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The hot optimal transportation meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions. (English) Zbl 1442.74252
Summary: We present a monolithic incremental Lagrangian framework based on meshfree methods, the Hot Optimal Transportation Meshfree (HOTM) method, for a robust and efficient solution of the dynamic response of materials under extreme thermomechanical conditions, possibly involving extremely large deformation, phase transition and multiphase mixing. The HOTM method combines the Optimal Transportation Meshfree (OTM) method and the variational thermomechanical constitutive updates. The variational structure of a dynamic system with general internal dissipative mechanisms is discretized in time by applying the Optimal Transportation theory, while material points and nodes are introduced for the spatial discretization. A phase-aware constitutive model is developed to describe the history-dependent material behavior in various phases due to melting, vaporization and solidification. The fully discretized conservation equations of linear momentum and energy are solved simultaneously using an operator splitting algorithm to predict the deformation, temperature and internal variables of the computational domain. The convergence property of the meshfree solution of the energy conservation equation is studied in a three-dimensional transient heat conduction problem by comparing to the analytical solutions. Accuracy of the HOTM method is also assessed in the example of upsetting a metallic billet up to a compression ratio of 95% under various external heating and cooling strategies. The scope and robustness of the HOTM method are demonstrated in the application of the laser cladding technology.
MSC:
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74F05 Thermal effects in solid mechanics
80M22 Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer
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[1] Lindgren, L.-E., Numerical modelling of welding, Comput. Methods Appl. Mech. Engrg., 195, 48-49, 6710-6736 (2006) · Zbl 1120.74822
[2] Joy Varghese, V. M.; Suresh, M. R.; Siva Kumar, D., Recent developments in modeling of heat transfer during tig welding—a review, Int. J. Adv. Manuf. Technol., 64, 5-8, 749-754 (2013)
[3] Huespe, AE; Cardona, ALBERTO; Fachinotti, VICTOR, Thermomechanical model of a continuous casting process, Comput. Methods Appl. Mech. Engrg., 182, 3-4, 439-455 (2000) · Zbl 1121.74352
[4] Li, Chunsheng; Thomas, Brian G., Thermomechanical finite-element model of shell behavior in continuous casting of steel, Metall. Mater. Trans. B, 35, 6, 1151-1172 (2004)
[5] Wong, Kaufui V.; Hernandez, Aldo, A review of additive manufacturing, ISRN Mech. Eng., 2012 (2012)
[6] Frazier, William E., Metal additive manufacturing: a review, J. Mater. Eng. Perform., 23, 6, 1917-1928 (2014)
[7] Schoinochoritis, Babis; Chantzis, Dimitrios; Salonitis, Konstantinos, Simulation of metallic powder bed additive manufacturing processes with the finite element method: A critical review, Proc. Inst. Mech. Eng. B, 231, 1, 96-117 (2017)
[8] Simo, J. C.; Miehe, Ch., Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Engrg., 98, 1, 41-104 (1992) · Zbl 0764.73088
[9] Zavarise, G.; Wriggers, P.; Stein, E.; Schrefler, B. A., Real contact mechanisms and finite element formulation—a coupled thermomechanical approach, Internat. J. Numer. Methods Engrg., 35, 4, 767-785 (1992) · Zbl 0775.73305
[10] Galantucci, L. M.; Tricarico, L., Thermo-mechanical simulation of a rolling process with an fem approach, J. Mater Process. Technol., 92, 494-501 (1999)
[11] Chen, C. M.; Kovacevic, R., Finite element modeling of friction stir welding—thermal and thermomechanical analysis, Int. J. Mach. Tools Manuf., 43, 13, 1319-1326 (2003)
[12] Peultier, B.; Ben Zineb, T.; Patoor, E., Macroscopic constitutive law of shape memory alloy thermomechanical behaviour. application to structure computation by fem, Mech. Mater., 38, 5-6, 510-524 (2006)
[13] Miller, Scott F.; Shih, Albert J., Thermo-mechanical finite element modeling of the friction drilling process, J. Manuf. Sci. Eng., 129, 3, 531-538 (2007)
[14] Donea, Jean; Fasoli-Stella, P.; Giuliani, S., Lagrangian and Eulerian Finite Element Techniques for Transient Fluid-Structure Interaction Problems (1977), IASMiRT
[15] Donea, Jean; Giuliani, S.; Halleux, Jean-Pierre, An arbitrary lagrangian-eulerian finite element method for transient dynamic fluid-structure interactions, Comput. Methods Appl. Mech. Engrg., 33, 1-3, 689-723 (1982) · Zbl 0508.73063
[16] Olovsson, Lars; Nilsson, Larsgunnar; Simonsson, Kjell, An ale formulation for the solution of two-dimensional metal cutting problems, Comput. Struct., 72, 4-5, 497-507 (1999) · Zbl 1050.74676
[17] Gadala, M. S., Recent trends in ale formulation and its applications in solid mechanics, Comput. Methods Appl. Mech. Engrg., 193, 39-41, 4247-4275 (2004) · Zbl 1068.74075
[18] Liu, G. R.; Liu, M. B.; Li, Shaofan, Smoothed particle hydrodynamics—a meshfree method, Comput. Mech., 33, 6, 491 (2004)
[19] Limido, Jérôme; Espinosa, Christine; Salaün, Michel; Lacome, Jean-Luc, Sph method applied to high speed cutting modelling, Int. J. Mech. Sci., 49, 7, 898-908 (2007)
[20] Das, R.; Cleary, P. W., Novel application of the mesh-free sph method for modelling thermo-mechanical responses in arc welding, Int. J. Mech. Mater. Des., 11, 3, 337-355 (2015)
[21] Onate, E.; Rojek, J., Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems, Comput. Methods Appl. Mech. Engrg., 193, 27-29, 3087-3128 (2004) · Zbl 1079.74646
[22] Eberhard, Peter; Gaugele, Timo, Simulation of cutting processes using mesh-free lagrangian particle methods, Comput. Mech., 51, 3, 261-278 (2013) · Zbl 1398.74461
[23] Uhlmann, Eckart; Gerstenberger, Robert; Kuhnert, Jörg, Cutting simulation with the meshfree finite pointset method, Procedia CIRP, 8, 391-396 (2013)
[24] Reséndiz-Flores, Edgar O.; Saucedo-Zendejo, Félix R., Two-dimensional numerical simulation of heat transfer with moving heat source in welding using the finite pointset method, Int. J. Heat Mass Transfer, 90, 239-245 (2015)
[25] Lu, Y. Y.; Belytschko, T.; Gu, Lu, A new implementation of the element free galerkin method, Comput. Methods Appl. Mech. Engrg., 113, 3-4, 397-414 (1994) · Zbl 0847.73064
[26] Wang, H. S., A meshfree variational multiscale methods for thermo-mechanical material failure, Theor. Appl. Fract. Mech., 75, 1-7 (2015)
[27] Liu, Wing Kam; Jun, Sukky; Li, Shaofan; Adee, Jonathan; Belytschko, Ted, Reproducing kernel particle methods for structural dynamics, Internat. J. Numer. Methods Engrg., 38, 10, 1655-1679 (1995) · Zbl 0840.73078
[28] Chen, J. K.; Beraun, J. E.; Carney, T. C., A corrective smoothed particle method for boundary value problems in heat conduction, Internat. J. Numer. Methods Engrg., 46, 2, 231-252 (1999) · Zbl 0941.65104
[29] Li, Chen; He-Ping, Ma; Yu-Min, Cheng, Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems, Chin. Phys. B, 22, 5, 050202 (2013)
[30] Cueto, Elias; Chinesta, Francisco, Meshless methods for the simulation of material forming, Int. J. Mater. Form., 8, 1, 25-43 (2015)
[31] Hosseini, Seyed Mahmoud; Sladek, Jan; Sladek, Vladimir, Meshless local petrov-galerkin method for coupled thermoelasticity analysis of a functionally graded thick hollow cylinder, Eng. Anal. Bound. Elem., 35, 6, 827-835 (2011) · Zbl 1259.74084
[32] Dai, Baodong; Zheng, Baojing; Liang, Qingxiang; Wang, Linghui, Numerical solution of transient heat conduction problems using improved meshless local petrov-galerkin method, Appl. Math. Comput., 219, 19, 10044-10052 (2013) · Zbl 1307.80008
[33] Rodriguez, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J., The particle finite element method (pfem) in thermo-mechanical problems, Internat. J. Numer. Methods Engrg., 107, 9, 733-785 (2016) · Zbl 1352.74426
[34] Sulsky, Deborah; Chen, Zhen; Schreyer, Howard L., A particle method for history-dependent materials, Comput. Methods Appl. Mech. Engrg., 118, 1-2, 179-196 (1994) · Zbl 0851.73078
[35] Love, E.; Sulsky, Deborah L., An unconditionally stable, energy-momentum consistent implementation of the material-point method, Comput. Methods Appl. Mech. Engrg., 195, 33-36, 3903-3925 (2006) · Zbl 1118.74054
[36] Zhang, Duan Z.; Zou, Qisu; Brian VanderHeyden, W.; Ma, Xia, Material point method applied to multiphase flows, J. Comput. Phys., 227, 6, 3159-3173 (2008) · Zbl 1329.76288
[37] Chen, Jiun-Shyan; Hillman, Michael; Chi, Sheng-Wei, Meshfree methods: progress made after 20 years, J. Eng. Mech., 143, 4, 04017001 (2017)
[38] Li, B.; Habbal, F.; Ortiz, M., Optimal transportation meshfree approximation schemes for fluid and plastic flows, Internat. J. Numer. Methods Engrg., 83, 12, 1541-1579 (2010) · Zbl 1202.74200
[39] Li, B.; Kidane, A.; Ravichandran, G.; Ortiz, M., Verification and validation of the optimal transportation meshfree (otm) simulation of terminal ballistics, Int. J. Impact Eng., 42, 25-36 (2012)
[40] Kidane, A.; Lashgari, A.; Li, B.; McKerns, M.; Ortiz, M.; Owhadi, H.; Ravichandran, G.; Stalzer, M.; Sullivan, TJ, Rigorous model-based uncertainty quantification with application to terminal ballistics, part i: Systems with controllable inputs and small scatter, J. Mech. Phys. Solids, 60, 5, 983-1001 (2012)
[41] Adams, M.; Lashgari, A.; Li, B.; McKerns, M.; Mihaly, J.; Ortiz, M.; Owhadi, H.; Rosakis, AJ; Stalzer, M.; Sullivan, TJ, Rigorous model-based uncertainty quantification with application to terminal ballistics-part ii. Systems with uncontrollable inputs and large scatter, J. Mech. Phys. Solids, 60, 5, 1002-1019 (2012)
[42] Kamga, P-HT; Li, B.; McKerns, M.; Nguyen, LH; Ortiz, M.; Owhadi, H.; Sullivan, TJ, Optimal uncertainty quantification with model uncertainty and legacy data, J. Mech. Phys. Solids, 72, 1-19 (2014)
[43] Ganeriwala, Rishi; Zohdi, Tarek I., A coupled discrete element-finite difference model of selective laser sintering, Granul. Matter, 18, 2, 21 (2016)
[44] Russell, M. A.; Souto-Iglesias, A., Numerical simulation of laser fusion additive manufacturing processes using the sph method, Comput. Methods Appl. Mech. Engrg., 341, 163-187 (2018)
[45] Fürstenau, Jan-Philipp; Wessels, Henning; Weißenfels, Christian; Wriggers, Peter, Generating virtual process maps of slm using powder-scale sph simulations, Comput. Part. Mech., 1-23 (2019)
[46] Wessels, H.; Weißenfels, C.; Wriggers, P., Metal particle fusion analysis for additive manufacturing using the stabilized optimal transportation meshfree method, Comput. Methods Appl. Mech. Engrg., 339, 91-114 (2018)
[47] Wessels, H.; Bode, T.; Weißenfels, C.; Wriggers, P.; Zohdi, T. I., Investigation of heat source modeling for selective laser melting, Comput. Mech., 63, 5, 949-970 (2019) · Zbl 07053703
[48] Benamou, Jean-David; Brenier, Yann, A computational fluid mechanics solution to the monge-kantorovich mass transfer problem, Numer. Math., 84, 3, 375-393 (2000) · Zbl 0968.76069
[49] Arroyo, Marino; Ortiz, Michael, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, Internat. J. Numer. Methods Engrg., 65, 13, 2167-2202 (2006) · Zbl 1146.74048
[50] Foca, Mathieu, On a Local Maximum Entropy Interpolation Approach for Simulation of Coupled Thermo-Mechanical Problems. Application to the Rotary Frictional Welding Process (2015), Ecole Centrale de Nantes (ECN), (PhD thesis)
[51] Weißenfels, C.; Wriggers, P., Stabilization algorithm for the optimal transportation meshfree approximation scheme, Comput. Methods Appl. Mech. Engrg., 329, 421-443 (2018)
[52] Fan, Jiang; Liao, Huming; Ke, Renjie; Kucukal, Erdem; Gurkan, Umut A.; Shen, Xiuli; Lu, Jian; Li, Bo, A monolithic lagrangian meshfree scheme for fluid-structure interaction problems within the otm framework, Comput. Methods Appl. Mech. Engrg., 337, 198-219 (2018)
[53] Yang, Qiang; Stainier, Laurent; Ortiz, Michael, A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids, J. Mech. Phys. Solids, 54, 2, 401-424 (2006) · Zbl 1120.74367
[54] Stainier, Laurent; Ortiz, Michael, Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity, Int. J. Solids Struct., 47, 5, 705-715 (2010) · Zbl 1183.74037
[55] Stainier, Laurent, Consistent incremental approximation of dissipation pseudo-potentials in the variational formulation of thermo-mechanical constitutive updates, Mech. Res. Commun., 38, 4, 315-319 (2011) · Zbl 1272.74142
[56] Stainier, Laurent, A variational approach to modeling coupled thermo-mechanical nonlinear dissipative behaviors, (Advances in Applied Mechanics, Vol. 46 (2013), Elsevier), 69-126
[57] Fan, Zongyue; Li, Bo, Meshfree simulations for additive manufacturing process of metals, Integr. Mater. Manuf. Innov., 8, 2, 144-153 (2019)
[58] Halphen, Bernard; Nguyen, Quoc Son, Sur les matériaux standard généralisés, J. Méc., 14, 39-63 (1975) · Zbl 0308.73017
[59] Ziegler, H., An Introduction to Thermomechanics (1977), North-Holland · Zbl 0358.73001
[60] Lee, Erastus H., Elastic-plastic deformation at finite strains, J. Appl. Mech., 36, 1, 1-6 (1969) · Zbl 0179.55603
[61] Hencky, Heinrich, Uber die form des elastizitatsgesetzes bei ideal elastischen stoffen, Z. Tech. Phys., 9, 215-220 (1928) · JFM 54.0851.03
[62] Lubarda, Vlado A., Elastoplasticity Theory (2001), CRC press · Zbl 1014.74001
[63] Lyon, S. P.; Johnson, J. D., The Los Alamos National Laboratory EOS Database Report NoTechnical report, LA-UR-92-3407 (1992)
[64] Bonacina, Comini; Comini, G.; Fasano, A., Numerical solution of phase-change problems, Int. J. Heat Mass Transfer, 16, 10, 1825-1832 (1973)
[65] Biot, Maurice Antony, Linear thermodynamics and the mechanics of solids, (Proceedings of the Third US National Congress of Applied Mechanics, American Society of Mechanical Engineers (1958), Citeseer)
[66] Har, Jason; Tamma, Kumar, Advances in Computational Dynamics of Particles, Materials and Structures (2012), John Wiley & Sons · Zbl 1248.74001
[67] McCann, Robert J., A convexity principle for interacting gases, Adv. Math., 128, 1, 153-179 (1997) · Zbl 0901.49012
[68] Fan, Jiang; Liao, Huming; Wang, Hao; Hu, Junheng; Chen, Zhiying; Lu, Jian; Li, Bo, Local maximum-entropy based surrogate model and its application to structural reliability analysis, Struct. Multidiscip. Optim., 57, 1, 373-392 (2018)
[69] Amar, Adam; Calvert, Nathan; Kirk, Benjamin, Development and verification of the charring ablating thermal protection implicit system solver, (49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (2011)), 144
[70] Bejan, Adrian; Kraus, Allan D., Heat Transfer Handbook, Vol. 1 (2003), John Wiley & Sons
[71] Arpaci, Vedat S., Conduction Heat Transfer (1966), Addison-Wesley · Zbl 0144.46703
[72] Mazumder, J., 1 - laser-aided direct metal deposition of metals and alloys, (Brandt, Milan, Laser Additive Manufacturing. Laser Additive Manufacturing, Woodhead Publishing Series in Electronic and Optical Materials (2017), Woodhead Publishing), 21-53
[73] Devesse, Wim; De Baere, Dieter; Guillaume, Patrick, Modeling of laser beam and powder flow interaction in laser cladding using ray-tracing, J. Laser Appl., 27, S2, S29208 (2015)
[74] Brackbill, Jeremiah U.; Kothe, Douglas B.; Zemach, Charles, A continuum method for modeling surface tension, J. Comput. Phys., 100, 2, 335-354 (1992) · Zbl 0775.76110
[75] Dong, Chen-shi; Wang, Guo-zhao, Curvatures estimation on triangular mesh, J. Zhejiang Univ.-Sci. A, 6, 1, 128-136 (2005) · Zbl 1086.65009
[76] Schopphoven, T.; Gasser, A.; Wissenbach, K.; Poprawe, R., Investigations on ultra-high-speed laser material deposition as alternative for hard chrome plating and thermal spraying, J. Laser Appl., 28, 2, 022501 (2016)
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