Noureddine Damil

• Professor
• Research Director at Université Hassan II Casablanca

Background: Nowadays, numerical algorithms make it possible to more accurately simulate the behavior of cardiac tissue, and in particular its electrical activity, in order to identify possible cardiac pathologies. Numerical methods used to simulate cardiac electrical activity, governed by unsteady non-linear PDEs, require very high computation time...

In this work, a 3D micromechanical model is developed to describe the behavior of macromolecular chains and to reflect the hyperelastic behavior of rubber-like materials. This model generalizes the 2D model recently developed in Ouardi (2023). The behavior law is defined by the minimization of a potential energy, each macromolecular chain has been...

In this research, we propose an algorithm to study the buckling of thin Functionally Graded Material (FGM) shells, utilizing a novel implementation of the asymptotic numerical method (ANM). Our approach integrates a three-step process: representation of variables and loading conditions through a truncated Taylor series, discretization using the fin...

This paper examines the study of stability regions in the case of interaction between buckling and lateral buckling of thin-walled beams with bi-symmetric open sections. By adimensionalizing the nonlinear equations obtained using a nonlinear theory of non-uniform torsion based on finite displacements formulated by Attard [1], we refer the reader to...

In this work, we focus on the wrinkling phenomenon of Functionally Graded Material (FGM) membranes under uniaxial tensile traction using the Asymptotic Numerical Method (ANM). The objective of this study is to use a comprehensive model based on the Föppl-von Kármán theory. The obtained non-linear equations are solved using the ANM algorithm, aiming...

In this study, we develop a method grounded in the Weighted Least Squares (WLS) approach to address two-dimensional nonlinear elasticity problems, focusing specifically on the analysis of cracked structures. We construct shape functions within a local support domain using the WLS approximation, which, when coupled with a High-Order Continuation met...

In this article, we show that the reduced model proposed in our recent article to study the wrinkling of homogeneous elastic membranes does not reproduce the wrinkling observed in the case of an FGM-type composite membrane. New reduced models are then proposed to investigate the wrinkling of membranes made from Functionally Graded Materials (FGM)....

In this work we propose a microstructurally motivated hyperelastic model to describe the behavior of elastomer materials. At the scale of the Representative Volume Element (RVE), composed of randomly oriented macromolecular chains, we assume that the segments of the chains are deformable and that there is a bending energy between two consecutive se...

In this study, we present a new high-order implicit algorithm to simulate cardiac electrophysiological waves. Several cardiac pathologies are due to a malfunction in the propagation of the wave causing the contraction of the heart: the cardiac action potential. Its dynamics are described by a system of nonlinear and nonstationary partial differenti...

In this work, a mesh-free indicator is proposed to detect the bifurcation points of incompressible viscous fluid flow in a 2D sudden expansion. This indicator is mainly based on the high order mesh-free algorithm (HO-MFA) to solve the nonlinear problems obtained from the linear stability analysis. The Padé approximants are then used to improve the...

A high-order algorithm to compute elastoplastic structures in large deformation . We will asses the robustness of this algorithm by studying four loading processes and and we will check the quality of the solution with the help of the residual curve.

his paper investigates the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. First, the equilibrium equations have been transformed into dimensionless ones, and within a nonlinear stability model, various dimensionless parameters are...

Data-driven computational homogenization has been proposed recently for the analyses of composite structures. Its basic idea is to construct an equivalent stress–strain database of composites via offline homogenization on the representative volume element and conduct online macroscopic simulation through distance-minimizing data-driven computing. T...

In this paper, a mesh-free approach is presented for the numerical analysis of frictional contact in the framework of Linear Elastic Fracture Mechanics (LEFM). This approach (WLS-HOCM) is obtained by combining a Weighted Least Square approximation (WLS) under a strong formulation with a High Order Continuation Method (HOCM), the Coulomb friction mo...

In this work, we show how to introduce improved vectorial Padé approximants in the Asymptotic Numerical Method (ANM) for solving elasto-plasticity problems in finite transformation. In this way, we have proposed an algorithm, based on Taylor series which has shown its efficiency for computing elasto-plastic structures in large deformations. We show...

In this paper, a new numerical model is proposed to detect numerically the Hopf bifurcation point of incompressible fluid flows problems. The concept of this model consists to propose a Hopf bifurcation indicator which is solved by a High Order Mesh Free Algorithm (HO‐MFA) using the Moving Least Squares (MLS) approximation. This numerical model is...

The present study investigates the buckling strength of braced thin-walled columns under bending and torsional modes. Unlike the well-known bending modes, the torsion buckling modes of braced columns are not adequately assessed in design and are often overlooked. In order to control the buckling behaviour, the effects of elastic discrete springs in...

This paper discusses the efficiency of an algorithm based on the Asymptotic Numerical Method (ANM) to solve large strain plasticity problems. In the framework of ANM, the non-smooth constitutive law has to be replaced by a smooth one in order to be able to represent the solution path in the form of Taylor series. For this purpose, we propose to gen...

In this paper, a high-order algorithm, based on the Asymptotic Numerical Method (ANM) is proposed, for the numerical solution of large-transformation elastoplasticity problems in a 2D case. The ANM algorithm combines three techniques: a Taylor series representation, a discretization technique and a continuation procedure. In order to use the Taylor...

In the present paper, an efficient mesh-free approach is established to determine the stress intensity factors in the vicinity of the crack tip. This efficient mesh-free approach is based on the Weighted Least Squares method (WLS) combined with the stresses extrapolation method and with the visibility criterion to evaluate the Stress Intensity Fact...

Abstract In this paper, we propose a dimensionless numerical mesh-free model for the simulation of the compressible isother-mal viscous flows. The novelty of this work consists to formulate the Navier-Stokes equations under a dimensionlessform and to solve them by a high order mesh-free algorithm to simulate the compressible fluid flows. This algorith...

This paper presents a one-dimensional finite element (FE) model for computing the nonlinear dynamic behavior of thin-walled composite beams with open variable cross-sections under arbitrary external dynamic loading. We propose a one-dimensional model of beams that takes into account the large torsion and flexion-torsion coupling without any assumpt...

We discuss a reduced-order modeling technique based on Fourier series for membrane wrinkling when the orientation of the wrinkles is not uniform. Indeed, the orientation of the wrinkles depends on geometry and loading, for instance in the case of perforated membrane or with non uniform residual stresses. This Fourier-based reduction technique is an...

In this paper, we propose to investigate numerically the steady bifurcation points and bifurcated branches in fluid mechanics by employing high order mesh‐free geometric progression algorithms. These algorithms are based on the use of the Geometric Progression (GP) in a high order mesh‐free approach. The first proposed algorithm is applied on a str...

In this paper, a high order mesh-free continuation for nonlinear elasticity problems is presented. This proposal consists to introduce the Weighted Least Squares (WLS) in a High Order Continuation (HOC). The WLS has been employed to create shape functions using a local support domain. The HOC permits to transform the nonlinear problems in a success...

In this paper, we propose for the first time to extend the application field of the high order mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This approach is based on a high order algorithm which combines a Taylor series expansion, a continuation technique and a Moving Least Squares method (MLS). The Taylor series exp...

The present study investigates the flexural torsional buckling strength of braced thin-walled beams. Except the well-known bending modes, the torsion buckling modes of braced beams are not adequately assessed in design and are often overlooked. In order to control the buckling behaviour, the effects of elastic discrete springs in bending and torsio...

In this paper and in the framework of the Asymptotic Numerical Method (ANM), we investigate numerically improved vectorial Padé Approximants. The ANM is a branch-by-branch continuation algorithm, each branch is represented by a vectorial Taylor series with respect to a path parameter. In the ANM, the vectorial Padé approximants have been introduced...

Abstract. This paper aims to investigate, in large displacement and torsion context, the nonlinear dynamic behavior of thin-walled beams with open cross section subjected to various loadings by high-order implicit solvers. These homotopy transformations consist to modify the nonlinear discretized dynamic problem by introducing an arbitrary invertib...

This paper aims to investigate, in large displacement and torsion context, the nonlinear dynamic behavior of thin-walled beams with open cross section subjected to various loadings by high-order implicit solvers. These homotopy transformations consist to modify the nonlinear discretized dynamic problem by introducing an arbitrary invertible pre-con...

In this work, we have investigated numerically the disappearance of wrinkles from a tended membrane by the Asymptotic Numerical Method (ANM) using the finite-element DKT18. The ANM is a path-following technique that has been used to solve bifurcation problems. We show numerically the influence of the terms corresponding to the membrane displacement...

In this work, we investigate numerically efficient vectorial Padé approximants in the Asymptotic Numerical Method (ANM). These efficient vectorial Padé approximants are deduced from a new matrix generalized definition of vectorial Padé representations. A comparison between the proposed vectorial Padé approximants and the classical Padé approximants...

In this work, the Asymptotic Numerical Method (ANM) with a Moving Least Squares method (MLS) for the simulation of a compressible fluid flow is presented. The strong formulation of compressible viscous isothermal Navier-Stokes equations is the starting point. This proposed high order implicit algorithm is based on the implicit Euler scheme, a homot...

The aim of this work consists to model and simulate the vibrations of magnetostrictive actuators. The mechanical modeling of the actuator is performed using a one-dimensional magnetostrictive rod attached to an elastic spring. The formulation of problem is carried out using the Euler-Bernoulli theory of elastic beams taking into account the couplin...

Les matériaux magnétostrictifs sont des matériaux intelligents qui ont une large gamme d'applications pour l'actionnement et la détection [1,2]. Ils ont été largement utilisés dans l'industrie du développement de divers dispositifs, tels que des actionneurs, des capteurs, des transducteurs, des haut-parleurs, des amortisseurs de vibrations, des rel...

In this paper, we propose a new analytical formula to define the next branch in the Asymptotic Numerical Method (ANM) using the Padé approximants. The proposed formula is based on the computation of the relative error of two consecutive Padé approximants. This formula is obtained by developing the relative error with respect to the path parameter....

The aim of this work consists to model and simulate the vibrations of magnetostrictive actuators. The mechanical modeling of the actuator is performed using a one-dimensional magnetostrictive rod attached to an elastic spring. The formulation of problem is carried out using the Euler-Bernoulli theory of elastic beams taking into account the couplin...

In this work, we study the forced nonlinear vibrations with large amplitude and large torsion of composite thin walled beams with open variable cross sections under external dynamic loads using a high order implicit algorithm. The used algorithm is based on the temporal and spatial discretizations, the homtopoy transformation, Taylor series expansi...

Ce travail concerne la modélisation par éléments finis de la vibration non linéaire des poutres en rotation. L’analyse proposée est faite en utilisant un algorithme implicite d’ordre élevé avec pré-conditionneur. Cette modélisation prend en compte les grandes rotations. Les équations du mouvement sont établies sans aucune approximation sur l’amplit...

Ce travail a pour objectif l’étude numérique de l’influence du rapport d’aspect et de l’épaisseur d’une feuille mince soumise à une traction sur la disparition du plissement. Deux modèles de la déformation sont utilisés : le modèle de von Kàrmàn et un modèle de von Kàrmàn Amélioré. Les équations non linéaires obtenues sont résolues par la Méthode A...

In this work, we propose to investigate numerically the incompressible flows by the Asymptotic Numerical Method (ANM) with the Moving Least Square (MLS). The mathematical formulation is based on the Navier-Stokes equations written in a strongly formulation to avoid all difficulties of the numerical integration. The used algorithm is developed to in...

Dans ce travail, on présente une comparaison entre les domaines de validité des solutions d’un problème de post-flambement des structures cherchées par la Méthode Asymptotique Numérique. Cette comparaison sera faite aussi bien sur les longueurs de ces domaines que sur leur détermination par une méthode numérique et par une méthode analytique qu’on...

In this work, we propose to investigate numerically the incompressible flows by the Asymptotic Numerical Method (ANM) with the Moving Least Square (MLS). The mathematical formulation is based on theNavier-Stokes equations written in a strongly formulation to avoid all difficulties of the numerical integration. The used algorithm is developed to inv...

In this work, we study the forced nonlinear vibrations with large amplitude and large torsion of composite thinwalled beams with open variable cross sections under external dynamic loads using a high order implicit algorithm. The used algorithm is based on the temporal and spatial discretizations, the homtopoy transformation, Taylor series expansio...

In this work, we propose an analytical formula that allows the determination of the validity range of a vectorial Padé approximant. The purpose of this formula is to reduce the computation time required for this determination. Indeed, as the search for this domain is done, generally by applying the dichotomy method [1] to the relative error between...

In this work, we propose some regularization techniques to adapt the implicit high order algorithm based on the coupling of the asymptotic numerical methods (ANM) (Cochelin et al., Méthode Asymptotique Numérique, Hermès-Lavoisier, Paris, 2007; Mottaqui et al., Comput. Methods Appl. Mech. Eng. 199 (2010) 1701-1709; Mottaqui et al., Math. Model. Nat....

Piezoelectric nanostructures of the beam type find wide applications in the field of nanoelectromechanical systems (NEMS) because of their superior mechanical properties and their electromechanical coupling. The nanostructured piezoelectric materials exhibit size-dependent properties, which are different from their macroscopic counterparts. To pred...

The main objective of this work is to develop an approach for studying the buckling of piezoelectric nanobeams under axial compression. The developed approach is obtained by combining the classical piezoelectric Euler-Bernoulli beams and the surface elasticity Gurtin-Murdoch models. The buckling loads of the axially compressed piezoelectric nanobea...

The main objective of this work is to propose some regularization techniques for modeling contact actions in a clutch system and to solve the obtained nonlinear dynamic problem by a high-order algorithm. This device is modeled by a discrete mechanical system with eleven degrees of freedom. In several works, the discontinuous models of the contact a...

Ce travail vise la simulation de la réponse dynamique non linéaire des poutres à parois minces et à sections constante ouvertes sous chargements dynamiques quelconques. La formulation théorique du problème est basée sur un modèle tridimensionnel complet de poutres tenant compte des grands déplacements, des grandes torsions et du couplage flexion-to...

Nous proposons, dans ce travail, une nouvelle approche pour la modélisation des plissements locaux et du couplage entre le comportement local et global dans les structures sandwich 2D. Une analyse de Fourier à deux échelles permet ainsi de transformer un modèle sandwich 2D en un nouveau modèle sandwich 2D réduit dont seule l’enveloppe de l'instabil...

On se propose, dans ce travail, de discuter trois nouvelles stratégies de continuation utilisant de nouveaux approximants de Padé récemment proposés dans [2] et [3]. En effet, nous avons démontré dans [2] qu’on peut construire plusieurs approximants de Padé sans passer par la technique d’orthonormalisation de Gram-Schmidt. La première stratégie pro...

On se propose, dans ce travail, de discuter trois nouvelles stratégies de continuation utilisant de nouveaux approximants de Padé récemment proposés dans [2] et [3]. En effet, nous avons démontré dans [2] qu’on peut construire plusieurs approximants de Padé sans passer par la technique d’orthonormalisation de Gram-Schmidt. La première stratégie pro...

In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences generally neglected in the derived expressions of the...

The paper is concerned by multi-scale methods to describe instability pattern formation, especially the method of Fourier series with variable coefficients. In this respect, various numerical tools are available. For instance in the case of membrane models, shell finite element codes can predict the details of the wrinkles, but with difficulties du...

In this paper, we will introduce and discuss new parameterizations to solve elastoplasticity problems by using the Asymptotic Numerical Method (ANM). The elastic–plastic transition and the elastic unloading are taken into account by using the regularization technique proposed in Assidi et al. (2009) [1] and Zahrouni et al. (2005) [2]. The ANM is a...

In this paper, we will introduce and discuss new parameterizations to solve elastoplasticity problems by using the Asymptotic Numerical Method (ANM). The elastic–plastic transition and the elastic unloading are taken into account by using the regularization technique proposed in Assidi et al. (2009) [1] and Zahrouni et al. (2005) [2]. The ANM is a...

Le flambage des nanotubes de carbone à double parois soumis à des forces de compression axiales est analysé moyennant l'approche de la mécanique moléculaire des structures. Les nanotubes de carbone sont modélisés par des treillis de poutres en considérant les liaisons entre les atomes de carbone comme des éléments de poutres 3D à deux nœuds et à se...

En se basant sur un algorithme implicite d'ordre élevé appliqué à un modèle tridimensionnel complet de poutre, on se propose, dans ce travail, d'analyser de la dynamique des poutres à parois minces et à sections ouvertes soumises à des excitations extérieures. L'algorithme utilisé prend en compte les grandes torsions et le couplage flexion torsion....

Dans ce travail, nous proposons un modèle élément fini 3D pour l'analyse numérique de la vibration libre et forcée des poutres à paroi mince et à section ouverte. L'analyse proposée est basée sur un algorithme implicite d'ordre élevé avec pré-conditionneur. Cette modélisation prend en compte les grandes torsions et le couplage flexion-torsion. Les...

La MAN est une méthode numérique permettant d'obtenir la solution d'un problème non linéaire comme une succession de branches. Chaque branche est représentée par une série vectorielle que l'on obtient en n'inversant qu'une seule matrice de rigidité tangente. La représentation en série peut être remplacée par une représentation rationnelle ce qui pe...

The authors have developed a beam finite element model in large torsion context for thin-walled beams with arbitrary cross sections [1]. In the model, the trigonometric functions of the twist angle θx (c = cos θx − 1 and s = sin θx) were included as additional variables in the whole model without any assumption. In the present paper, three other 3D...

Based on a 3D non-linear model of large torsion of thin-walled open cross section beams under arbitrary external eccentric loads and the Asymptotic Numerical method (ANM), we investigate the buckling and post-buckling behaviors of these structures. The equilibrium and material constitutive equations are established without any assumption on the tor...

" L’étude des structures à parois minces sous chargements quelconques est rarement abordée dans la littérature. L’objectif de ce travail est de présenter un modèle théorique et numérique pour le calcul du flambage de poutres formées de profils ouverts à parois minces sous chargements quelconques, et de faire une analyse statique en grands déplaceme...

The Asymptotic Numerical Method (ANM) is a family of algorithms for path following problems, where each step is based on the computation of truncated vector series [1]. The Vector Padé approximants were introduced in the ANM to improve the domain of validity of vector series and to reduce the number of steps needed to obtain the entire solution pat...

Membrane modeling in the presence of wrinkling is revisited from a multi-scale point of view. In the engineering literature, wrinkling is generally accounted at a macroscopic level by nonlinear constitutive laws without compressive stiffness, but these models ignore the properties of wrinkles, such as their wavelength, their size and spatial distri...

In this paper, in the framework of the Asymptotic Numerical Method ANM [6], we define and build a new type of Vector Pad´e approximant from a vector series by extending the definition of the Padé approximant of a scalar series without any orthonormalization procedure [13, 14]. By this way, we define a new class of Vector Pad´e approximants which ca...