Mounir Baccar Fakhreddine Dammak Editors Advances in

Lecture Notes in Mechanical Engineering

Mohamed KharratMounir BaccarFakhreddine Dammak Editors

Advances in Mechanical Engineering, Materials and MechanicsSelected contributions from the 7th International Conference on Advances in Mechanical Engineering and Mechanics, ICAMEM 2019, December 16–18, 2019, Hammamet, Tunisia

Lecture Notes in Mechanical Engineering

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Mohamed Kharrat • Mounir Baccar •

Fakhreddine DammakEditors

Advances in MechanicalEngineering, Materialsand MechanicsSelected contributions from the 7thInternational Conference on Advancesin Mechanical Engineering and Mechanics,ICAMEM 2019, December 16–18, 2019,Hammamet, Tunisia

123

EditorsMohamed KharratLaboratory of Electromechanical SystemsNational School of Engineers of SfaxSfax, Tunisia

Fakhreddine DammakLaboratory of Electromechanical SystemsNational School of Engineers of SfaxSfax, Tunisia

Mounir BaccarComputational Fluid Dynamicsand Transfer PhenomenaNational School of Engineers of SfaxSfax, Tunisia

ISSN 2195-4356 ISSN 2195-4364 (electronic)Lecture Notes in Mechanical EngineeringISBN 978-3-030-52070-0 ISBN 978-3-030-52071-7 (eBook)https://doi.org/10.1007/978-3-030-52071-7

© The Editor(s) (if applicable) and The Author(s), under exclusive licenseto Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whetherthe whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, andtransmission or information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

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https://doi.org/10.1007/978-3-030-52071-7

Preface

The 7th edition of the “International Conference on Advances in MechanicalEngineering and Mechanics” (ICAMEM 2019) was held in Hammamet, Tunisia,from 16 to 18 December 2019. The conference was organized by the Laboratory ofElectromechanical Systems (LASEM) at the National School of Engineers of Sfax(ENIS) and the Tunisian Scientific Society (TSS) in collaboration with a number ofuniversity institutions from Tunisia and outside Tunisia.

Since its first edition in 2002, the ICAMEM Conference has been held forseveral editions to bring together specialists, academicians, researchers andindustrialists from international community working in research areas related tomechanical engineering and mechanics. ICAMEM 2019 has allowed the scientificcommunity from several regions of the world to exchange research ideas andexperiences. The conference was organized in seven specialized symposiumsfocused on the following themes:

• Applied Mechanics• Industrial Applications and Technology Transfer• Design and Manufacturing• Thermal Sciences and Renewable Energy• Systems and Dynamics• Materials• Fluid Mechanics

Eight keynote speakers, who are leaders in the field of mechanical engineeringand mechanics at the international scale, have participated at ICAMEM 2019. Theyare namely:

• Pr. Abdessattar Abdelkefi, Mechanical & Aerospace Engineering, New MexicoState University, USA.

• Pr. Mohamed S. Ghidaoui, Department of Civil and EnvironmentalEngineering, Hong Kong University of Science and Technology, Hong Kong.

• Pr. Antoine Chateauminois, Soft Matter Sciences & Engineering Laboratory(SIMM), ESPCI Paris, France.

v

• Pr. Bruno Brunone, Department of Civil and Environmental Engineering, WaterEngineering Laboratory, University of Perugia, Italy.

• Pr. Walter Arnold, Department of Materials Science and Engineering, SaarlandUniversity, Germany.

• Pr. Mohamed Slim El Bahi, Laboratory of Microstructure Studies andMechanics of Materials, University of Lorraine, France.

• Pr. Nizar Ben Salah, Laboratory of Mechanics, Materials and Processes,National Superior School of Engineers of Tunis, University of Tunis, Tunisia

• Pr. Amine Ammar, LAMPA, ENSAM Angers, France

More than 200 papers were accepted for ICAMEM 2019, and participants dis-cussed during three days the latest advances in mechanical engineering andmechanics. Only 62 papers have been selected to be presented as chapters in thisbook. Each chapter was thoroughly reviewed by at least two reviewers from theconsidered topics. The organizers would like to thank all members of the ScientificCommittee for their sacrifices. Our thanks go also to all the ICAMEM 2019 par-ticipants, authors and especially Springer for their support.

December 2019 Mohamed KharratICAMEM 2019 General Chair

vi Preface

Contents

Applied Mechanics

Dynamic and Post-buckling Analysis of Structures Like-ShellUsing a Quadrilateral Shell Element with In-plane DrillingRotational Degree of Freedom and a Conservative Implicit TimeIntegration Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Djamel Boutagouga and Said Mamouri

Influence of Material Gradient Index on Stress Distributionof Functionally Graded Dental Implants . . . . . . . . . . . . . . . . . . . . . . . . 11Sameh Elleuch, Hanen Jrad, Mondher Wali, and Fakhreddine Dammak

Parameter Identification of a Viscohyperelastic Constitutive Modelfor Fiber Reinforced Thermoplastic Composites . . . . . . . . . . . . . . . . . . 18M. Allouch, M. Kamoun, J. Mars, M. Wali, and F. Dammak

Industrial Applications and Technology Transfer

The Importance of Ergonomic Risk and the Methods to Followfor a Problem of Assembly Line Balancing . . . . . . . . . . . . . . . . . . . . . . 27Jihene Sdiri, Khaoula El Bedoui, and Kamel Mehdi

Modeling of the Cutting Effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Taoufik Kamoun and Kamel Guemri

Improving Performance of Production Lines: Integrationof Maintenance and Quality Policies: A Literature Review . . . . . . . . . . 38Z. Boumallessa, H. Chouikhi, M. Elleuch, and H. Bentaher

vii

Design and Manufacturing

The Impact of Abrasive Water Jet Cutting on Tensile Behaviorof Woven Fabric CFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Adel Abidi, Sahbi Ben Salem, Abderrezak Bezazi,and Haithem Boumediri

Modeling of Heat Transfer and Transport Phenomena DuringLaser Welding Of Aluminum/Magnesium Alloys . . . . . . . . . . . . . . . . . . 57S. Ben Halim, S. Bannour, K. Abderrazek, W. Kriaa, and M. Autric

Optimal Planning of Multi-pass Turning Operations . . . . . . . . . . . . . . . 63Toufik Ameur

Ductile Damage Prediction of DD13 Sheet Material in Single PointIncremental Forming Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70A. Bouhamed, L. Ben Said, H. Jrad, M. Wali, and F. Dammak

Effect of Shot Peening Parameters on Parabolic Leaf Spring’sResidual Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Sari Guimaji, Akram Khalifa, and Raouf Fathallah

Influence of Sliding Speed and Normal Loads on the WearResistance of Hardox 500 Steel Ground Surfaces . . . . . . . . . . . . . . . . . . 84Kamel Bensaid and Nabil Ben Fredj

Development of STEP-NC Compliant Manufacturingfor Machining Strategies of Aeronautical Components . . . . . . . . . . . . . . 91Romdhane Ben Khalifa and Noureddine Ben Yahia

Numerical Study for the Cutting of Unidirectional CFRP . . . . . . . . . . . 99A. Hassouna, S. Mzali, F. Zemzemi, and S. Mezlini

2-Axis Tool Strategy Applied on NC Lathe Machineto Manufacture Revolved Parts by Means of SPIFProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105L. Ben Said, A. Bouhamed, M. Wali, and F. Dammak

Evaluating Assembly Sequences with the Assembly ToolsOperation Space Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Akram Bedeoui, Riadh Benhadj, Moez Trigui, and Nizar Aifaoui

Evaluating the Capability Index of a Process IntegratingSampling Plan and the Measurement System Number of DistinctCategories NDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118Adel Brik, Mohamed Goddi, and Nabil Ben Fredj

Simulation of Low Velocity Impact of Epoxy-Flax FibersComposite Using Solid Shell Finite Element . . . . . . . . . . . . . . . . . . . . . . 124A. Chaker, S. Koubaa, J. Mars, F. Gehring, F. Dammak, and A. Vivet

viii Contents

Finite Element Residual Stress Computation for CombinedGrinding/Burnishing Applied to 100Cr6 Steel . . . . . . . . . . . . . . . . . . . . 131Yasmine Charfeddine, Sawsen Youssef, Salem Sghaier, and Hédi Hamdi

Inspection on a Three-Dimensional Measuring Machinefor a Virtual Model for Additive Manufacturing . . . . . . . . . . . . . . . . . . 138Hacene Ameddah, Rabia Selloum, and Mourad Brioua

Simulation of the Local Heating Effect on Incremental SheetForming Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144M. Sbayti, R. Bahloul, and H. Belhadjsalah

A CAD Model for the Tolerancing of Non-rigidParts Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Anis Korbi, Mehdi Tlija, Borhen Louhichi, and Abdelmajid Benamara

A Developed Static Model for Tool Deflectionin Ball-End Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Rami Mallek, Moez Smaoui, Maher Baili, Gilles Dessein,and Zoubeir Bouaziz

Thermal Sciences and Renewable Energy

Effect of Steam Explosion and Torrefaction Treatments of WoodChips on the Heating Value of Pellets . . . . . . . . . . . . . . . . . . . . . . . . . . 171Safa Arous, Mariem Mharssi, Hassine Bouafif, Besma Bouslimi,Chedly Bradai, and Ahmed Koubaa

A CFD Investigation of a Turbulent Flow in a Corrugated PlateHeat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Sirine Chtourou, Hassene Djemel, Mohamed Kaffel, and Mounir Baccar

CFD Simulation of CO2 Adsorption onto Activated Carbonfor Gas Separation and Storage Applications . . . . . . . . . . . . . . . . . . . . . 187Skander Jribi, Boutheina Zallama, and Takahiko Miyazaki

Enhancement of Fixed-Wing Space Drone Performance ThroughThermoelectric Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194Devyn Rice, Samah Ben Ayed, Stephen Johnstone,and Abdessattar Abdelkefi

Simulation of Cellulose Pyrolysis Kinetics . . . . . . . . . . . . . . . . . . . . . . . 200Amal Masmoudi, Moez Hammami, and Mounir Baccar

Systems and Dynamics

Free Vibration Analysis of Torsional Line Shaftsof Four-Stroke Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Abdelouahab Rezaiguia, Salah Guenfoud, and Debra F. Laefer

Contents ix

Stability Analysis of One Degree of Freedom System Equippedwith Friction Vibration Absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218Aymen Nasr, Charfeddine Mrad, and Rachid Nasri

Materials

Study of Fe-W-P Coating Performance Under Scratch Test:Modeling and Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227F. Zouch, A. Bahri, and K. Elleuch

Corrosion Resistance Enhancement of AISI 304 Stainless Steelby Deep Rolling Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233Khouloud Gharbi, Naoufel Ben Moussa, and Nabil Ben Fredj

Numerical Simulation of Reciprocating Sliding Test: Effectsof Surface Topography on the Wear Behavior . . . . . . . . . . . . . . . . . . . . 240Fatma Elwasli, Slah Mzali, Farhat Zemzemi, and Salah Mezlini

Ni-Ti Superelastic Wire Coupled with Conventional BracketsDuring Bending Tests: Cross-section Effect Comparison . . . . . . . . . . . . 246Aroua Fathallah, Tarek Hassine, and Fehmi Gamaoun

A Comparative Investigation of the Tribologicaland the Mechanical Behavior of Polyester Powder CoatingsFilled with Graphite Depending on the Filling Percentageand the Size of the Graphite Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 252Nedia Gafsi, Mohamed Kharrat, Maher Dammak, Raquel Verdejo,Miguel Angel Lopez Manchado, and Massimiliano Barletta

Physicochemical, Morphological and Thermal Characterizationof Composites Based on Olive Wood Flour . . . . . . . . . . . . . . . . . . . . . . 259Nesrine Bouhamed, Slim Souissi, Pierre Marechal,Mohamed Ben Amar, and Olivier Lenoir

A Comparative Study on the Physical and Mechanical Behaviorof AA6082-T6 and AA5083- H116 Aluminum Alloys in FrictionStir Spot Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264Nasra Hannachi, Ali Khalfallah, Carlos Leitao, and Dulce M. Rodrigues

Tribological Characterization of Composites Basedon Si3N4 Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Amine Charfi, Ismail Dhaou, Mohamed Kharrat, Mohd Farooq Wani,and Maher Dammak

The Effect of the Loading Path History on the Fracture Loci . . . . . . . . 277Meriem Nouira, Marta Oliveira, Ali Khalfallah, José Alves,and Luís Menezes

x Contents

Characterization of CrAlN Films Synthesized by DC ReactiveMagnetron Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291K. Aouadi, C. Nouveau, A. Besnard, B. Tlili, A. Montagne,and M. Chafra

Mechanical Characterization of a Composite Sandwich Core UnderShear Stress Based on a Torsion Test . . . . . . . . . . . . . . . . . . . . . . . . . . 299Karim Mharsi, Pascal Casari, Amira Sellami, Jamal Fajoui,and Mohamed Kchaou

Study of the Wear Behavior of HDPE-MolybdenumDisulphide Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306A. Salem, M. Guezmil, W. Bensalah, and S. Mezlini

Microstructural and Mechanical Characterization of a Baby Diaper . . . 312Basma Ajmi, Mohamed Kchaou, Amilcar Ramalho, Amira Sellami,Antonio J. Gamez, and Nabil Bouzayani

Numerical Modelling of Undulatory Elastic Behavior of MetallicGlasses Ribbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320M. A. Yousfi, C. Ammari, K. Hajlaoui, and Z. Tourki

Application of the Acoustic Emission Technique for DamageMonitoring of 3D C/C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327Jacqueline Saliba, Jalal El Yagoubi, and Ludovic Hallo

Composite Materials in Epoxy Resin Matrix Using Curaua Fibers . . . . 333Gilberto Garcia Del Pino, Abderrezak Bezazi, Haithem Boumediri,Antonio Claudio Kieling, Jose Luis Valin Rivera, Jamile Dehaini,and Francisco Rolando Valenzuela Díaz

Composite Cross-Ply Laminates Stacking Sequence Effect on PostFlexural Fatigue Residual Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341Abderrezak Bezazi, Abderrahim El Mahi, Boudjema Bezzazi,Gilberto Garcia Del Pino, and Fabrizio Scarpa

Impact Simulation of PA66-GF Composites Using Finite SolidShell Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348S. Koubaa, A. Chaker, J. Mars, A. Vivet, and F. Dammak

Application of Factorial Design to Study the Effect of Recyclingof HDPE on Rheological and Mechanical Properties . . . . . . . . . . . . . . . 355Karama Elfehri, Ameur Chtourou, Sana Koubaa, and Basma Samet

Viscoelastic Mechanical Behavior of Fresh Human Boneof Lower Limbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Saida Benhmida, Dorra Salhi, Montassar Zrida,Ahmed Hichem Hamzaoui, and Hamza Essaddam

Contents xi

Insights into Researches on the Tribological, Microstructuraland Micromechanical Properties of ThermoplasticBased Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370Basma Ben Difallah, Mabrouka Akrout, Mohamed Kharrat,Maher Dammak, and Guy Monteil

Mechanical Characterization of PP/Alfa Bio-composite Obtainedby Thermocompression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379Ismahen Zaafouri, Montassar Zrida, Khaled Labidi,Ahmed Hichem Hamzaoui, and Moufida Borni

Modeling of Iron Based Shape Memory Alloys Behavior WithinFinite Strain Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385Achref Sallami, Walid Khalil, Tarak Bouraoui, and Tarak Ben Zineb

Surface Properties and Adhesion Behavior of PVD Thin Film UsingMulti-cyclic Nanoindentation and Scratch Test . . . . . . . . . . . . . . . . . . . 392Kaouther Khlifi, Hafedh Dhiflaoui, Najoua Barhoumi,and Ahmed Ben cheikh Larbi

Fluid Mechanics

Investigating the Free-Surface Flow Behavior Dueto Sluice-Gate Maneuvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405Ali Triki

Effect of Anchor Conditions on Structural Responses During FluidTransients in Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412Abdelaziz Ghodhbani, Ezzeddine Haj Taieb, and Mohsen Akrout

Investigation of Blade Exit Angle Effects on the Performanceof a Centrifugal Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420Faouzi Omri, Sami Elaoud, Noura Bettaieb, Issa Chalghoum,and Ezzeddine Hadj Taieb

New Proposed Design of Rotor Shaft Equipped with BladesInside a SSHE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428Rabeb Triki, Hassene Djemel, and Mounir Baccar

Different Applied Boundary Condition Within SSHE TreatingNon-Newtonian Shear Thinning Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . 435Rabeb Triki, Hassene Djemel, and Mounir Baccar

Experimental Investigation of Air Conditioningin a Bi-climatic Room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442Naima Boumediene, Florence Collet, Sylvie Pretot, Lazhar Ayed,and Sami Elaoud

xii Contents

Numerical Study of Droplets Coalescencein an Oil-Water Separator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449Zahreddine Hafsi, Sami Elaoud, Manoranjan Mishra, and Ines Wada

An Alternative Approach for Minimum Independent LoopsIdentification in Water Distribution Networks . . . . . . . . . . . . . . . . . . . . 455Oussama Choura, Zahreddine Hafsi, and Sami Elaoud

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

Contents xiii

Applied Mechanics

Dynamic and Post-buckling Analysisof Structures Like-Shell Using a QuadrilateralShell Element with In-plane Drilling RotationalDegree of Freedom and a Conservative Implicit

Time Integration Scheme

Djamel Boutagouga1(&) and Said Mamouri2

1 Civil Engineering Department, Laboratoire des Mines,University Larbi Tébessi - Tébessa, BP 02, 12000 Tébessa, Algeria

[email protected] University de Tahri Mohamed - Bechar, Béchar, Algeria

[email protected]

Abstract. In this work, post-buckling problems of structures like shell areinvestigated using an implicit conservative time integration dynamic scheme.We have proposed the use of a four nodded quadrilateral flat shell element, withthe drilling rotation degree of freedom (D. Boutagouga., A new enhancedassumed strain quadrilateral membrane element with drilling degree of freedomand modified shape functions, Int. J. Numer. Meth. Eng. 2017; 110:573–600)and based upon the updated Lagrangian formulation. An implicit conservativescheme (K.J, Bathe., G, Noh., Insight into an implicit time integration schemefor structural dynamics. Comput. Struct. 2012; 98–99: 1–6) is chosen to obtainthe solution to the nonlinear dynamic behaviour and geometric nonlinear post-buckling response.Several numerical simulations are considered in the aim to investigate the

ability of the considered time integration scheme to deal with unstable branchesafter the limit point in non-linear post-buckling response of shell structures withno prerequisite structural damping, though it is required when using conven-tional time integration schemes. The obtained results illustrate a very satisfyingperformance of the implicit conservative-dissipative direct time integrationscheme combined with the quadrilateral shell element with drilling rotation.

Keywords: Nonlinear dynamic analysis � Post-buckling � Conservativedissipative Scheme � Quadrilateral shell element � Drilling rotation

1 Introduction

In geometrically nonlinear dynamic analysis, conservative and decaying time inte-gration schemes with second-order accuracy are highly desired. A robust time inte-gration algorithm must reveal the minimum numerical damping for low-frequencymodes and maximum numerical damping for high-frequency parasitic modes.

© The Editor(s) (if applicable) and The Author(s), under exclusive licenseto Springer Nature Switzerland AG 2020M. Kharrat et al. (Eds.): ICAMEM 2019, LNME, pp. 3–10, 2020.https://doi.org/10.1007/978-3-030-52071-7_1

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Energy preservation appears to be the most important since it provides uncondi-tional stability in the nonlinear regime if the total mechanical energy can be conserved.However, when dealing with nonlinear systems, especially complex structures like-shell, numerical dissipation becomes crucial. Indeed, high-frequency modes are purelynumerical due to the implications of the discrete equations and they do not reflect thehigh frequencies of the physical problem.

In order to obtain such desired geometric nonlinear dynamic response, geometricnonlinearity of structures like-shell is considered in this work. The Updated LagrangianCo-rotational Description of motion is adopted, in which, large translations and rota-tions are decomposed into large rigid and relatively small translations and rotations. Forthis purpose, starting from a quadrilateral membrane element with rotational d.o.f lesssensitive to mesh distortion via the use of modified shape functions by Boutagouga(2017), a flat shell finite element is constructed after combining the membrane elementwith the quadrilateral discrete Kirchhoff plate element developed by Batoz andBen-Tahar (1982). Then, based on the Co-rotational formulation for geometricallynonlinear static and dynamic analysis established by the authors in former works(Boutagouga et al. 2010; Boutagouga and Djeghaba 2014; Boutagouga and Djeghaba2016; Mamouri et al. 2015), the nonlinear dynamic analysis is established based on aConservative dissipative time integration algorithm presented by Bathe and Noh(2012).

2 The Nonlinear Dynamic Updated Lagrangian Formulationfor the Flat Shell Element

The Co-rotational approach founded by (Wempner 1969; Belytschko and Hsieh 1973;Belytschko and Hsieh 1974), enables to simplify the ULD using a Co-rotationalcoordinate frame that translates and rotates with the finite element. The status ofequilibrium of a deformable body at time (t + Dt) is characterized by a minimum ofenergy expressed in standard form as:

dp ¼ dWint � dWext ¼ 0 ð1Þ

In the Updated Lagrangian Description of motion, all kinematic and mechanicalquantities are measured in reference to the last known configuration C tð Þ. Consideringthe equilibrium of a deformable body at time (t + Dt), the virtual displacementsprinciple is written in C tð Þ as:

Ztv

tTij � dteNLij þDijkl � tekl � dteij� �

d tv ¼ tþDtWext �Z

tv

tTij � dteij � d tv ð2Þ

In which:Deij, Deij*: refer to the linear and nonlinear parts of the Green’s strain increment, Tij

stands for Cauchy stress, and Dijkl is the constitutive matrix.

4 D. Boutagouga and S. Mamouri

The left term in (2) represents the tangent stiffness matrix [KT] that can be writtenas:

KT½ � ¼ K0½ � þ ½Kr�

with [K0]: small displacement matrix; [Kr]: geometric stiffness matrix.In this work, in which de drilling rotation is involved in the shell element for-

mulation, the geometric stiffness [Kr] it is written as:

Kr½ � ¼ Kmr 00 Kb

r

� �ð3Þ

See Boutagouga and Djeghaba (2016) for more details.The internal forces {Fint} are such as:

tfint ¼Z

tv

tTij � tBij � d tv ð4Þ

The incremental total external virtual work due to surface forces tþDtt tk and body

forces tþDtt fk expression is:

tþDtWext ¼Z

tA

tþDtt tk � d uk � d tAþ

Ztv

tþDtt fk � d uk � d tv ð5Þ

The term tþDtt fk arises from dynamic analysis, in which the body force components

are related to the mass inertia q and acceleration d €uk .

3 The Conservative Time Integration Scheme

Obviously, both implicit and explicit methods can be used to solve buckling and post-buckling problems. Explicit schemes are the most used because of their main advantageof being less expensive (Saigal et al. 1987; Hilburger et al. 1997; Kobayashi et al.2015; White et al. 2015). However, these schemes present the disadvantage of beingconditionally stable. In this investigation, we have considered the post-bucklingresponse of thin shells by using an implicit conservative decaying dynamic schemeproposed by Bathe and Noh (2012). The fundamental concept of this composite timeintegration scheme can be summarized as follows:

1. The time step (Dt) is split into two equal sub-steps of span (Dt/2) each.2. The trapezoidal rule is used over the first sub-step, which yields:

tþ Dt2 €u ¼ 16

Dt2tþ Dt

2 u� tu� �

� 8Dt

t _u� t€u

tþ Dt2 _u ¼ 4

Dttþ Dt

2 u� tu� �

� t _u

8<: ð6Þ

Dynamic and Post-buckling Analysis of Structures Like-Shell 5

Mtþ Dt2 €uþCtþ Dt

2 _uþ tþ Dt2 f ¼ tþ Dt

2R ð7Þ

ðb1Mþ b3CþKTÞtþ Dt2 u ¼ tþ Dt

2RþMðb1ut � b2 _ut þ €utÞþCðb3ut þ _utÞ ð8Þ

with: b1 ¼ 16Dt2; b2 ¼ �8

Dt ; b3 ¼ 4Dt and

tþ Dt2R ¼ tþ Dt

2Fext � tþ Dt2 fint is the residue.

K, M and C are the structural stiffness, mass and damping matrices respectively.3. With the resulting equations of the first sub-step in hand, the 3-point Euler back-

ward method is used over the second sub-step, which gives:

tþDt _u ¼ 1Dt

tu� 4Dt

tþ Dt2 uþ 3

DttþDtu

tþDt€u ¼ 1Dt

t _u� 4Dt

tþ Dt2 _uþ 3

DttþDt _u

(ð9Þ

MtþDt€uþCtþDt _uþ tþDtf ¼ tþDtR ð10Þ

ð�3b2M � 3b4CþKTÞtþDtu ¼ tþDtRþMðb1tþ Dt2 uþ b2tuþ b3tþ

Dt2 _uþ b4t _uÞþCðb3tþ Dt

2 uþ b4tuÞð11Þ

with: b1 ¼ 12Dt2; b2 ¼ �3

Dt2; b3 ¼ 4Dt; b4 ¼ �1

Dt andtþDtR ¼ tþDtFext � tþDtfint.

4 Results

4.1 Non-linear Dynamic Analysis of a Clamped-Free Half-Cylinder Shell

We consider in this example the half-cylinder shell with clamped-free straight edgesrepresented in Fig. 1. The Half-cylinder is defined by the following geometry:R = 1.2 m, b = 2 m, h = 0.006 m. The adopted mechanical properties are: Young’smodulus E = 73 GPa, Poisson’s ratio m = 0.3 and material density q = 2700 kg/m3.

b

R

A

X

Y

Z P1

P3 P2

M

Fig. 1. Clamped-free half-cylinder: geometry and mesh


The Half-cylinder is subjected to the transient concentrated loading (P1, P2 and P3),acting at point A presented in Fig. 1, with: P1 P2 P3f g ¼ �1 �1 �1f g � P0ðtÞ.

P0ðtÞ ¼ 0:05 1� cosðptÞð Þ; t� 2:00; t[ 2:0

�

where t is in seconds and P0 is in Newton. A mesh of 8 � 4 quadrilateral elements isused for modelling the half-cylinder. The example was performed with the Newmark’strapezoidal and Bathe conservative dissipative Schemes for a time period of 6 s, usinga time step Dt = 0.05 s. The corresponding results are shown in Figs. 2 and 3.

Fig. 2. Kinetic, strain and total energies variation with time

Fig. 3. Time history of the displacement components at point A


4.2 Post Buckling of a Spherical Shallow Shell

In this example, the efficiency of the considered algorithm combined with the co-rotational formulation in dissipating high frequencies is investigated, see Mamouriet al. (2015) for more details. It is used here to plot the post-buckling curve of thegeometrically nonlinear static behaviour of a spherical shell with four articulated edges,subjected to the concentrated load P, as shown in Fig. 4. Due to the double symmetryof the problem, only one-quarter of the spherical shell is considered. The shellgeometric and mechanical properties are: R = 2540 mm; 2a = 784.90 mm;h = 99.45 mm; E = 68950 N/mm2 and m = 0.3.

The static nonlinear response is plotted in the load-deflection curve represented inFig. 5 using dynamic analysis algorithms.

P

2a

R

2a

R

Fig. 4. Cylindrical shell: geometry and mesh


5 Conclusion

This work aims to evaluate the capability of nonlinear dynamic analysis based upon theCo-rotational Lagrangian Formulation to obtain the solution to the geometric nonlinearpost-buckling response of structures like-shell with conservative dissipative direct timeintegration algorithms. The studied Algorithm is tested for a quadrilateral flat shellfinite element with drilling rotation. The scheme is found to be conservative, and

Fig. 5. Post buckling nonlinear response


efficient for damping out high-frequency modes and thus assuring the stability of thenonlinear response with no need for structural damping. The performances of thestudied algorithm are illustrated through several numerical examples.

References

Boutagouga, D.: A new enhanced assumed strain quadrilateral membrane element with drillingdegree of freedom and modified shape functions. Int. J. Num. Meth. Eng. 110, 573–600(2017)

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Boutagouga, D., Gouasmia, A., Djeghaba, K.: Geometrically nonlinear analysis of thin shell by aquadrilateral finite element with in-plane rotational degrees of freedom. Eur. J. Comput.Mech. 19(8), 707–724 (2010)

Boutagouga, D., Djeghaba, K.: Geometrically nonlinear dynamic analysis of thin shells by afour-node quadrilateral element with in-plane rotational degree of freedom. Eur. J. Comput.Mech. 23(3–4), 161–177 (2014)

Boutagouga, D., Djeghaba, K.: Nonlinear dynamic co-rotational formulation for membraneelements with in-plane drilling rotational degree of freedom. Eng. Comput. 33(3), 667–697(2016)

Mamouri, S., Mourid, E., Ibrahimbegovic, A.: Study of geometric non-linear instability of 2Dframe structures. Eur. J. Comput. Mech. 24(6), 256–278 (2015)

Bathe, K.J., Noh, G.: Insight into an implicit time integration scheme for structural dynamics.Comput. Struct. 98–99, 1–6 (2012)

Saigal, S., Yang, T.Y., Kapania, R.K.: Dynamic buckling of imperfection-sensitive shellstructures. J. Aircr. 24(10), 718–724 (1987)

Hilburger, M.W., Waas, A.M., Starnes Jr., J.H.: Modeling the dynamics response andestablishing post-buckling/post snap-thru equilibrium of discrete structures via a transientanalysis. J. Appl. Mech. 64(3), 590–595 (1997)

Kobayashi, T., Mihara, Y., Fujii, F.: Path-tracing analysis for post-buckling process of elasticcylindrical shells under axial compression. Thin-Walled Struct. 61, 180–187 (2015)

White, S.C., Weaver, P.M., Chauncey Wu, K.: Post-buckling analyses of variable stiffnesscomposite cylinders in axial compression. Compos. Struct. 123, 190–203 (2015)

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Belytschko, T., Hsieh, B.J.: Nonlinear transient finite element analysis with covected co-ordinates. Int. J. Num. Meth. Eng. 7, 255–271 (1973)

Belytschko, T., Hsieh, B.J.: Nonlinear transient analysis of shells and solids of revolution byconvected elements. AIAA J. 12(8), 1031–1035 (1974)


Influence of Material Gradient Index on StressDistribution of Functionally Graded

Dental Implants

Sameh Elleuch1(&), Hanen Jrad1, Mondher Wali1,2,and Fakhreddine Dammak1

1 Laboratory of Electromechanical Systems (LASEM), National EngineeringSchool of Sfax, University of Sfax, Route de Soukra km 4, 3038 Sfax, Tunisia

{sameh.elleuch,fakhreddine.dammak}@enis.tn,

[email protected], [email protected] Department of Mechanical Engineering, College of Engineering,

King Khalid University, Abha, Saudi Arabia

Abstract. Dental implant have important role in restoration of damaged or lostteeth, but some problem is found in their utilization. In fact, the chewing forcesare applied directly in the bone system, which necessitates studying the rela-tionship between the stress distributions and the characteristics of dental implantnear bone system interface and dental implant. Recently functionally gradedmaterials FGM play an important role on dental clinical implant applicationthanks to their abilities and advantages of their mechanical properties. Theobjective of this study is to focus on mechanical properties of FGM denalimplant in order to investigate the effect of the material gradient index on thestress distribution around dental prosthesis. The FGM properties change grad-ually from titanium (Ti) to hydroxyapatite (HAP). The implant body is subjectedto an axial load to simulate masticatory forces. The effect of FGM properties onreduction of stress distributions in the implant-prosthesis components arehighlighted.

Keywords: Dental implant � Functionally graded material � Stressdistributions � Finite element analysis

1 Introduction

Dental implant is a popular clinical surgery to solve problem of missing tooth. Dentalimplantation treatment has developed into one of the most successful prosthetic tech-nologies. A critical progress made in this area was the development of biocompatiblematerials to enable an engineered device (implant) to integrate within its surroundingbony tissues. The challenge to face in prosthetics is to develop both biologically andmechanically compatible biomaterials for this purpose. Functionally graded materials(FGMs) are the advanced materials with varying properties in dimensions. These aremade of two or more constituent phases with continuous and smoothly varying com-position in preferred directions. In recent year, these materials are gaining attention haveperformed in many applications such as aeronautic industries, cutting tools, nuclear

© The Editor(s) (if applicable) and The Author(s), under exclusive licenseto Springer Nature Switzerland AG 2020M. Kharrat et al. (Eds.): ICAMEM 2019, LNME, pp. 11–17, 2020.https://doi.org/10.1007/978-3-030-52071-7_2




https://doi.org/10.1007/978-3-030-52071-7_2

engineering and dental implant. Many researchers have shown great interest in mod-elling FG materials, namely (Jrad et al. 2018a, b, 2019; Mallek et al. 2019a, b, c;Mellouli et al. 2019a, b, c and Bouhamed et al. 2019a, b) using different shells theories.

Few existing research has been reported to develop an optimized design of func-tionally graded material (FGM) dental implant for promoting a long-term success.

In the present study, finite element model is proposed to evaluate the mechanicalperformance of HAP/Ti FGM dental implant. The influence of gradient material indexof FGM implant is examined. Stress distribution (maximum Von Mises stress) in dentalimplant and bone system which are general performance indicator are investigated. Thepresent work can serve as guideline for the design of optimized FGM dental implant.

2 Modeling and Materials

2.1 Finite Element Analysis

The dental implant/supporting bone system presented in Fig. 1 comprises aTitanium/Hydroxyapatite implant, an abutment, and surrounding cortical bone andcancellous bone in the mandibular section. The mandible segment with an implant(16 mm in height and 4 mm in diameter) and a superstructure is modeled assuming anaxisymmetric geometrical model. The cancellous bone is surrounded by a 2 mm thickcortical bone layer.

The material properties used in this study are taken from literature and are listed inTable 1. Implants and abutments are made of titanium alloy. For functional grading,hydroxyapatite is used. All materials are considered isotropic and homogenous.(Sazesh et al. 2017)

Fig. 1. Views of finite element model of FGM dental implant system

12 S. Elleuch et al.

ABAQUS software is used to analyze the model, the component are meshed withhexadehom elements. The number of elements was approximately 30,000, withapproximately 26,000 nodes. The interface between the implant and the bones isassumed as perfectly bonded property. Loading of 100 N is applied (Fig. 1) to thecenter of abutment according to (Kaman and Celik 2013)

2.2 FGM Implant

In this study, dental implant is considered made of Ti/HAP FGM model. The implantproperties change gradually from hydroxyapatite to titanium along longitudinaldirection using a power law with parameter n as follows, (Sazesh et al. 2017)

Vc ¼ 12þ z

h

� �n

ð1Þ

Vc ¼ 1� Vm ð2Þ

Where Vc is volume fraction of HAP, Vm is volume fraction of titanium, n is materialgradient index and h is height of dental implant. In this case, material properties can beobtained as:

E ¼ VcEc þVmEm ð3Þ

t ¼ Vctc þVmtm ð4Þ

E and t denote respectively the Young modulus and Poisson’s ratio. In addition, c andm symbolize respectively the ceramic (HAP) and metal (Ti) materials.

The material gradient index are considered as n = 0, 0.2, 0.5, 1, 2, 5 and 10.

3 Results and Discussions

The purpose of this section is to evaluate the stress distribution on FGM dental implantsystem. The maximum Von Mises stress with different material gradient index on theFGM dental implant and the bone system under static loading are presented in Fig. 2and 3. It can be seen that the maximum Von Mises stress increase when the materialgradient index increase.

Table 1. Material properties.

Material E(GPa) t Ref

Abutment 110 0.35 Yang and Xiang 2007Titanium (Ti) 110 0.35 Lin et al. 2006HAP 40 0.27 Hedia and Mahmoud 2004Cortical bone 14 0.30 Rho et al. 1993Cancellous bone 3 0.30 Rho et al. 1993

Influence of Material Gradient Index on Stress Distribution 13

The maximum stress is focused at the first thread of the implant (Fig. 2), which is ajunction point with the bone.

Fig. 2. Stress distribution on FGM dental implant for different material gradient index n

Fig. 3. Maximum Von Mises stress (MPa) on bone system for different material gradient index n


From Fig. 2 and 3, maximal values of stress in both FGM dental implant and bonesystem is respectively 39.26 MPa and 6 MPa obtained when the power index n = 10.Indeed, the maximum stress value on the bone system are smaller than FGM dentalimplant

Morever, it is observed that the material gradient index have significant effect onmaximum Von Mises stress in static loading and will affect the stability of the implantsystem. The maximum displacements in FGM dental implant with different materialgradient index are presented in Fig. 4. It is shown that by increasing material gradientindex n, the displacement of FGM implant increases by reason of the decrease of elasticmodulus. From Fig. 4 it appears that the value of displacement in implant is smallunder static loading and maximum value is 0.0067 mm obtained when material gra-dient index n = 10 that is to say when having an important amount of titanium.Although titanium and its alloys have been widely adopted as such materials due totheir excellent biocompatibility. However, their mechanical prperties largely differfrom those in host bony tissues. Therefore, the use of FGM Ti/HAP can reduce dis-placement, improve stress distribution and have better biocompatibility.

4 Conclusion

This work aims to investigate numerically the effect of FGM to reduce stress con-centration in the implant prosthesis components. Problem is solved using ABAQUSpackage program. Results are summarized as follows:

– Maximum Von Mises stress values increases with increases material gradient indexn in both FGM dental implant and bone system.

– The maximum value of stress on the bone system are smaller than on dentalimplant.

– Maximum displacement on FGM dental implant increases with increases materialgradient index.

Fig. 4. Maximum displacement on FGM implant for different material gradient index n


Acknowledgments. This work is carried out thanks to the support and funding of TunisianMinistry of Higher Education and Scientific Research through the Project to encourage youngresearchers under grant number 19PEJC10-08.

References

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