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Peridynamic modeling and simulation of coupled thermomechanical removal of ice from frozen structures

  • Computational Models for ’Complex’ Materials and Structures, beyond the Finite Elements
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Abstract

In this work, a bond-based peridynamic de-icing model has been developed to simulate the thermo-mechanical ice removal process of frozen structures. In the proposed numerical method, the influence of the deformation on the thermal states is considered. In this work, the ice is treated as an elastic brittle material in the framework of bond-based peridynamics, which can capture ice cracking during temperature increase and other temperature-dependent features of ice. Moreover, the characteristics of thermal load induced crack patterns in an ice sheet are discussed. The developed simulation method is verified and validated in a de-icing system of an aluminum sheet covered with ice, which is done by comparing the results obtained from peridynamic simulation with that obtained from finite element method (FEM) simulation. The results show good consistency between the peridynamic simulation and the FEM simulation. On the other hand, we find that the peridynamic simulations can directly capture the ice crack initiation and the crack propagation during the entire ice removal process, which is difficult to obtain from the FEM simulations.

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Abbreviations

\(\varvec{\xi }_{A B}\) :

The bond vector in reference configuration, see Eq. (1)

\(\varvec{\eta }_{AB}\) :

The relative displacement vector in current configuration, see Eq. (2)

\({{H}_{{{x}_{A}}}}\) :

The horizon of particle \({{\mathbf{x}}}_{A}\)

\({\mathbf{f}}({\xi },{\eta },t)\) :

The body force density function, see Eq. (4)

s :

The bond stretch, see Eq. (5)

c :

The micro-modulus, see Eq. (9)

\(\kappa \) :

Bulk modulus of the material

\(G_0\) :

The energy release rate, see Eq. (11)

\({\mathbf{h}}\) :

The heat flow density, see Eq. (14)

\(f_{h}\) :

The heat flow density function, see Eq. (15)

\(c_{\nu }\) :

The specific heat capacity

\(\alpha \) :

The coefficient of thermal expansion

\(\varTheta ({{\mathbf{x}}_{A}},t)\) :

The temperature at material point \({\mathbf{x}}_{A}\)

e :

The extension between the two material points, see Eq. (18)

\(\dot{e}\) :

The time rate of change of e,see Eq. (19)

\(\rho {{s}_{b}}({{\mathbf{x}}_{A}},t)\) :

The heat source contributed to the heat generation

\(\dot{\varvec{\eta }}\) :

The time rate of change of \(\varvec{\eta }\)

\({\mathbf{b}}({{\mathbf{x}}_{{\text {A}}}},t)\) :

The vector of body force density

\(\bar{\varTheta }\) :

The average value of the temperature change, see Eq. (21)

\(T_A\) :

The temperature at the material point \({\mathbf{x}}_{A}\)

\(T_B\) :

The temperature at the material point \({\mathbf{x}}_{B}\)

\(T_0\) :

The reference temperature

\(\varGamma \) :

The number of the transferred wave, which is a positive real number

\(\varsigma \) :

The plural

\(\varDelta t\) :

Thermal time step size, see Eq. (31)

References

  1. Alpay S, Madenci E (2013) Crack growth prediction in fully-coupled thermal and deformation fields using peridynamic theory. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, p 1477

  2. Bobaru F, Duangpanya M (2012) A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities. J Comput Phys 231(7):2764–2785

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Cheng H, Zhang A, Ming F (2017) Study on coupled dynamics of ship and flooding water based on experimental and SPH methods. Phys Fluids 29(10):107101

    Article  ADS  Google Scholar 

  4. Cui P, Zhang AM, Wang S, Khoo BC (2018) Ice breaking by a collapsing bubble. J Fluid Mech 841:287–309

    Article  ADS  MATH  Google Scholar 

  5. Du Q, Zhu C (2018) On measuring key parameters of an electro-impulse deicing system. Proc Inst Mech Eng Part G J Aerosp Eng p 0954410018770866

  6. Fan H, Li S (2017) A Peridynamics-SPH modeling and simulation of blast fragmentation of soil under buried explosive loads. Comput Methods Appl Mech Eng 318:349–381

    Article  ADS  MathSciNet  Google Scholar 

  7. Ferezghi YS, Sohrabi M, Nezhad S (2017) Dynamic analysis of non-symmetric functionally graded (FG) cylindrical structure under shock loading by radial shape function using meshless local petrov–galerkin (MLPG) method with nonlinear grading patterns. CMES Comput Model Eng Sci 113(4):497–520

    Google Scholar 

  8. Gao Y, Oterkus S (2019) Ordinary state-based peridynamic modelling for fully coupled thermoelastic problems. Contin Mech Thermodyn 31(4):907–937

    Article  ADS  MathSciNet  Google Scholar 

  9. Giamati MJ (1997) Electrothermal de-icing system. US Patent 5,657,951

  10. Goehner RD, Glover NI, Hensley DG (1987) Electro-impulse de-icing system for aircraft (1987). US Patent 4,678,144

  11. Hedayati E, Mohammad Vahedi M (2017) Numerical investigation of penetration in ceramic/aluminum targets using smoothed particle hydrodynamics method and presenting a modified analytical model. CMES Comput Model Eng Sci 113(3):295–323

    Google Scholar 

  12. Howard KW, Beck PJ (1993) Hydrogeochemical implications of groundwater contamination by road de-icing chemicals. J Contam Hydrol 12(3):245–268

    Article  Google Scholar 

  13. Huynh T, Huynh AB, Huynh AM (2010) Power line de-icing apparatus (2010). US Patent App. 12/730,002

  14. Huynh TM, Huynh AMT, Huynh AB (2013) Power line de-icing apparatus (2013). US Patent 8,373,095

  15. Kilic B, Madenci E (2010) Peridynamic theory for thermomechanical analysis. IEEE Trans Adv Packag 33(1):97–105

    Article  Google Scholar 

  16. La Placa S, Post B (1960) Thermal expansion of ice. Acta Crystallogr 13(6):503–505

    Article  Google Scholar 

  17. Labeas GN, Diamantakos ID, Sunaric MM (2006) Simulation of the electroimpulse de-icing process of aircraft wings. J Aircr 43(6):1876–1885

    Article  Google Scholar 

  18. Laforte J, Allaire M, Laflamme J (1998) State-of-the-art on power line de-icing. Atmos Res 46(1–2):143–158

    Article  Google Scholar 

  19. Lai X, Liu L, Li S, Zeleke M, Liu Q, Wang Z (2018) A non-ordinary state-based peridynamics modeling of fractures in quasi-brittle materials. Int J Impact Eng 111:130–146

    Article  Google Scholar 

  20. Lai X, Ren B, Fan H, Li S, Wu C, Regueiro R, Liu L (2014) Peridynamics simulations of geomaterial fragmentation by impulse loads. Int J Numer Anal Methods Geomech 39:1304–1330

    Article  Google Scholar 

  21. Li S, Wang G (2008) Introduction to Micromechanics and Nanomechanics, World Scientific Pub.

  22. Li Y, Ma L, Yang Z, Guan X, Nie Y, Yang Z (2018) Statistical multiscale analysis of transient conduction and radiation heat transfer problem in random inhomogeneous porous materials. CMES Comput Model Eng Sci 115(1):1–24

    Google Scholar 

  23. Liu M, Wang Q, Lu W (2017) Peridynamic simulation of brittle-ice crushed by a vertical structure. Int J Nav Archit Ocean Eng 9(2):209–218

    Article  Google Scholar 

  24. Liu R, Xue Y, Lu X, Cheng W (2018) Simulation of ship navigation in ice rubble based on peridynamics. Ocean Eng 148:286–298

    Article  Google Scholar 

  25. Ming F, Zhang A, Cheng H, Sun P (2018) Numerical simulation of a damaged ship cabin flooding in transversal waves with smoothed particle hydrodynamics method. Ocean Eng 165:336–352

    Article  Google Scholar 

  26. Möhle E, Haupt MC, Horst P (2013) Coupled numerical simulation and experimental validation of the electroimpulse de-icing process. J Aircr 50(1):96–102

    Article  Google Scholar 

  27. Nikravesh S, Gerstle W (2018) Improved state-based peridynamic lattice model including elasticity, plasticity and damage. CMES Comput Model Eng Sci 116(3):323–347

    Google Scholar 

  28. Oterkus S, Madenci E (2014) Peridynamics for fully coupled thermomechanical analysis of fiber reinforced laminates. In: 55th AIAA/ASMe/ASCE/AHS/sc structures, structural dynamics, and materials conference, p 0694

  29. Oterkus S, Madenci E, Agwai A (2014) Fully coupled peridynamic thermomechanics. J Mech Phys Solids 64:1–23

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Oterkus S, Madenci E, Agwai A (2014) Peridynamic thermal diffusion. J Comput Phys 265:71–96

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Palacios J, Smith E, Rose J, Royer R (2011) Instantaneous de-icing of freezer ice via ultrasonic actuation. AIAA J 49(6):1158–1167

    Article  ADS  Google Scholar 

  32. Peng Y, Zhang A, Ming F (2018) A thick shell model based on reproducing kernel particle method and its application in geometrically nonlinear analysis. Comput Mech 62(3):309–321

    Article  MathSciNet  MATH  Google Scholar 

  33. Rashid T, Khawaja HA (2016) Edvardsen: review of marine icing and anti-/de-icing systems. J Mar Eng Technol 15:79–87

    Article  Google Scholar 

  34. Rutherford RB, Dudman RL (2001) Aircraft de-icing system. US Patent 6,330,986

  35. Schulson EM (2001) Brittle failure of ice. Eng Fract Mech 68(17–18):1839–1887

    Article  Google Scholar 

  36. Thomas SK, Cassoni RP, MacArthur CD (1996) Aircraft anti-icing and de-icing techniques and modeling. J Aircr 33(5):841–854

    Article  Google Scholar 

  37. Tong Q, Li S (2016) Multiscale coupling of molecular dynamics and peridynamics. J Mech Phys Solids 95:169–187

    Article  ADS  MathSciNet  Google Scholar 

  38. Villeneuve E, Harvey D, Zimcik D, Aubert R, Perron J (2015) Piezoelectric deicing system for rotorcraft. J Am Helicopter Soc 60(4):1–12

    Article  Google Scholar 

  39. Volat C, Farzaneh M, Leblond A (2005) De-icing/anti-icing techniques for power lines: current methods and future direction. In: Proceedings of the 11th international workshop on atmospheric icing of structures, Montreal, Canada, vol 2005

  40. Wang P, Zhang AM, Ming F, Sun P, Cheng H (2019) A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics. J Fluid Mech 860:81–114

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Wang PP, Meng ZF, Zhang AM, Ming FR, Sun PN (2019) Improved particle shifting technology and optimized free-surface detection method for free-surface flows in smoothed particle hydrodynamics. Comput Methods Appl Mech Eng 357:112580

    Article  ADS  MathSciNet  Google Scholar 

  42. Wang Q, Wang Y, Zan Y, Lu W, Bai X, Guo J (2018) Peridynamics simulation of the fragmentation of ice cover by blast loads of an underwater explosion. J Mar Sci Technol 23(1):52–66

    Article  Google Scholar 

  43. Wang Y, Zhou X, Kou M (2018) Numerical studies on thermal shock crack branching instability in brittle solids. Eng Fract Mech 204:157–184

    Article  Google Scholar 

  44. Wang Y, Zhou X, Kou M (2018) Peridynamic investigation on thermal fracturing behavior of ceramic nuclear fuel pellets under power cycles. Ceram Int 44(10):11512–11542

    Article  Google Scholar 

  45. Wang YT, Zhou XP (2019) Peridynamic simulation of thermal failure behaviors in rocks subjected to heating from boreholes. Int J Rock Mech Min Sci 117:31–48

    Article  Google Scholar 

  46. Wu T, Qiu W (2018) Simulation of stochastic ice force process of vertical offshore structure based on spectral model. CMES Comput Model Eng Sci 115(1):047–066

    Google Scholar 

  47. Wu X, Yang D, Zhang X, MA L, FAN B (2010) Modeling and simulation of aircraft electric pulse de-icing system. J Syst Simul 4:1064–1066

    Google Scholar 

  48. Ye L, Wang C, Chang X, Zhang H (2017) Propeller-ice contact modeling with peridynamics. Ocean Eng 139:54–64

    Article  Google Scholar 

  49. Zhang A, Ming F, Cao X (2014) Total lagrangian particle method for the large-deformation analyses of solids and curved shells. Acta Mech 225(1):253–275

    Article  MathSciNet  MATH  Google Scholar 

  50. Zhang F, Gao Y, Yao H, Wang Y, Luo K (2019) Structural parameter sensitivity analysis of an aircraft anti-icing cavity based on thermal efficiency. Int J Aerosp Eng 2019:7851260

  51. Zhang Y, Dong W, Wang B, Liao K (2012) Study on de-icing criterion of electro-impulse de-icing simulation. Jisuanji Gongcheng yu Yingyong(Comput Eng Appl) 48(3):232–233

  52. Zumwalt G, Friedberg R (1986) Designing an electro-impulse de-icing system. In 24th Aerospace sciences meeting, pp 545–554

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Acknowledgements

This work is performed at the University of California Berkeley. Ms. Y. Song and Mr. R. Liu gratefully acknowledge the financial support from the Chinese Scholar Council (CSC) (CSC Grant No. 201706680094).

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Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China

    Ying Song, Renwei Liu & Zhuang Kang

  2. Department of Civil and Environmental Engineering, University of California, Berkeley, USA

    Ying Song, Renwei Liu & Shaofan Li

  3. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710129, China

    Feng Zhang

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  1. Ying Song
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Correspondence to Shaofan Li.

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Song, Y., Liu, R., Li, S. et al. Peridynamic modeling and simulation of coupled thermomechanical removal of ice from frozen structures. Meccanica 55, 961–976 (2020). https://doi.org/10.1007/s11012-019-01106-z

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