A tribute to my "Maestro" Gianpietro Del Piero

n/

Asymptotic analysis of an elastic thin interphase with mismatch strain

International audienceThis paper proposes the study of the equilibrium problem, where two elastic bodies are bonded to a thinelastic film under mismatchstrain conditions resulting in a state of residual stress. The asymptotic behavior of the film/adherent system is modeled as the film thickness tends to zero, using a method based on asymptotic expansions and energy minimization procedures. This method yields a family of non-local imperfect interface laws, which define a jump in the displacement and the traction vector fields. The amplitudes of the jumps turn out to be correlated with the state of residual stress and the elastic properties of the materials. As an example, the interface law is calculated at order zero in the case of a pure homogeneous mismatchstrain and a thin isotropic film consisting of Blatz-Ko material

Asymptotic behavior of a hard thin linear elastic interphase: an energy approach

International audienceThe mechanical problem of two elastic bodies separated by a thin elastic film is studied here. The stiffness of the three bodies is assumed to be similar. The asymptotic behavior of the film as its thickness tends to zero is studied using a method based on asymptotic expansions and energy minimization. Several cases of interphase material symmetry are studied (from isotropy to triclinic symmetry). In each case, non-local relations are obtained relating the jumps in the displacements and stress vector fields at order one to these fields at order zero

Modelling Adhesion by Asymptotic Techniques

Chapter 6International audienceIn this chapter, a review of theoretical and numerical asymptotic studies on thin adhesive layers is proposed. A general mathematical method is presented for modelling the mechanical behavior of bonding and interfaces. This method is based on a simple idea that the adhesive film is supposed to be very thin; the mechanical problem depends strongly on the thinness of the adhesive. It is quite natural, mathematically and mechanically, to consider the limit problem, that is, the asymptotic problem obtained when the thickness and, possibly, the mechanical characteristics of the adhesive thin layer tend to zero. This asymptotic analysis leads to a limit problem with a mechanical constraint on the surface, to which the layer shrinks. The formulation of the limit problem includes the mechanical and geometrical properties of the layer. This limit problem is usually easier to solve numerically by using finite elements software. Theoretical results (i.e. limit problems) can be usually obtained by using at least four mathematical techniques: gamma-convergence, variational analysis, asymptotic expansions and numerical studies. In the chapter, some examples will be presented: comparable rigidity between the adhesive and the adherents, soft interfaces, adhesive governed by a non convex energy and imperfect adhesion between adhesive and adherents. Some numerical examples will also be given and, finally, an example of a numerical algorithm will be presented

Imperfect interfaces as asymptotic models of thin curved elastic adhesive interphases

International audienceWe obtain a limit model for a thin curved anisotropic interphase adherent to two elastic media. Our method is based on asymptotic expansions and energy minimization procedures. The model of perfect interface is obtained at the first order, while an imperfect interface model is obtained at the next order. The conditions of imperfect contact, given in a parallel orthogonal curvilinear coordinate system, involve the interphase material properties, the first order displacement and traction vectors, and their derivatives. An example of implementation of the imperfect interface condition is given for a composite sphere assemblage

Modeling of stiff interfaces: from statics to dynamics

International audienceIn this paper, some results on the asymptotic behavior of stiff thin interfaces in elasto-statics are recalled. A specific study of stiff interfaces in elastodynamics is presented and a numerical procedure is given

Appeal No. 0376: Redman Oil Company, Inc. v. J. Michael Biddison, Chief, Division of Oil and Gas

Chief\u27s Order 89-51

Numerical analysis of two non-linear soft thin layers

International audienceIn a first part, we consider a bar with extremities subject to a given displacement and made by two elastic bodies with linear stress-strain relation separated by an adhesive layer of thickness $h$. The material of the adhesive is characterized by a non convex (piecewise quadratic) strain energy density with elastic modulus $k$. After considering the equilibrium problem of the bar and determining the stable and metastable solutions, we let $(h,k)$ tending to zero and we obtain the corresponding asymptotic contact laws, linking the stress to the jump of the displacement at the adhesive interface. The second part of the paper is devoted to the bi-dimensional problem of two elastic bodies separated by a thin soft adhesive. The behaviour of the adhesive is non associated elastic-plastic. As in the first part, we study the asymptotic contact laws

The Applicability of the Attorney-Client Privilege to a Corporation -- The Current Evolution of an Accepted Rule of Law

International audienceIn the present study, we focus our attention to a specific type of composite, constituted by two media, called the adherents, bonded together with a thin interphase layer, called the adhesive. We assume that the composite constituents are made of different multi-physic materials with highly contrasted constitutive properties. The study considers a generic multi-physic coupling in a very general framework and can be adapted to well-known multi-physic behaviors, such as piezoelectricity, thermo-elasticity, aswell as to multifield microstructural theories, such as micropolar elasticity

a simplified multiscale model of degenerate graphite clusters in grey cast iron

Abstract To take into account the weakening effect of defects clusters in real microstructures, we propose a multiscale model in a two-dimensional setting. At a small scale, single defects are described as elliptical voids randomly distributed and randomly oriented in an isotropic matrix. Using an effective field method proposed by Tandon and Weng [5,6], the effective properties of a porous equivalent material can be estimated in a simple closed form. At a larger scale, defects clusters are modelled as single large elliptical inclusions characterized by the weakened effective properties calculated in the first step and embedded in an infinite, elastic, isotropic matrix under remote loading. The method allows to examine the dependence of defects interaction on some basic microstructure parameters (porosity density, voids aspect ratio, inclusion aspect ratio)