation. We show that U is the sum of an extensional displacement and an inextensional one. We establish a priori estimates and then we characterize the unfolded limits of the rods-structure displacements. Eventually we pass to the limit in the linearized elasticity system and using all results in [5], on the one hand we obtain a variational problem that is satisfied by the limit extensional displacement, and on the other hand, a variational problem coupling the limit of inextensional displacement and the limit of the rods torsion angles