Skip to main content
Top
Published in:
Cover of the book

2022 | OriginalPaper | Chapter

1. Introduction and Preliminaries

Authors : James U. Gleaton, David Han, James D. Lynch, Hon Keung Tony Ng, Fabrizio Ruggeri

Published in: Fiber Bundles

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Over the last sixty years, fiber bundle models (FBMs) have played an indispensable role in “Modelling Critical and Catastrophic Phenomena.” The phrase in quotes is part of the title of a book on FBM (Bhattacharyya & Chakrabarti, 2006). This book consists of several tutorial introductory chapters, one of which is by Kun et al. (2006) entitled “Extensions of fibre bundle models,” where they state that “The fibre bundle model is one of the most important theoretical approaches to investigate the fracture and breakdown (BD) of disordered media extensively used both by the engineering and physics community.” The chapters after the introductory ones are specialized applications of the FBM in the geosciences.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Bažant, Z. P., & Le, J.-L. (2017). Probabilistic mechanics of quasibrittle structures—strength, lifetime, and size effect. Cambridge University Press.CrossRefMATH Bažant, Z. P., & Le, J.-L. (2017). Probabilistic mechanics of quasibrittle structures—strength, lifetime, and size effect. Cambridge University Press.CrossRefMATH
go back to reference Bhattacharyya, P., & Chakrabarti, B. K. (2006). Modelling critical and catastrophic phenomena in geoscience—a statistical physics approach. Springer.CrossRefMATH Bhattacharyya, P., & Chakrabarti, B. K. (2006). Modelling critical and catastrophic phenomena in geoscience—a statistical physics approach. Springer.CrossRefMATH
go back to reference Boufass, S., Hader, A., Tanasehte, M., Sbiaai, H., Achik, I., & Boughaleb, Y. (2020). Modelling of composite materials energy by fiber bundle model. The European Physical Journal Applied Physics, 92(1), 10401.CrossRef Boufass, S., Hader, A., Tanasehte, M., Sbiaai, H., Achik, I., & Boughaleb, Y. (2020). Modelling of composite materials energy by fiber bundle model. The European Physical Journal Applied Physics, 92(1), 10401.CrossRef
go back to reference Cohen, D., Schwarz, M., & Or, D. (2011). An analytical fiber bundle model for pullout mechanics of root bundles. Journal of Geophysical Research: Earth Surface, 116, F03010.CrossRef Cohen, D., Schwarz, M., & Or, D. (2011). An analytical fiber bundle model for pullout mechanics of root bundles. Journal of Geophysical Research: Earth Surface, 116, F03010.CrossRef
go back to reference Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187–220.MathSciNetCrossRefMATH Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187–220.MathSciNetCrossRefMATH
go back to reference Daniels, H. E. (1945). The statistical theory of the strength of bundles of threads I. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 183(995), 405–435.MathSciNetMATH Daniels, H. E. (1945). The statistical theory of the strength of bundles of threads I. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 183(995), 405–435.MathSciNetMATH
go back to reference Ebrahimi, N., McCullough, K., & Xiao, Z. (2013a). Reliability of sensors based on nanowire networks. IIE Transactions, 45(2), 215–228.CrossRef Ebrahimi, N., McCullough, K., & Xiao, Z. (2013a). Reliability of sensors based on nanowire networks. IIE Transactions, 45(2), 215–228.CrossRef
go back to reference Ebrahimi, N., McCullough, K., & Xiao, Z. (2013b). Reliability of sensors based on nanowire networks with either an equilateral triangle lattice or a hexagonal lattice structure. IEEE Transactions on Nanotechnology, 12(1), 81–95.CrossRef Ebrahimi, N., McCullough, K., & Xiao, Z. (2013b). Reliability of sensors based on nanowire networks with either an equilateral triangle lattice or a hexagonal lattice structure. IEEE Transactions on Nanotechnology, 12(1), 81–95.CrossRef
go back to reference Hansen, A., Hemmer, P. C., & Pradhan, S. (2015). The fiber bundle model: Modeling failure in materials. Wiley-VCH, Weinheim.CrossRef Hansen, A., Hemmer, P. C., & Pradhan, S. (2015). The fiber bundle model: Modeling failure in materials. Wiley-VCH, Weinheim.CrossRef
go back to reference Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.MathSciNetCrossRefMATH Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.MathSciNetCrossRefMATH
go back to reference Kun, F., Raischel, F., Hidalgo, R. C., & Herrmann, H. J. (2006). Extensions of fibre bundle models. In Modelling critical and catastrophic phenomena in geoscience (pp. 57–92). Springer. Kun, F., Raischel, F., Hidalgo, R. C., & Herrmann, H. J. (2006). Extensions of fibre bundle models. In Modelling critical and catastrophic phenomena in geoscience (pp. 57–92). Springer.
go back to reference Leckey, K., Müller, C. H., Szugat, S., & Maurer, R. (2020). Prediction intervals for load-sharing systems in accelerated life testing. Quality and Reliability Engineering International, 36(6), 1895–1915.CrossRef Leckey, K., Müller, C. H., Szugat, S., & Maurer, R. (2020). Prediction intervals for load-sharing systems in accelerated life testing. Quality and Reliability Engineering International, 36(6), 1895–1915.CrossRef
go back to reference Lehmann, P., & Or, D. (2012). Hydromechanical triggering of landslides: From progressive local failures to mass release. Water Resources Research, 48(3), W03535.CrossRef Lehmann, P., & Or, D. (2012). Hydromechanical triggering of landslides: From progressive local failures to mass release. Water Resources Research, 48(3), W03535.CrossRef
go back to reference Li, S., Gleaton, J., & Lynch, J. (2019). What is the shape of a bundle? An analysis of Rosen’s fibrous composites experiments using the chain-of-bundles model. Scandinavian Journal of Statistics, 46(1), 59–86.MathSciNetCrossRefMATH Li, S., Gleaton, J., & Lynch, J. (2019). What is the shape of a bundle? An analysis of Rosen’s fibrous composites experiments using the chain-of-bundles model. Scandinavian Journal of Statistics, 46(1), 59–86.MathSciNetCrossRefMATH
go back to reference Mishnaevsky, L. (2013). Micromechanical modelling of wind turbine blade materials. In P. Brøndsted, & R. P. Nijssen (Eds.), Advances in wind turbine blade design and materials (pp. 298–324). Woodhead Publishing Series in Energy. Mishnaevsky, L. (2013). Micromechanical modelling of wind turbine blade materials. In P. Brøndsted, & R. P. Nijssen (Eds.), Advances in wind turbine blade design and materials (pp. 298–324). Woodhead Publishing Series in Energy.
go back to reference Orgéas, L., Dumont, P., & Corre, S. L. (2015). Rheology of highly concentrated fiber suspensions. In F. Chinesta, & G. Ausias (Eds.), Rheology of non-spherical particle suspensions (pp. 119–166). Elsevier. Orgéas, L., Dumont, P., & Corre, S. L. (2015). Rheology of highly concentrated fiber suspensions. In F. Chinesta, & G. Ausias (Eds.), Rheology of non-spherical particle suspensions (pp. 119–166). Elsevier.
go back to reference Pugno, N. (2014). A review on the design of superstrong carbon nanotube or graphene fibers and composites. In M. J. Schulz, V. N. Shanov, & Z. Yin (Eds.), Nanotube superfiber materials (pp. 495–518). William Andrew Publishing. Pugno, N. (2014). A review on the design of superstrong carbon nanotube or graphene fibers and composites. In M. J. Schulz, V. N. Shanov, & Z. Yin (Eds.), Nanotube superfiber materials (pp. 495–518). William Andrew Publishing.
go back to reference Reiweger, I., Schweizer, J., Dual, J., & Herrmann, H. J. (2009). Modelling snow failure with a fibre bundle model. Journal of Glaciology, 55(194), 997–1002.CrossRef Reiweger, I., Schweizer, J., Dual, J., & Herrmann, H. J. (2009). Modelling snow failure with a fibre bundle model. Journal of Glaciology, 55(194), 997–1002.CrossRef
Metadata
Title
Introduction and Preliminaries
Authors
James U. Gleaton
David Han
James D. Lynch
Hon Keung Tony Ng
Fabrizio Ruggeri
Copyright Year
2022
DOI
https://doi.org/10.1007/978-3-031-14797-5_1

Premium Partners