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2019 | OriginalPaper | Chapter

45. Smoothed Particle Hydrodynamics for Ductile Solid Continua

Authors : Peter Eberhard, Fabian Spreng

Published in: Handbook of Mechanics of Materials

Publisher: Springer Singapore

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Abstract

In this chapter, a numerical simulation model for ductile solid continua is presented. It is based on the Smoothed Particle Hydrodynamics (SPH) method, which serves to spatially discretize and, thus, solve the governing equations of continuum mechanics. Due to the meshless, Lagrangian character of the SPH spatial discretization technique, the introduced model is naturally well-suited for the simulation of continua featuring large deformations, major changes in topology, material failure including structure disintegration, and/or a large number of contacts with the environment occurring at the same time. For this reason, it has the potential to become a beneficial complement to the well-established numerical solid models, which mainly make use of mesh-based methods. To that end, however, the original SPH discretization scheme is to be variously extended and modified as discussed in detail in the course of this chapter. Besides, also its efficient implementation, i.e. the efficient numerical solution of the SPH-discretized governing equations of continuum mechanics, is addressed. The quality of the developed SPH formulation for ductile solids including its versatility and accuracy is demonstrated on the basis of two exemplary applications, namely, the industrial processes of friction stir welding and orthogonal metal cutting. It is shown as part of this contribution that, in either case, the proposed SPH model for ductile solid continua is capable of reproducing both the mechanical and the thermal macroscopic behavior of the real processed material in the simulation.

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Literature
1.
go back to reference Gurtin ME. An introduction to continuum mechanics. San Diego: Academic Press; 1981.MATH Gurtin ME. An introduction to continuum mechanics. San Diego: Academic Press; 1981.MATH
2.
go back to reference Gingold RA, Monaghan JJ. Smoothed Particle Hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc. 1977;181(3):375–89.MATHCrossRef Gingold RA, Monaghan JJ. Smoothed Particle Hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc. 1977;181(3):375–89.MATHCrossRef
3.
go back to reference Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J. 1977;82(12):1013–24.CrossRef Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J. 1977;82(12):1013–24.CrossRef
5.
go back to reference Liu MB, Liu GR. Smoothed Particle Hydrodynamics (SPH): an overview and recent developments. Arch Comput Method E. 2010;17(1):25–76.MathSciNetMATHCrossRef Liu MB, Liu GR. Smoothed Particle Hydrodynamics (SPH): an overview and recent developments. Arch Comput Method E. 2010;17(1):25–76.MathSciNetMATHCrossRef
7.
go back to reference Violeau D. Fluid mechanics and the SPH method: theory and applications. Oxford: Oxford University Press; 2012.MATHCrossRef Violeau D. Fluid mechanics and the SPH method: theory and applications. Oxford: Oxford University Press; 2012.MATHCrossRef
8.
go back to reference Dehnen W, Aly H. Improving convergence in Smoothed Particle Hydrodynamics simulations without pairing instability. Mon Not R Astron Soc. 2012;425(2):1068–82.CrossRef Dehnen W, Aly H. Improving convergence in Smoothed Particle Hydrodynamics simulations without pairing instability. Mon Not R Astron Soc. 2012;425(2):1068–82.CrossRef
9.
go back to reference Wendland H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math. 1995;4(1):389–96.MathSciNetMATHCrossRef Wendland H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math. 1995;4(1):389–96.MathSciNetMATHCrossRef
10.
go back to reference Amicarelli A, Marongiu JC, Leboeuf F, Leduc J, Neuhauser M, Fang L, Caro J. SPH truncation error in estimating a 3D derivative. Int J Numer Meth Eng. 2011;87(7):677–700.MathSciNetMATHCrossRef Amicarelli A, Marongiu JC, Leboeuf F, Leduc J, Neuhauser M, Fang L, Caro J. SPH truncation error in estimating a 3D derivative. Int J Numer Meth Eng. 2011;87(7):677–700.MathSciNetMATHCrossRef
11.
go back to reference Belytschko T, Krongauz Y, Dolbow J, Gerlach C. On the completeness of meshfree particle methods. Int J Numer Meth Eng. 1998;43(5):785–819.MathSciNetMATHCrossRef Belytschko T, Krongauz Y, Dolbow J, Gerlach C. On the completeness of meshfree particle methods. Int J Numer Meth Eng. 1998;43(5):785–819.MathSciNetMATHCrossRef
12.
13.
go back to reference Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 2000.CrossRef Batchelor GK. An introduction to fluid dynamics. Cambridge: Cambridge University Press; 2000.CrossRef
14.
15.
go back to reference Acheson DJ. Elementary fluid dynamics. Oxford: Clarendon; 1990.MATH Acheson DJ. Elementary fluid dynamics. Oxford: Clarendon; 1990.MATH
16.
go back to reference Dill EH. Continuum mechanics: elasticity, plasticity, viscoelasticity. Boca Raton: CRC; 2006. Dill EH. Continuum mechanics: elasticity, plasticity, viscoelasticity. Boca Raton: CRC; 2006.
17.
go back to reference Sod GA. Survey of several Finite Difference methods for systems of nonlinear hyperbolic conservation laws. J Comput Phys. 1978;27(1):1–31.MathSciNetMATHCrossRef Sod GA. Survey of several Finite Difference methods for systems of nonlinear hyperbolic conservation laws. J Comput Phys. 1978;27(1):1–31.MathSciNetMATHCrossRef
18.
go back to reference Monaghan JJ, Gingold RA. Shock simulation by the particle method SPH. J Comput Phys. 1983;52(2):374–89.MATHCrossRef Monaghan JJ, Gingold RA. Shock simulation by the particle method SPH. J Comput Phys. 1983;52(2):374–89.MATHCrossRef
19.
go back to reference Monaghan JJ. Smoothed Particle Hydrodynamics. Annu Rev Astron Astr. 1992;30:543–74.CrossRef Monaghan JJ. Smoothed Particle Hydrodynamics. Annu Rev Astron Astr. 1992;30:543–74.CrossRef
20.
go back to reference Glatzmaier GA. Introduction to modeling convection in planets and stars: magnetic field, density stratification, rotation. Princeton: Princeton University Press; 2014.MATH Glatzmaier GA. Introduction to modeling convection in planets and stars: magnetic field, density stratification, rotation. Princeton: Princeton University Press; 2014.MATH
23.
24.
go back to reference Burshtein AI. Introduction to thermodynamics and kinetic theory of matter. 2nd ed. Berlin: Wiley; 2005.CrossRef Burshtein AI. Introduction to thermodynamics and kinetic theory of matter. 2nd ed. Berlin: Wiley; 2005.CrossRef
25.
go back to reference Doghri I. Mechanics of deformable solids: linear, nonlinear, analytical and computational aspects. Berlin: Springer; 2000.MATHCrossRef Doghri I. Mechanics of deformable solids: linear, nonlinear, analytical and computational aspects. Berlin: Springer; 2000.MATHCrossRef
26.
go back to reference Simo JC, Hughes TJR. Computational inelasticity. 2nd ed. New York: Springer; 1998.MATH Simo JC, Hughes TJR. Computational inelasticity. 2nd ed. New York: Springer; 1998.MATH
28.
go back to reference Paterson MS, Wong TF. Experimental rock deformation – the brittle field. 2nd ed. Berlin: Springer; 2005. Paterson MS, Wong TF. Experimental rock deformation – the brittle field. 2nd ed. Berlin: Springer; 2005.
29.
go back to reference Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: American Defense Preparedness Association, Royal Netherlands Society of Engineers. Proceedings of the 7th international symposium on ballistics, The Hague; 19–21 Apr 1983. pp. 541–7. Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: American Defense Preparedness Association, Royal Netherlands Society of Engineers. Proceedings of the 7th international symposium on ballistics, The Hague; 19–21 Apr 1983. pp. 541–7.
30.
go back to reference Spreng F. Smoothed Particle Hydrodynamics for ductile solids [dissertation]. Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 48. Aachen: Shaker Verlag; 2017. Spreng F. Smoothed Particle Hydrodynamics for ductile solids [dissertation]. Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 48. Aachen: Shaker Verlag; 2017.
31.
go back to reference Farren WS, Taylor GI. The heat developed during plastic extension of metals. P Roy Soc Lond A Mat. 1925;107(743):422–51.CrossRef Farren WS, Taylor GI. The heat developed during plastic extension of metals. P Roy Soc Lond A Mat. 1925;107(743):422–51.CrossRef
32.
go back to reference Johnson GR, Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech. 1985;21(1):31–48.CrossRef Johnson GR, Cook WH. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech. 1985;21(1):31–48.CrossRef
33.
go back to reference Grady DE, Kipp ME. Continuum modelling of explosive fracture in oil shale. Int J Rock Mech Min. 1980;17(3):147–57.CrossRef Grady DE, Kipp ME. Continuum modelling of explosive fracture in oil shale. Int J Rock Mech Min. 1980;17(3):147–57.CrossRef
35.
go back to reference Gray JP, Monaghan JJ, Swift RP. SPH elastic dynamics. Comput Method Appl Mech. 2001;190(49–50):6641–62.MATHCrossRef Gray JP, Monaghan JJ, Swift RP. SPH elastic dynamics. Comput Method Appl Mech. 2001;190(49–50):6641–62.MATHCrossRef
36.
go back to reference Müller A. Dynamic refinement and coarsening for the Smoothed Particle Hydrodynamics method [dissertation]. Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 46. Aachen: Shaker Verlag; 2017. Müller A. Dynamic refinement and coarsening for the Smoothed Particle Hydrodynamics method [dissertation]. Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 46. Aachen: Shaker Verlag; 2017.
37.
go back to reference Randles PW, Libersky LD. Smoothed Particle Hydrodynamics: some recent improvements and applications. Comput Method Appl Mech. 1996;139(1–4):375–408.MathSciNetMATHCrossRef Randles PW, Libersky LD. Smoothed Particle Hydrodynamics: some recent improvements and applications. Comput Method Appl Mech. 1996;139(1–4):375–408.MathSciNetMATHCrossRef
38.
go back to reference Shapiro PR, Martel H, Villumsen JV, Owen JM. Adaptive Smoothed Particle Hydrodynamics, with application to cosmology: methodology. Astrophys J Suppl Ser. 1996;103(2):269–330.CrossRef Shapiro PR, Martel H, Villumsen JV, Owen JM. Adaptive Smoothed Particle Hydrodynamics, with application to cosmology: methodology. Astrophys J Suppl Ser. 1996;103(2):269–330.CrossRef
39.
go back to reference Owen JM, Villumsen JV, Shapiro PR, Martel H. Adaptive Smoothed Particle Hydrodynamics: methodology. II. Astrophys J Suppl Ser. 1998;116(2):155–209.CrossRef Owen JM, Villumsen JV, Shapiro PR, Martel H. Adaptive Smoothed Particle Hydrodynamics: methodology. II. Astrophys J Suppl Ser. 1998;116(2):155–209.CrossRef
40.
go back to reference Thacker RJ, Tittley ER, Pearce FR, Couchman HMP, Thomas PA. Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations. Mon Not R Astron Soc. 2000;319(2):619–48.CrossRef Thacker RJ, Tittley ER, Pearce FR, Couchman HMP, Thomas PA. Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations. Mon Not R Astron Soc. 2000;319(2):619–48.CrossRef
41.
go back to reference Springel V, Hernquist L. Cosmological Smoothed Particle Hydrodynamics simulations: the entropy equation. Mon Not R Astron Soc. 2002;333(3):649–64.CrossRef Springel V, Hernquist L. Cosmological Smoothed Particle Hydrodynamics simulations: the entropy equation. Mon Not R Astron Soc. 2002;333(3):649–64.CrossRef
42.
go back to reference Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: Clarendon Press; 1989.MATH Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: Clarendon Press; 1989.MATH
43.
go back to reference Schinner A. Fast algorithms for the simulation of polygonal particles. Granul Matter. 1999;2(1):35–43.CrossRef Schinner A. Fast algorithms for the simulation of polygonal particles. Granul Matter. 1999;2(1):35–43.CrossRef
44.
go back to reference Müller M, Schirm S, Teschner M, Heidelberger B, Gross M. Interaction of fluids with deformable solids. Comput Anim Virtual Worlds. 2004;15(3–4):159–71.CrossRef Müller M, Schirm S, Teschner M, Heidelberger B, Gross M. Interaction of fluids with deformable solids. Comput Anim Virtual Worlds. 2004;15(3–4):159–71.CrossRef
45.
go back to reference Monaghan JJ, Kos A, Issa N. Fluid motion generated by impact. J Waterw Port C-ASCE. 2003;129(6):250–9.CrossRef Monaghan JJ, Kos A, Issa N. Fluid motion generated by impact. J Waterw Port C-ASCE. 2003;129(6):250–9.CrossRef
46.
go back to reference Hut P, Makino J, McMillan S. Building a better leapfrog. Astrophys J. 1995;443(2):L93–6.CrossRef Hut P, Makino J, McMillan S. Building a better leapfrog. Astrophys J. 1995;443(2):L93–6.CrossRef
47.
go back to reference Mishra RS, Ma ZY. Friction stir welding and processing. Mat Sci Eng R. 2005;50(1–2):1–78.CrossRef Mishra RS, Ma ZY. Friction stir welding and processing. Mat Sci Eng R. 2005;50(1–2):1–78.CrossRef
48.
go back to reference Tang W, Guo X, McClure JC, Murr LE, Nunes A. Heat input and temperature distribution in friction stir welding. J Mater Process Manu. 1998;7(2):163–72.CrossRef Tang W, Guo X, McClure JC, Murr LE, Nunes A. Heat input and temperature distribution in friction stir welding. J Mater Process Manu. 1998;7(2):163–72.CrossRef
49.
go back to reference Armarego EJA, Brown RH. The machining of metals. Englewood Cliffs: Prentice-Hall; 1969. Armarego EJA, Brown RH. The machining of metals. Englewood Cliffs: Prentice-Hall; 1969.
50.
go back to reference Boothroyd G, Knight WA. Fundamentals of machining and machine tools. 3rd ed. Boca Raton: CRC; 2006. Boothroyd G, Knight WA. Fundamentals of machining and machine tools. 3rd ed. Boca Raton: CRC; 2006.
Metadata
Title
Smoothed Particle Hydrodynamics for Ductile Solid Continua
Authors
Peter Eberhard
Fabian Spreng
Copyright Year
2019
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-6884-3_28

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