. .. , 2.5 Model sensitivity II: loads and boundary conditions

. .. ,

. .. Résumé-en-français,

Y. Bibliography-abe, K. Mori, and T. Kato, Joining of high strength steel and aluminium alloy sheets by mechanical clinching with dies for control of metal flow, Journal of Materials Processing Technology, vol.212, issue.4, pp.884-889, 2012.

M. Backman and W. Goldsmith, The mechanics of penetration of projectiles into targets, International Journal of Engineering Sciences, vol.16, p.91, 1978.

Y. Bai and T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, International Journal of Plasticity, vol.24, issue.6, pp.1071-1096, 2008.

Y. Bai and T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, International Journal of Fracture, vol.161, issue.1, 2010.

Y. Bai and T. Wierzbicki, A comparative study of three groups of ductile fracture loci in the 3d space, Engineering Fracture Mechanics, vol.135, pp.147-167, 2015.

Y. Bao and T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences, vol.46, issue.1, p.110, 2004.

Y. Bao and T. Wierzbicki, On the cut-off value of negative triaxiality for fracture, Engineering Fracture Mechanics, vol.72, issue.7, pp.1049-1069, 2005.

I. Barsoum and J. Faleskog, Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence, International Journal of Solids and Structures, vol.48, issue.6, p.126, 2011.

Y. Beth-ann, Rapid nailing method for joining materials, 2014.

P. Bouchard, T. Laurent, and L. Tollier, Numerical modeling of self-pierce riveting-From riveting process modeling down to structural analysis, Journal of Materials Processing Technology, vol.202, issue.1-3, pp.290-300, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00834966

P. Bridgman, Studies in large plastic flow and fracture, p.110, 1952.

M. Bäker, Finite element simulation of high-speed cutting forces, Journal of Materials Processing Technology, vol.176, issue.1-3, pp.117-126, 2006.

T. Børvik, A. H. Clausen, M. Eriksson, T. Berstad, O. Sture-hopperstad et al., Experimental and numerical study on the perforation of AA6005-T6 panels, International Journal of Impact Engineering, vol.32, issue.1-4, pp.35-64, 2005.

T. Børvik, O. Hopperstad, and T. Berstad, On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical study, European Journal of Mechanics -A/Solids, vol.22, issue.1, p.95, 2003.

T. Børvik, O. S. Hopperstad, M. Langseth, and K. A. Malo, Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates, International Journal of Impact Engineering, vol.28, issue.4, pp.413-464, 2003.

R. Cacko, Review of different material separation criteria in numerical modeling of the self-piercing riveting process-SPR. Archives of Civil and Mechanical Engineering, vol.8, 2008.

N. Candau, C. Pradille, J. Bouvard, and N. Billon, On the use of a fourcameras stereovision system to characterize large 3d deformation in elastomers, Polymer Testing, vol.56, pp.314-320, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01414261

T. Cao, Models for ductile damage and fracture prediction in cold bulk metal forming processes: a review, International Journal of Material Forming, vol.10, issue.2, p.126, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01203082

T. Cao, C. Bobadilla, P. Montmitonnet, and P. Bouchard, A comparative study of three ductile damage approaches for fracture prediction in cold forming processes, Journal of Materials Processing Technology, vol.216, pp.385-404, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01090138

T. Cao, J. Gachet, P. Montmitonnet, and P. Bouchard, A Lodedependent enhanced Lemaitre model for ductile fracture prediction at low stress triaxiality, Engineering Fracture Mechanics, pp.80-96, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00987142

T. Cao, M. Mazière, K. Danas, and J. Besson, A model for ductile damage prediction at low stress triaxialities incorporating void shape change and void rotation, International Journal of Solids and Structures, vol.63, p.126, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01165304

M. Carandente, R. Dashwood, I. Masters, and L. Han, Improvements in numerical simulation of the SPR process using a thermo-mechanical finite element analysis, Journal of Materials Processing Technology, vol.236, issue.103, pp.148-161, 2016.

Y. Chastel and L. Passemard, Joining Technologies for Future Automobile Multi-material Modules, Procedia Engineering, vol.81, issue.2, pp.2104-2110, 2014.

S. Chocron, B. Erice, A. , and C. E. , A new plasticity and failure model for ballistic application, International Journal of Impact Engineering, vol.38, issue.8-9, p.101, 2011.

M. Cockroft and D. Latham, Ductility and workability of metals, Journal of the Institute of Metals, vol.101, pp.33-39, 1968.

R. Corbett and J. , Impact loading of plates and shells by freeflying projectiles: a review, International Journal of Impact Engineering, vol.18, issue.2, pp.141-230, 1996.

G. Cowper and P. Symonds, Strain-hardening and strain-rate effects in the impact loading of cantilever beams, 1957.

M. Dehra, High velocity formability and factors affecting it, p.93, 2006.

S. Dey, T. Børvik, O. Hopperstad, and M. Langseth, On the influence of constitutive relation in projectile impact of steel plates, International Journal of Impact Engineering, vol.34, issue.3, p.94, 2007.

S. Dey, T. Børvik, X. Teng, T. Wierzbicki, and O. Hopperstad, On the ballistic resistance of double-layered steel plates: An experimental and numerical investigation, International Journal of Solids and Structures, vol.44, issue.20, p.93, 2007.

T. Draht and A. Kolac, Process monitoing for High-Speed Joining. United States Patent and Trademark Office, vol.595, p.17, 2012.

T. Draht and G. Meschut, Method for establishing connection and a nail for this purpose. United States Patent and Trademark Office, vol.782, p.9, 2014.

B. Erice and F. Gálvez, A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion, International Journal of Solids and Structures, vol.51, issue.1, pp.93-110, 2014.

W. Farren and G. Taylor, The heat developed during plastic extension of metals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.107, pp.422-451, 1925.

S. Fayolle, Etude de la modélisation de la pose et de la tenue mécanique des assemblages par déformation plastique, vol.3, p.104, 2009.

S. Fayolle, P. Bouchard, and K. Mocellin, Modelling the strength of self-piercing riveted joints, Self-Piercing, pp.79-107, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01052922

E. Felder, Effet thermique de la mise en forme -Theorie et phénomènes volumiques. Techniques de l'ingénieur, (M3012). xv, 51, vol.52, p.53, 2001.

F. Flüggen and O. Hahn, Einseitiges Fügen von Blech-Profil-Konstruktionen mit lösbaren und nicht lösbaren Hilfsfügeelementen, 2010.

H. Folgar-ribadas, T. Böddeker, A. Chergui, M. Ivanjko, F. Gili et al., Joining TWIP-Steel simulation models, Structural Integrity Procedia, vol.5, pp.516-523, 2017.

P. S. Follansbee and U. F. Kocks, A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable, Acta metallica, vol.36, issue.1, pp.81-93, 1988.

M. J. Forrestal and T. L. Warren, Perforation equations for conical and ogival nose rigid projectiles into aluminum target plates, International Journal of Impact Engineering, vol.36, issue.2, pp.220-225, 2009.

L. A. Freitag and P. M. Knupp, Tetrahedral mesh improvement via optimization of the element condition number, International Journal for Numerical Methods in Engineering, vol.53, issue.6, pp.1377-1391, 2002.

G. Gary, Comportement des métaux à grande vitesse de déformation: modélisation. Techniques de l'ingénieur. Matériaux métalliques, 2002.

F. Goldspiegel, K. Mocellin, and P. Michel, Numerical Simulation of High-Speed Nailing Process, AIP Conference Proceedings, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01674405

I. Gotlib, An Analysis of High-Speed Impact Nailing for Lightweight Automotive Structures. Master's thesis, 2014.

P. Groche, S. Wohletz, M. Brenneis, C. Pabst, and F. Resch, Joining by forming-A review on joint mechanisms, applications and future trends, Journal of Materials Processing Technology, vol.214, issue.10, pp.1972-1994, 2014.

G. Gruben, O. Hopperstad, and T. Børvik, Evaluation of uncoupled ductile fracture criteria for the dual-phase steel Docol 600dl, International Journal of Mechanical Sciences, vol.62, issue.1, pp.133-146, 2012.

F. Grytten, T. Børvik, O. Hopperstad, and M. Langseth, Low velocity perforation of AA5083-H116 aluminium plates, International Journal of Impact Engineering, vol.36, issue.4, pp.597-610, 2009.

A. L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, 1977.

N. Hoang, M. Langseth, R. Porcaro, and A. Hanssen, The effect of the riveting process and aging on the mechanical behaviour of an aluminium selfpiercing riveted connection, European Journal of Mechanics -A/Solids, vol.30, issue.5, pp.619-630, 2011.

J. K. Holmen, O. S. Hopperstad, and T. Børvik, Low-velocity impact on multilayered dual-phase steel plates, International Journal of Impact Engineering, vol.78, pp.161-177, 2015.

O. Hopperstad, T. Børvik, M. Langseth, K. Labibes, A. et al., On the influence of stress triaxiality and strain rate on the behaviour of a structural steel. Part I. Experiments, European Journal of Mechanics -A/Solids, vol.22, issue.1, pp.1-13, 2003.

Z. Huang and J. Yanagimoto, Dissimilar joining of aluminum alloy and stainless steel thin sheets by thermally assisted plastic deformation, Journal of Materials Processing Technology, vol.225, issue.2, pp.393-404, 2015.

D. Hußmann, Weiterentwicklung des Bolzensetzens für innovative Fahrzeugkonzepte des automobilen Leichtbaus, 2008.

. Iso, ISO 6892-1 Metallic materials -Tensile testing -Part 1: Method of test at room temperature. International Organization for Standardization, vol.109, 2009.

. Iso, Mechanical joining -Destructive testing of joints -Specimen dimensions and test procedure for tensile shear testing of single joints, vol.12996, 2013.

. Iso, Resistance welding -Destructive testing of welds -Specimen dimensions and procedure for cross tension testing of resistance spot and embossed projection welds, vol.14272, 2016.

P. Jeunechamps, Simulation numérique, à l'aide d'algorithmes thermomécaniques implicites, de matériaux endommageables pouvant subir de grandes vitesses de déformation, Sciences Appliquées. 93, vol.115, p.121, 2008.

C. Johnson, A constitutive model and data for metals subjected to large strains, high strain rates and temperatures. 7th Symposium Ballistic, La Haye, vol.93, pp.541-547, 1983.

C. Johnson, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engineering Fracture Mechanics, 1985.

K. L. Johnson, Contact mechanics, p.37, 1985.

M. Jäckel, C. Kraus, and T. Kropp, Effects of Increased Tool Velocity on Mechanical Joining of Steel and Aluminum Sheet Metals. Procedia CIRP, vol.23, pp.24-28, 2014.

R. Kaboli, F. Podlesak, and P. Mayr, Numerical simulation of spin-blindriveting of magnesium and fibre-reinforced plastic composite. Key Engineering Materials, 2015.

B. M. Klingner and J. R. Shewchuk, Aggressive tetrahedral mesh improvement, Proceedings of the 16th international meshing roundtable, pp.3-23, 2008.

K. Kpenyigba, T. Jankowiak, A. Rusinek, R. Pesci, W. et al., Effect of projectile nose shape on ballistic resistance of interstitial-free steel sheets, International Journal of Impact Engineering, vol.79, pp.83-94, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01166247

F. Lambiase and A. Di-ilio, Damage analysis in mechanical clinching: Experimental and numerical study, Journal of Materials Processing Technology, vol.230, 2016.

B. Langrand, Contribution à la caractérisation numérique et expérimentale d'assemblages structuraux rivetés sous sollicitation dynamique, 1998.

C. Lee, J. Lee, H. Ryu, K. Lee, B. Kim et al., Design of hole-clinching process for joining of dissimilar materials -Al6061-T4 alloy with DP780 steel, hot-pressed 22mnb5 steel, and carbon fiber reinforced plastic, Journal of Materials Processing Technology, vol.214, issue.10, p.103, 2014.

J. Lemaitre and J. Chaboche, Mechanics of solid materials, vol.97, p.99, 1994.

S. H. Lo, Optimization of tetrahedral meshes based on element shape measures, Computers & structures, vol.63, issue.5, pp.951-961, 1997.

K. Martinsen, S. Hu, and B. Carlson, Joining of dissimilar materials, CIRP Annals -Manufacturing Technology, vol.64, issue.2, pp.679-699, 2015.

G. Meschut, V. Janzen, and T. Olfermann, Innovative and highly productive joining technologies for multi-material lightweight car body structures, 2014.

G. Meschut, M. Matzke, R. Hoerhold, and T. Olfermann, Hybrid Technologies for Joining Ultra-high-strength Boron Steels with Aluminum Alloys for Lightweight Car Body Structures, Procedia CIRP, vol.23, issue.2, pp.19-23, 2014.

A. Molinari, S. Mercier, J. , and N. , Dynamic Failure of Ductile Materials, Procedia IUTAM, vol.10, pp.201-220, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01097175

K. Mori, N. Bay, L. Fratini, F. Micari, and A. E. Tekkaya, Joining by plastic deformation, CIRP Annals -Manufacturing Technology, vol.62, issue.2, pp.673-694, 2013.

J. Mucha, The numerical analysis of the effect of the joining process parameters on self-piercing riveting using the solid rivet, Archives of Civil and Mechanical Engineering, vol.14, issue.3, pp.444-454, 2014.

K. Nahshon and J. Hutchinson, Modification of the Gurson Model for shear failure, European Journal of Mechanics -A/Solids, vol.27, issue.1, p.102, 2008.

K. Nahshon and Z. Xue, A modified Gurson model and its application to punch-out experiments, Engineering Fracture Mechanics, vol.76, issue.8, pp.997-1009, 2009.

C. Ortiz, Computational modelling of impact damage of brittle material, International Journal of Solids Structures, vol.33, pp.2899-2938, 1996.

M. Ortiz and G. Camacho, Adaptive lagrangian modelling of ballistic penetration of metallic targets, Computer methods in applied mechanics and engineering, vol.142, pp.269-301, 1995.

V. N. Parthasarathy, C. M. Graichen, and A. F. Hathaway, A comparison of tetrahedron quality measures, Finite Elements in Analysis and Design, vol.15, issue.3, pp.255-261, 1994.

R. Porcaro, A. Hanssen, M. Langseth, A. , and A. , Self-piercing riveting process: An experimental and numerical investigation, Journal of Materials Processing Technology, vol.171, issue.1, p.103, 2006.

D. L. Preston and D. L. Tonks, Model of plastic deformation for extreme loading conditions, Journal of Applied Physics, issue.211, p.94, 2003.

K. Rakvåg, T. Børvik, and O. Hopperstad, A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests, International Journal of Solids and Structures, vol.51, issue.3-4, pp.808-821, 2014.

R. Recht and T. Ipson, The dynamics of terminal ballistics, p.37, 1962.

J. R. Rice and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields, Journal of Mechanics and Physics of Solids, vol.101, 1969.

C. C. Roth, E. Lms, and . Polytechnique, Experimental and numerical investigation of ductile fracture initiation at low, intermediate and high strain rates, p.115, 2015.

. Roux, Assemblage mécanique: stratégies d'optimisation des procédés et d'identification des comportements mécaniques des matériaux, p.116, 2011.

A. Schmidt, W. Gilbert, and O. Boston, A thermal balance method and mechanical investigation for evaluating machinability, ASME, vol.67, pp.225-232, 1945.

N. Scholl, F. Minuth-hadi, and K. Thiele, Modelling the strain rate dependent hardening of constructional steel using semi-empirical models, Journal of Constructional Steel Research, vol.145, pp.414-424, 2018.

H. Schreier, J. Orteu, and M. A. Sutton, Image Correlation for Shape, Motion and Deformation Measurements, p.113, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01729219

M. Steinig, RIVTAC® : The Innovative High Speed Joining Process. Böllhoff Automation GmbH, p.17, 2012.

G. Taylor and H. Quinney, The latent energy remaining in metals after cold working, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.143, pp.307-327, 1934.

X. Teng, High Velocity Impact Fracture. PhD, Massachusetts Institute of Technology, vol.119, p.121, 2005.

X. Teng and T. Wierzbicki, Evaluation of six fracture models in high velocity perforation, Engineering Fracture Mechanics, vol.73, issue.12, pp.1653-1678, 2006.

T. Draht, Entwicklung des Bolzensetzens für Blech-Profil-Verbindungen im Fahrzeugbau, 2006.

V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a roundtensile bar, Acta Metallurgica, vol.32, issue.1, pp.157-169, 1984.

V. V. Vershinin, Validation of metal plasticity and fracture models through numerical simulation of high velocity perforation, International Journal of Solids and Structures, 2015.

T. Wierzbicki, Y. Bao, Y. Lee, and Y. Bai, Calibration and evaluation of seven fracture models, International Journal of Mechanical Sciences, vol.47, issue.4-5, pp.719-743, 2005.

P. Wiethop, Stanznageln -Prozesssimulation mit Hilfe der Finiten Elemente Methode, vol.104, pp.36-40, 2010.

M. Wilkins, R. Streit, and J. Reaugh, Cumulative-strain-damage model of ductile fracture: simulation and prediction of engineering fracture tests, p.102, 1980.

L. Xue and T. Wierzbicki, Ductile fracture initiation and propagation modeling using damage plasticity theory, Engineering Fracture Mechanics, vol.75, issue.11, pp.3276-3293, 2008.

L. Xue and T. Wierzbicki, Numerical simulation of fracture mode transition in ductile plates, International Journal of Solids and Structures, vol.46, issue.6, pp.1423-1435, 2009.

S. Yadav, E. A. Repetto, G. Ravichandran, and M. Ortiz, A computational study of the influence of thermal softening on ballistic penetration in metals, International Journal of Impact Engineering, vol.25, issue.8, pp.787-803, 2001.

F. Zerilli and R. Armstrong, Dislocation mechanics based analysis of dynamics material behavior, Journal de Physique Colloques, vol.49, issue.C3, pp.529-534, 1988.
URL : https://hal.archives-ouvertes.fr/jpa-00227797

S. Zhao, F. Xu, J. Guo, and X. Han, Experimental and numerical research for the failure behavior of the clinched joint using modified Rousselier model, Journal of Materials Processing Technology, vol.214, issue.10, p.103, 2014.

J. A. Zukas, Impact dynamics: theory and experiment, vol.36, p.91, 1980.

, Algorithm 1: Mesh quality computation in FORGE ® user-subroutine Input : Node location matrix X loc of size 3 × 4, respectively 3 space dimensions and 4 nodes Output: Quality value such as 0 > Q > 1

. =-x-loc,

, 2) = X loc (i, 1) ? X loc (i, 3)

, X loc (i, 1) ? X loc (i, 4)

. =-x-loc,

. =-x-loc,

, 6) = X loc (i, 3) ? X loc (i, 4)

, P (1) = v(2, 1).v(3, 2) ? v(3, 1)

, l(i) = [v(1, i).v(1, i) + v(2, i).v(2, i) + v(3, i)

. Q-=-min,