Abstract

Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Metal cutting processes are present in big industries (automotive, aerospace, home appliance, etc.) that manufacture big products, but also high tech industries where small piece but high precision is needed. The importance of machining is such that, it is the most common manufacturing processes for producing parts and obtaining specified geometrical dimensions and surface finish, its cost represent 15% of the value of all manufactured products in all industrialized countries.

Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear.

The study of metal cutting is difficult from an experimental point of view, because of the high speed at which it takes place under industrial machining conditions (experiments are difficult to carry out), the small scale of the phenomena which are to be observed, the continuous development of tool and workpiece materials and the continuous development of tool geometries, among others reasons.

Simulation of machining processes in which the workpiece material is highly deformed on metal cutting is a major challenge of the finite element method (FEM). The principal problem in using a conventional FE model with langrangian mesh is mesh distortion in the high deformation. Traditional Langrangian approaches such as FEM cannot resolve the large deformations very well. Element distortion has been always matter of concern which limited the analysis to incipient chip formation in some studies. Instead, FEM with an Eulerian formulation require the knowledge of the chip geometry in advance, which, undoubtedly, restricts the range of cutting conditions capable of being analyzed. Furthermore serrated and discontinuous chip formation cannot be simulated.

The main objective of this work is precisely to contribute to solve some of the problems described above through the extension of the Particle Finite Element Method (PFEM) to thermo-mechanical problems in solid mechanics which involve large strains and rotations, multiple contacts and generation of new surfaces, with the main focus in the numerical simulation of metal cutting process. In this work, we exploit the particle and lagrangian nature of PFEM and the advantages of finite element discretization to simulate the different chip shapes (continuous and serrated) that appear when cutting materials like steel and titanium at different cutting speeds. The new ingredients of PFEM are focused on the insertion and remotion of particles, the use of constrained Delaunay triangulation and a novel transfer operator of the internal variables.

The remotion and insertion of particles circumvents the difficulties associated to element distortion, allowing the separation of chip and workpiece without using a physical or geometrical criterion. The constrained Delaunay improves mass conservation and the chip shape through the simulation, and the transfer allows us to minimize the error due to numerical diffusion.

The thermo-mechanical problem, formulated in the framework of continuum mechanics, is integrated using an isothermal split in conjunction with implicit, semi-explicit and IMPLEX schemes. The tool has been discretized using a standard three-node triangle finite element. The workpiece has been discretized using a mixed displacement-pressure finite element to deal with the incompressibility constraint imposed by plasticity. The mixed finite element has been stabilized using the Polynomial Pressure Projection (PPP), initially applied in the literature to the Stokes equation in the field of fluid mechanics.

The behavior of the tool is described using a Neo-Hookean Hyperelastic constitutive model. The behavior of the workpiece is described using a rate dependent, isotropic, finite strain j2 elastoplasticity with three different yields functions used to describe the strain hardening, the strain rate hardening and the thermal softening (Simo, Johnson Cook, Baker) of different materials under a wide variety of cutting conditions. The friction at the tool chip interface is modeled using the Norton-Hoff friction law. The heat transfer at the tool chip interface includes heat transfer due to conduction and friction.

To validate the proposed mixed displacement-pressure formulation, we present three benchmark problems which validate the approach, namely, plain strain Cook´s membrane, the Taylor impact test and a thermo-mechanical traction test. The isothermal-IMPLEX split presented in this work has been validated using a thermo-mechanical traction test.

Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of metal cutting processes a set of representative numerical simulations are presented in this work, among them: cutting using a rate independent yield function, cutting using different rake angles, cutting with a deformable tool and a frictionless approach, cutting with a deformable tool including friction and heat transfer, the transition from continuous to serrated chip formation increasing the cutting speed. We have assembled several numerical tec niques which enable the simulation of orthogonal cutting processes. Our simulations demonstrate the ability of the PFEM to predict chip morphologies consistent with experimental observations.

Also, our results show that the suitable selection of the global time integration scheme may involve savings in computation time up to 9 times.

Furthermore, this work present a sensibility analysis to cutting conditions by means of a Design of Experiments (DoE). The Design of Experiments carried out with PFEM has been compared with DoE carried out with AdvantaEdge, Deform, Abaqus and Experiments. The results obtained with PFEM and other numerical simulations are very similar, while, a comparison of numerical simulations and experiments show some differences in the output variables that depend on the friction phenomena. The results suggest that is necessary to improve the modelization of the friction at the tool-chip interface.

PDF file

The PDF file did not load properly or your web browser does not support viewing PDF files. Download directly to your device: Download PDF document

References

[1] M. P. Groover, Fundamentals of Modern Manufacturing: Materials, Processes, and Systems, 2006.

[2] E. Trent and P. Wright, Metal cutting, Fourth Edition ed., 2000.

[3] M. Heinstein and D. Segalman, "Simulation of Orthogonal Cutting with Smooth Particles Hydrodynamics," Sandia National Laboratories1997.

[4] F. Fleissner, T. Gaugele, and P. Eberhard, "Applications of the discrete element method in mechanical engineering," Multibody system dynamics vol. 18, pp. 81-94, 2007.

[5] R. Ambati, X. Pan, H. Yuan, and X. Zhang, "Application of material point methods for cutting process simulations," Computational Materials Science, vol. 57, pp. 102-110, 2012.

[6] L. Illoul and P. Lorong, "On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing," Computer and Structures, vol. 89, pp. 940–958, 2011.

[7] M. Vaz, D. R. J. Owen, V. Kalhori, M. Lundblad, and L. E. Lindgren, "Modelling and Simulation of Machining Processes," Archives of Computational Methods in Engineering, vol. 14, pp. 173-204, 2007.

[8] K. S. Al-Athel and M. S. Gadala, "The Use of Volume of Solid (VOS) in Simulating Metal Cutting with Chamfered and Blunt Tools," International Journal of Mechanical Sciences, vol. Vol. 53, pp. 23-30, 2010.

[9] E. Uhlmann, R. Gerstenberger, M. Graf von der Schulenburg, J. Kurnert, and A. Mattes, "The Finite Pointset Method for the Meshfree Numerical Simulation of Chip Formation," presented at the 12 Cirp Conference on Modelling of Machining Operations, San Sebastian, Spain, 2009.

[10] D. J. Benson and S. Okazawa, "Contact in a multi-material Eulerian finite element formulation," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4277-4298, 2004.

[11] M. Cremonesi, A. Frangi, and U. Perego, "A Lagrangian finite element approach for the analysis of fluid–structure interaction problems," International Journal for Numerical Methods in Engineering, vol. 84, pp. 610-630, 2010.

[12] J. Limido, C. Espinosa, M. Salaün, and J. L. Lacome, "SPH method applied to high speed cutting modelling," International Journal of Mechanical Sciences, vol. 49, pp. 898–908, 2007.

[13] C. R. Dohrmann and P. B. Bochev, "A stabilized finite element method for the Stokes problem based on polynomial pressure projections," International Journal for Numerical Methods in Fluids, vol. 46, pp. 183–201, 2004.

[14] P. B. Bochev, C. R. Dohrmann, and M. D. Gunzburger, "Stabilization of Low-Order Mixed Finite Elements for the Stokes Equations," SIAM Journal on Numerical Analysis, vol. 44, pp. 82-101, 2008.

[15] L. Filice, F. Micari, S. Rizzuti, and D. Umbrello, "A critical analysis on the friction modelling in orthogonal machining," International Journal of Machine Tools and Manufacture, vol. 47, pp. 709-714, 2007.

[16] P. J. Arrazola, D. Ugarte, and X. Domínguez, "A new approach for the friction identification during machining through the use of finite element modeling," International Journal of Machine Tools & Manufacture vol. 48, pp. 173-183, 2008.

[17] P. J. Arrazola and T. Özel, "Investigations on the effects of friction modeling in finite element simulation of machining," International Journal of Mechanical Sciences, vol. 52, pp. 31–42, 2010.

[18] A. J. Haglund, H. A. Kishawy, and R. J. Rogers, "An exploration of friction models for the chip–tool interface using an Arbitrary Lagrangian–Eulerian finite element model," Wear, vol. 265, pp. 452–460, 2008.

[19] F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, 1954.

[20] J. F. Archard, "Elastic Deformation and the Laws of Friction," Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 243, pp. 190-205, December 24, 1957 1957.

[21] T. H. C. Childs, K. Maekawa, T. Obikawa, and Y. Yamane, Metal Machining: Theory and Applications. Amsterdam, 2000.

[22] M. H. Dirikolu, T. H. C. Childs, and K. Maekawa, "Finite element simulation of chip flow in metal machining," International Journal of Mechanical Sciences, vol. 43, pp. 2699-2713, 2001.

[23] T. H. C. Childs, M. I. Mahdi, and G. Barrow, "On the Stress Distribution Between the Chip and Tool During Metal Turning," CIRP Annals - Manufacturing Technology, vol. 38, pp. 55-58, 1989.

[24] G. S. Sekhon and J. L. Chenot, "Numerical simulation of continuous chip formation during non-steady orthogonal cutting simulation," Engineering Computations, vol. 10, 1993.

[25] T. D. Marusich and M. Ortiz, "Modelling and simulation of high-speed machining," International Journal for Numerical Methods in Engineering, vol. 38, pp. 3675–3694, 1995.

[26] D. R. J. Owen and M. Vaz Jr, "Computational techniques applied to high-speed machining under adiabatic strain localization conditions," Computer Methods in Applied Mechanics and Engineering, vol. 171, pp. 445–461, 1999.

[27] J. S. Strenkowski and J. T. Carroll, "A Finite Element Model of Orthogonal Metal Cutting," Journal of Engineering for IndustryTransactions of the Asme vol. 107, pp. 349-354, 1985.

[28] K. Komvopoulos and S. A. Erpenbeck, " Finite Element Modeling of Orthogonal Metal Cutting," Journal of Engineering for Industry, ASME Trans, vol. 113, pp. 253–267, 1991.

[29] A. J. Shih, "Finite element analysis of the rake angle effects in orthogonal metal cutting," International Journal of Mechanical Sciences, vol. 38, pp. 1-17, 1995.

[30] A. Raczy, M. Elmadagli, W. J. Altenhof, and A. T. Alpas, "An eulerian finite-element model for determination of deformation state of a copper subjected to orthogonal cutting," Metalurgical and Materials Transactions A, vol. 35, pp. 2393-2400, 2004.

[31] M. S. Gadalaa, M. R. Movahhedya, and J. Wangb, "On the mesh motion for ALE modeling of metal forming processes," Finite Elements in Analysis and Design, vol. 38, pp. 435–459, 2002.

[32] M. S. Gadala, "Recent trends in ALE formulation and its applications in solid mechanics," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4247-4275, 2004.

[33] L. Olovsson, L. Nilsson, and K. Simonsson, "An ALE formulation for the solution of two-dimensional metal cutting problems," Computers & Structures, vol. 72, pp. 497–507, 1999.

[34] R. Rakotomalala, P. Joyot, and M. Touratier, "Arbitrary Lagrangian-Eulerian thermomechanical finite-element model of material cutting," Communications in Numerical Methods in Engineering, vol. 9, pp. 975–987, 1993.

[35] H. T. Y. Yang, M. Heinstein, and J. M. Shih, "Adaptive 2D finite element simulation of metal forming processes," International Journal for Numerical Methods in Engineering, vol. 28, pp. 1409-1428, 1989.

[36] P. O. D. Micheli and K. Mocellin, "Explicit F.E. formulation with modified linear tetrahedral elements applied to high speed forming processes," International Journal Of Material Forming, vol. 1, pp. 1411-1414, 2008.

[37] F. Auricchio, L. Beirão da Veiga, C. Lovadina, and A. Reali, "An analysis of some mixed-enhanced finite element for plane linear elasticity," Computer Methods in Applied Mechanics and Engineering, vol. 194, pp. 2947-2968, 2005.

[38] A. J. Chorin, "A Numerical Method for Solving Incompressible Viscous Flow Problems," Journal of Computational Physics, vol. 135, pp. 118-125, 1997.

[39] E. Oñate, J. Rojek, R. L. Taylor, and O. C. Zienkiewicz, "Finite calculus formulation for incompressible solids using linear triangles and tetrahedra," International Journal for Numerical Methods in Engineering, vol. 59, pp. 1473–1500, 2004.

[40] C. Agelet de Saracibar, M. Chiumenti, Q. Valverde, and M. Cervera, "On the orthogonal subgrid scale pressure stabilization of finite deformation J2 plasticity," Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 1224–1251, 2006.

[41] M. Chiumenti, Q. Valverde, C. Agelet de Saracibar, and M. Cervera, "A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations," Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 5253–5264, 2002.

[42] M. Chiumenti, Q. Valverde, C. Agelet de Saracibar, and M. Cervera, "A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra," International Journal of Plasticity, vol. 20, pp. 1487–1504, 2003.

[43] M. Cervera, M. Chiumenti, Q. Valverde, and C. Agelet de Saracibar, "Mixed linear/linear simplicial elements for incompressible elasticity and plasticity," Computer Methods in Applied Mechanics and Engineering, vol. 192, pp. 5249–5263, 2003.

[44] F. M. Andrade Pires, E. A. de Souza Neto, and D. R. J. Owen, "On the finite element prediction of damage growth and fracture initiation in finitely deforming ductile materials," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 5223–5256, 2004.

[45] E. A. de Souza Neto, F. M. Andrade Pires, and D. R. J. Owen, "F-barbased linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking," International Journal for Numerical Methods in Engineering, vol. 62, pp. 353–383, 2005.

[46] G. T. Camacho and M. Ortiz, "Computational modelling of impact damage in brittle materials," International Journal of Solids and Structures, vol. 33, pp. 2899-2938, 1996.

[47] Y. Guo, M. Ortiz, T. Belytschko, and E. A. Repetto, "Triangular composite finite elements," International Journal for Numerical Methods in Engineering, vol. 47, pp. 287-316, 2000.

[48] J. Bonet and A. J. Burton, "A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications," Communications in Numerical Methods in Engineering, vol. 14, pp. 437-449, 1998.

[49] J. Bonet, H. Marriott, and O. Hassan, "Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications," International Journal for Numerical Methods in Engineering, vol. 50, pp. 119-133, 2001.

[50] F. M. Andrade Pires, E. A. de Souza Neto, and J. L. de la Cuesta Padilla, "An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains," Communications in Numerical Methods in Engineering, vol. 20, pp. 569-583, 2004.

[51] M. A. Puso and J. Solberg, "A stabilized nodally integrated tetrahedral," International Journal for Numerical Methods in Engineering, vol. 67, pp. 841- 867, 2006.

[52] P. O. D. Micheli and K. Mocellin, "2D high speed machining simulations using a new explicit formulation with linear triangular elements," International Journal of Machining and Machinability of Materials, vol. 9, pp. 266 - 281, 2011.

[53] C. R. Dohrmann, M. W. Heinstein, J. Jung, S. W. Key, and W. R. Witkowski, "Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes," International Journal for Numerical Methods in Engineering, vol. 47, pp. 1549-1568, 2000.

[54] J. Bonet, H. Marriott, and O. Hassan, "An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications," Communications in Numerical Methods in Engineering, vol. 17, pp. 551-561, 2001.

[55] F. Greco, D. Umbrello, S. D. Renzo, L. Filice, I. Alfaro, and E. Cueto, "Application of the nodal integrated finite element method to cutting: a preliminary comparison with the "traditional" FEM approach," Advanced Materials Research, pp. 172-181, 2011.

[56] J. Marti and P. Cundall, "Mixed discretization procedure for accurate modelling of plastic collapse," International Journal for Numerical and Analytical Methods in Geomechanics, vol. 6, pp. 129-139, 1982.

[57] C. Detournay and E. Dzik, "Nodal Mixed Discretization for tetrahedral elements," presented at the 4th International FLAC Symposium on Numerical Modeling in Geomechanics, Minneapolis, 2006.

[58] M. Bäker, J. Rösler, and C. Siemers, "A finite element model of high speed metal cutting with adiabatic shearing," Computers & Structures, vol. 80, pp. 495–513, 2002.

[59] J. Rojek, E. Oñate, and R. L. Taylor, "CBS-based stabilization in explicit solid dynamics," International Journal for Numerical Methods in Engineering, vol. 66, pp. 1547-1568, 2006.

[60] A. Curnier and P. Alart, "A Generalized Newton Method for Contact Problems with Friction," Journal De Mecanique Theorique Et Appliquee, vol. 7, pp. 67-82, 1988.

[61] J. O. Hallquist, G. L. Goudreau, and D. J. Benson, "Sliding interfaces with contact-impact in large-scale Lagrangian computations," Computer Methods in Applied Mechanics and Engineering, vol. 51, pp. 107-137, 1985.

[62] J. H. Heegaard and A. Curnier, "An augmented Lagrangian method for discrete large-slip contact problems," International Journal for Numerical Methods in Engineering, vol. 36, pp. 569-593, 1993.

[63] R. Michalowski and Z. Mroz, "Associated and non-associated sliding rules in contact friction problems," Archiwum Mechaniki Stosowanej, vol. 30, pp. 259-276, 1978.

[64] D. Perić and D. R. J. Owen, "Computational model for 3-D contact problems with friction based on the penalty method," International Journal for Numerical Methods in Engineering, vol. 35, pp. 1289-1309, 1992.

[65] P. Wriggers and J. C. Simo, "A note on tangent stiffness for fully nonlinear contact problems," Communications in Applied Numerical Methods, vol. 1, pp. 199-203, 1985.

[66] P. Papadopoulos and R. L. Taylor, "A mixed formulation for the finite element solution of contact problems," Computer Methods in Applied Mechanics and Engineering, vol. 94, pp. 373-389, 1992.

[67] J. C. Simo and T. A. Laursen, "An augmented lagrangian treatment of contact problems involving friction," Computers & Structures, vol. 42, pp. 97-116, 1992.

[68] P. Wriggers and G. Zavarise, "Thermomechanical contact—a rigorous but simple numerical approach," Computers & Structures, vol. 46, pp. 47-53, 1993.

[69] P. Wriggers and C. Miehe, "Contact constraints within coupled thermomechanical analysis—A finite element model," Computer Methods in Applied Mechanics and Engineering, vol. 113, pp. 301-319, 1994.

[70] G. Zavarise, P. Wriggers, and B. A. Schrefler, "On augmented Lagrangian algorithms for thermomechanical contact problems with friction," International Journal for Numerical Methods in Engineering, vol. 38, pp. 2929-2949, 1995.

[71] K. A. Fischer and P. Wriggers, "Frictionless 2D Contact formulations for finite deformations based on the mortar method," Computational Mechanics, vol. 36, pp. 226-244, 2005.

[72] M. Tur, F. J. Fuenmayor, and P. Wriggers, "A mortar-based frictional contact formulation for large deformations using Lagrange multipliers," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 2860-2873, 2009.

[73] S. Hüeber and B. I. Wohlmuth, "Thermo-mechanical contact problems on non-matching meshes," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 1338-1350, 2009.

[74] J. Oliver, S. Hartmann, J. C. Cante, R. Weyler, and J. A. Hernández, "A contact domain method for large deformation frictional contact problems. Part 1: Theoretical basis," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 2591-2606, 2009.

[75] S. Hartmann, J. Oliver, R. Weyler, J. C. Cante, and J. A. Hernández, "A contact domain method for large deformation frictional contact problems. Part 2: Numerical aspects," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 2607-2631, 2009.

[76] T. Belytschko and M. O. Neal, "Contact-impact by the pinball algorithm with penalty and Lagrangian methods," International Journal for Numerical Methods in Engineering, vol. 31, pp. 547-572, 1991.

[77] J. Bruchon, H. Digonnet, and T. Coupez, "Using a signed distance function for the simulation of metal forming processes: Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach," International Journal for Numerical Methods in Engineering, vol. 78, pp. 980-1008, 2009.

[78] K. Komvopoulos and S. A. Erpenbeck, "Finite Element Modeling of Orthogonal Metal Cutting," Journal of Engineering for Industry, vol. 113, pp. 253-267, 1991.

[79] O. C. Zienkiewicz and J. Z. Zhu, "The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity," International Journal for Numerical Methods in Engineering, vol. 33, pp. 1365- 1382, 1992.

[80] M. Ortiz and J. J. Quigley IV, "Adaptive mesh refinement in strain localization problems," Computer Methods in Applied Mechanics and Engineering, vol. 90, pp. 781-804, 1991.

[81] N.-S. Lee and K.-J. Bathe, "Error indicators and adaptive remeshing in large deformation finite element analysis," Finite Elements in Analysis and Design, vol. 16, pp. 99-139, 1994.

[82] D. Perić, M. Vaz Jr, and D. R. J. Owen, "On adaptive strategies for large deformations of elasto-plastic solids at finite strains: computational issues and industrial applications," Computer Methods in Applied Mechanics and Engineering, vol. 176, pp. 279-312, 1999.

[83] D. Perić, C. Hochard, M. Dutko, and D. R. J. Owen, "Transfer operators for evolving meshes in small strain elasto-plasticity," Computer Methods in Applied Mechanics and Engineering, vol. 137, pp. 331–344, 1996.

[84] C. Shet and X. Deng, "Finite element analysis of the orthogonal metal cutting process," Journal of Materials Processing Technology, vol. 105, pp. 95-109, 2000.

[85] G. Chen, C. Ren, X. Yang, X. Jin, and T. Guo, "Finite element simulation of high-speed machining of titanium alloy (Ti–6Al–4V) based on ductile failure model," The International Journal Of Advanced Manufacturing Technology vol. 56, pp. 1027-1038, 2011.

[86] D. Umbrello, "Finite element simulation of conventional and high speed machining of Ti6Al4V alloy," Journal of Materials Processing Technology, vol. 196, pp. 79-87, 2008.

[87] E. Ceretti, M. Lucchi, and T. Altan, "FEM simulation of orthogonal cutting: serrated chip formation," Journal of Materials Processing Technology, vol. 95, pp. 17-26, 1999.

[88] H. Borouchaki, P. Laug, A. Cherouat, and K. Saanouni, "Adaptive remeshing in large plastic strain with damage," International Journal for Numerical Methods in Engineering, vol. 63, pp. 1-36, 2005.

[89] D. Umbrello, S. Rizzuti, J. C. Outeiro, R. Shivpuri, and R. M'Saoubi, "Hardness-based flow stress for numerical simulation of hard machining AISI H13 tool steel," Journal of Materials Processing Technology, vol. 199, pp. 64-73, 2008.

[90] D. Umbrello, J. Hua, and R. Shivpuri, "Hardness-based flow stress and fracture models for numerical simulation of hard machining AISI 52100 bearing steel," Materials Science and Engineering: A, vol. 374, pp. 90-100, 2004.

[91] E. Uhlmann, R. Gerstenberger, and J. Kuhnert, "Cutting Simulation with the Meshfree Finite Pointset Method," Procedia CIRP, vol. 8, pp. 391-396, 2013.

[92] P. Eberhard and T. Gaugele, "Simulation of cutting processes using mesh-free Lagrangian particle methods," Computational Mechanics, pp. 1-18, 2012.

[93] D. J. Benson, "A mixture theory for contact in multi-material Eulerian formulations," Computer Methods in Applied Mechanics and Engineering, vol. 140, pp. 59-86, 1997.

[94] E. Vitali and D. J. Benson, "Contact with friction in multi-material arbitrary Lagrangian Eulerian formulations using X-FEM," Int. J. Numer. Meth. Eng vol. 76, pp. 893–921, 2008.

[95] F. H. Harlow, M. A. Ellison, and J. H. Reid, "The particle-in-cell computing method in fluid dynamics," Methods Comput. Phys, vol. 3, pp. 319–343, 1964.

[96] Z. Więckowski, "The material point method in large strain engineering problems," Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4417-4438, 2004.

[97] S. R. Idelsohn, E. Oñate, and F. D. Pin, "The particle finite element method: a powerful tool to solve incompressible flows with freesurfaces and breaking waves," International Journal for Numerical Methods in Engineering, vol. 61, pp. 964-989, 2004.

[98] E. Oñate, S. R. Idelsohn, M. A. Celigueta, and R. Rossi, "Advances in the particle finite element method for the analysis of fluid–multibody interaction and bed erosion in free surface flows," Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 1777-1800, 2008.

[99] E. Oñate, M. A. Celigueta, and S. R. Idelsohn, "Modeling bed erosion in free surface flows by the particle finite element method," ACTA GEOTECHNICA, vol. 1 pp. 237-252, 2006.

[100] J. Oliver, J. C. Cante, R. Weyler, C. González, and J. Hernandez, "Particle Finite Element Methods in Solid Mechanics Problems," Computational Methods in Applied Sciences, vol. 7, pp. 87-103, 2007.

[101] N. Calvo, S. R. Idelsohn, and E. Oñate, "The extended Delaunay tessellation," Engineering Computations: Int J for Computer-Aided Engineering, vol. 20, pp. 583-600, 2003.

[102] J. C. Simo and C. Miehe, "Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation," Computer Methods in Applied Mechanics and Engineering, vol. 98 pp. 41–104, 1992.

[103] J. Bonet and R. D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis: Cambridge University Press, 1997.

[104] J. C. Simo, "A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: part I. continuum formulation," Computer Methods in Applied Mechanics and Engineering archive, vol. 666, pp. 199-219, 1988.

[105] J. C. Simo, "A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part II: Computational aspects," Computer Methods in Applied Mechanics and Engineering, vol. 68, pp. 1-31, 1988.

[106] E. Voce, "A practical strain hardening function.," Metallurgia, 1955.

[107] J. C. Simo and T. J. R. Hughes., Computational Inelasticity. New York: Springer-Verlag, 1998.

[108] G. H. Johnson and W. H. Cook, "A constitutive model and data for metals subjected to large strains high strain rates and high temperatures," Proceedings of the 7th symposium on ballistics, 1983.

[109] M. Bäker, "Finite element simulation of high-speed cutting forces " Journal of Materials Processing Technology, vol. 176, pp. 117–126, 2006.

[110] T. Belytschko, W. K. Liu, and B. Moran, Nonlinear Finite Element for Continua and Structures.: Wiley, 2000.

[111] M. Čanađija and J. Brnić, "Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters," International Journal of Plasticity, vol. 20, pp. 1851-1874, 2004.

[112] J. Lubliner, Plasticity Theory: Dover Publications, 2008.

[113] W. D. Callister and D. G. Rethwisch, Materials Science and Engineering: An Introduction: Wiley, 2010.

[114] F. Armero and J. C. Simo, "A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems," International Journal for Numerical Methods in Engineering, vol. 35, pp. 737-766, 1992.

[115] J. Oliver, A. E. Huespe, and J. C. Cante, "An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems," Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 1865-1889, 2008.

[116] O. C. Zienkiewicz and J. Z. Zhu, "The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique," International Journal for Numerical Methods in Engineering, vol. 33, pp. 1331-1364, 1992.

[117] J. M. Carbonell, "Modeling of Ground Excavation with the Particle Finite Element Method," 2010.

[118] P. O. De Micheli and K. Mocellin, "A new efficient explicit formulation for linear tetrahedral elements non-sensitive to volumetric locking for infinitesimal elasticity and inelasticity," International Journal for Numerical Methods in Engineering, vol. 79, pp. 45-68, 2009.

[119] A. Ibrahimbegovic and L. Chorfi, "Covariant principal axis formulation of associated coupled thermoplasticity at finite strains and its numerical implementation," International Journal of Solids and Structures, vol. 39, pp. 499-528, 2002.

[120] Y. Tadi Beni and M. R. Movahhedy, "Consistent arbitrary Lagrangian Eulerian formulation for large deformation thermo-mechanical analysis," Materials & Design, vol. 31, pp. 3690-3702, 2010.

[121] P. J. Arrazola, "Modelisation numerique de la coupe: etude de sensibilite des parametres d’entree et identification du frottement entre outilcopeau," Doctoral Thesis, L'École Centrale de Nantes, l'Université de Nantes, France, 2003.

[122] P. M. Dixit and U. S. Dixit, Modeling of Metal Forming and Machining Processes: by Finite Element and Soft Computing Methods, 2008.

Back to Top

Document information

Published on 01/01/2015

Licence: CC BY-NC-SA license

Document Score

0

Views 143
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?