Skip to main content

Spatial Solutions Based on the Finite Element Method and the Monte Carlo Method—A Multi-scale Approach

  • Chapter
  • First Online:
Modeling Steel Deformation in the Semi-Solid State

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 47))

  • 604 Accesses

Abstract

This chapter presents a 3D solution to the problem of medium deformation in conditions of its simultaneous solidification. The proposed solution consists of four sub-models. These are a mechanical model based upon a rigid-plastic solution, and a thermal model based on the Fourier equation solution. Another key component model is the model of function of stress versus strain change. The developed methodologies of determining the mentioned functions are presented in details in Chap. 8.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Malinowski Z (2005) Numeryczne modele w przeróbce plastycznej i wymianie ciepła. AGH, Krakow, Poland

    Google Scholar 

  2. Hadala B, Cebo-Rudnicka A, Malinowski Z et al (2011) The influence of thermal stresses and strand bending on surface defects formation in continuously cast strands. Arch Metall Mater 56:367–377

    Article  Google Scholar 

  3. Malinowski Z, Rywotycki M (2009) Modelling of the strand and mold temperature in the continuous steel caster. Arch Civ Mech Eng 9:59–73

    Article  Google Scholar 

  4. Milkowska-Piszczek K, Rywotycki M, Falkus J et al (2015) A comparison of models describing heat transfer in the primary cooling zone of a continuous casting machine. Arch Metall Mater 60:239–244

    Google Scholar 

  5. Glowacki M (1998) Termomechaniczno-mikrostrukturalny model walcowania w wykrojach kształtowych. AGH, Krakow, Poland

    Google Scholar 

  6. Glowacki M (2012) Modelowanie matematyczne i symulacja odkształcania metali. AGH, Krakow, Poland

    Google Scholar 

  7. Glowacki M, Hojny M, Kuziak R (2012) Computer aided investigation of mechanical properties of semi-solid steels. AGH, Krakow, Poland

    Google Scholar 

  8. Hojny M (2014) Projektowanie dedykowanych systemów symulacji odkształcania stali w stanie półciekłym. Wzorek, Krakow, Poland

    Google Scholar 

  9. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals. Elsevier Butterworth-Heinemann, Oxford, UK

    MATH  Google Scholar 

  10. Szczygiol N (1997) Równania krzepnięcia w ujęciu metody elementów skończonych. Solidif Met Alloy 30:221–232

    Google Scholar 

  11. Lewis RW, Roberts PM (1987) Finite element simulation of solidification problems. Appl Sci Res 44:61–92

    Article  MATH  Google Scholar 

  12. Voller VR, Swaminathan CR, Thomas BG (1990) Fixed grid techniques for phase change problems: a review. Int J Numer Methods Eng 30:875–898

    Article  MATH  Google Scholar 

  13. Pietrzyk M (1992) Metody numeryczne w przerobce plastycznej metali. AGH, Krakow

    Google Scholar 

  14. Madej L (2010) Development of the modelling strategy for the strain localization simulation based on the digital material representation. AGH, Krakow

    Google Scholar 

  15. Mordechai S (ed) (2011) Application of monte carlo method in science and engineering. InTech, Rijeka

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcin Hojny .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Hojny, M. (2018). Spatial Solutions Based on the Finite Element Method and the Monte Carlo Method—A Multi-scale Approach. In: Modeling Steel Deformation in the Semi-Solid State. Advanced Structured Materials, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-67976-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67976-1_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67975-4

  • Online ISBN: 978-3-319-67976-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics