Hachmi Ben Dhia

Application of the Arlequin method to some structures with defects

The Arlequin method offers an alternative framework for the multimodel mechanical simulations. This paper aims at showing the promising potentialities of this approach to introduce defects in a sound model with great flexibility. The formulations and the related theoretical results are recalled and the key points for numerical implementation are discussed. Numerical examples illustrate their efficiency.

Hybrid frictional contact particles-in elements

By analyzing functional, geometrical and numerical integration aspects, hybrid frictional contact particles-in-elements are derived from the continuous hybrid formulation of 3D large transformation frictional contact problems given in [BEN 99] [BEN 00a]. The suggested approach is illustrated by some academic and industrial contact tests.

Global-local approaches: the Arlequin framework

Numerical approaches allowing for the local analysis of global models are listed, the Arlequin method being the topic of focus. By superposing mechanical states sharing energies, this method generates a partition of models framework that gives a consistent “plasticity” to the classical mechanical and numerical (mono-)modelling. It consists in a family of formulations of mechanical problems, each of them being derived by combining basic bricks whose choices are rigorously analysed. The effectiveness of this partition of models framework to allow concurrent multimodel and multiscale analysis is exemplified.

Level-Sets and Arlequin framework for dynamic contact problems

By introducing unknown Level-Sets fields on contact interface, the Signorini-Moreau dynamic contact conditions are written as equations. From this, a new continuous hybrid weakstrong formulation for dynamic contact between deformable solids is derived. In the global problem, the Level-Sets like fields are the intrinsic contact unknown ones. This problem is discretized by means of time, space and collocation schemes. Some numerical experimentations are carried out, showing the effectiveness of our approach. The paper is ended by showing a promising application of the multiscale Arlequin method to the multiscale impact problems.

Multimodeling of multi-alterated structures in the Arlequin framework

The goal of this work is the development of a numerical methodology for flexible and low-cost computation and/or design of complex structures that might have been obtained by a multialteration of a sound simple structure. The multimodel Arlequin framework is herein used to meet the flexibility and low-costs requirements. A preconditioned FETI-like solver is adapted to the solution of the discrete mixed Arlequin problems obtained by using the Finite Element Method. Enlightening numerical results are given.

Problèmes de contact frottant en grandes transformations: du continu au discret

ABSTRACT We suggest a weak, continous hybrid formulation for problems of frictional contact between three dimensional solids in large transformations. Unknown fields are the displacement, a scalar multiplier of contact and a semi-multiplier friction vector. This new formulation allows us a “natural” derivation of contact elements.

Contact in the Arlequin Framework

Local refinement of discrete contact problems is needed to analyze accurately contact zones and their neighborhoods. Let us mention in particular the fine estimation of the contact zone size, stress concentrations near contact edges, wear and so on. Classically, adaptive approaches are used to address this issue. The Arlequin method (cf. Ben Dhia (1998, 1999)) is suggested here as (hopefully) a more flexible numerical tool.

Analysis of an Averaging Operator for Atomic-to-Continuum Coupling Methods by the Arlequin Approach

A new coupling term for blending particle and continuum models with the Arlequin framework is investigated in this work. The coupling term is based on an integral operator defined on the overlap region that matches the continuum and particle solutions in an average sense. The present exposition is essentially the continuation of a previous work (Bauman et al., On the application of the Arlequin method to the coupling of particle and continuum models, Computational Mechanics, 42, 511–530, 2008) in which coupling was performed in terms of an H 1-type norm. In that case, it was shown that the solution of the coupled problem was mesh-dependent or, said in another way, that the solution of the continuous coupled problem was not the intended solution. This new formulation is now consistent with the problem of interest and is virtually mesh-independent when considering a particle model consisting of a distribution of heterogeneous bonds. The mathematical properties of the formulation are studied for a one-dimensional model of harmonic springs, with varying stiffness parameters, coupled with a linear elastic bar, whose modulus is determined by classical homogenization. Numerical examples are presented for one-dimensional and two-dimensional model problems that illustrate the approximation properties of the new coupling term and the effect of mesh size.

Computing Flatness Defects in Sheet Rolling by Arlequin and Asymptotic Numerical Methods

Rolling of thin sheets generally induces flatness defects due to thermo-elastic deformation of rolls. This leads to heterogeneous plastic deformations throughout the strip width and then to out of plane displacements to relax residual stresses. In this work we present a new numerical technique to model the buckling phenomena under residual stresses induced by rolling process. This technique consists in coupling two finite element models: the first one consists in a three dimensional model based on 8-node tri-linear hexahedron which is used to model the three dimensional behaviour of the sheet in the roll bite; we introduce in this model, residual stresses from a full simulation of rolling (a plane-strain elastoplastic finite element model) or from an analytical profile. The second model is based on a shell formulation well adapted to large displacements and rotations; it will be used to compute buckling of the strip out of the roll bite. We propose to couple these two models by using Arlequin method. The originality of the proposed algorithm is that in the context of Arlequin method, the coupling area varies during the rolling process. Furthermore we use the asymptotic numerical method (ANM) to perform the buckling computations taking into account geometrical nonlinearities in the shell model. This technique allows one to solve nonlinear problems using high order algorithms well adapted to problems in the presence of instabilities. The proposed algorithm is applied to some rolling cases where “edges-waves” and “center-waves” defects of the sheet are observed.