Skip to main content
SpringerLink
Log in

Local Approach to Damage and Fracture Analysis

  • Chapter
  • First Online:
Continuum Damage Mechanics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 185))

Abstract

Continuum damage mechanics facilitates not only the modeling of crack initiation due to damage development but also the analysis of the damage and fracture process up to the final fracture. The local approach to fracture by means of continuum damage mechanics and finite element method has developed as a systematic engineering method to analyze the whole process of damage and fracture. At the end of this book, we consider the notion, applicability and the fundamental issues of this approach. Section 11.1 is concerned with its procedure, applicability and the related numerical problems. In Section 11.2, the material instability and the resulting loss of uniqueness will be discussed as the major causes of the mesh-sensitivity in time-independent (rate-independent) strain-softening materials.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
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

Notes

  1. 1.

    This term was first proposed by Pineau (1980). In order to supplement the limitations of the linear- or nonlinear-fracture mechanics essentially based on the global fracture mechanics parameters, a new method of fracture analysis developed around the end of 1970s by modeling the fracture toughness at the crack tip by the use of the local fracture criterion. Pineau named this methodology “local approach to fracture”.

  2. 2.

    A rate boundary value problem is said to be well-posed, if it admits a finite number of linearly independent solutions which depend continuously on the data (especially, on boundary conditions) and which constitute diffuse modes of deformation (de Borst et al. 1993; Besson et al. 2010).

  3. 3.

    Bifurcation and the resulting localization in the general elastic-plastic and elastic-viscoplastic materials are referred to in Besson et al. (2010), where the problems of mesh dependence and its regularization in finite element analysis to be discussed in the subsequent Sections of 11.3 and 11.4 are also described.

References

  • Besson J, Cailletaud G, Chaboche J-L, Forest S, Blétry M (2010) Non-linear mechanics of materials. Springer, Dordrecht

    Google Scholar 

  • Bažant ZP (1990) Recent advances in failure localization and nonlocal models. In: Shah SP, Swartz SE, Wang ML (eds) Micromechanics of failure of quasi-ductile materials. Elsevier Applied Science, London, pp 12–32

    Google Scholar 

  • Bažant ZP, Jirasek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech Trans ASCE 128:1119–1149

    Article  Google Scholar 

  • Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Mater Struct 16:155–177

    Google Scholar 

  • Bažant ZP, Belytschko TB, Chang TP (1984) Continuum theory for strain- softening. J Eng Mech Trans ASCE 110:1666–1692

    Article  Google Scholar 

  • Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19:3–52

    Article  Google Scholar 

  • Bilby BA, Howard IC, Li ZH (1994) Mesh independent cell models for continuum damage theory. Fatigue Fract Eng Mater Struct 17:1221–1233

    Article  Google Scholar 

  • Billardon R, Doghri I (1989) Localization bifurcation analysis for damage softening elasto-plastic materials. In: Mazars J, Bažant ZP (eds) Cracking and damage – strain localization and size effect. Elsevier Applied Science, London, pp 295–307

    Google Scholar 

  • Chaboche JL (1986) Time independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188

    Article  MATH  Google Scholar 

  • de Borst R, Sluys LJ, Mühlhaus HB, Pamin J (1993) Fundamental issues in finite element analyses of localization of deformation. Eng Comput 10:99–121

    Article  Google Scholar 

  • de Vree JHP, Brekelmans WAM, van Gils MAJ (1995) Comparison of nonlocal approaches in continuum mechanics. Comput Struct 55:581–588

    Article  MATH  Google Scholar 

  • Ghrib F, Tinawi R (1995a) An application of damage mechanics for seismic analysis of concrete gravity dams. Earthquake Eng Struct Dyn 24:157–173

    Article  Google Scholar 

  • Ghrib F, Tinawi R (1995b) Nonlinear behaviour of concrete dams using damage mechanics. J Eng Mech ASCE 121:513–527

    Article  Google Scholar 

  • Hall FR, Hayhurst DR (1991) Modelling of grain size effects in creep crack growth using a non-local continuum damage approach. Proc R Soc London A 433:405–421

    Article  MATH  Google Scholar 

  • Hayhurst DR, Dimmer PR, Chernuka MW (1975) Estimates of the creep rupture lifetime of structures using the finite element method. J Mech Phys Solids 23:335–355

    Article  MATH  Google Scholar 

  • Hill R (1958) A general theory of uniqueness and stability in elastic-plastic solids. J Mech Phys Solids 16:236–249

    Article  Google Scholar 

  • Jubran JS, Cofer WF (1991) Ultimate strength analysis of structural components using the continuum damage mechanics approach. Comput Struct 39:741–752

    Article  Google Scholar 

  • Lemaitre J (1986) Local approach of fracture. Eng Fract Mech 25:523–537

    Article  Google Scholar 

  • Lemaitre J, Chaboche J-L, Benallal A, Desmorat R (2009) Mécanique des Matériaux Solides, 3e edn. Dunod, Paris

    Google Scholar 

  • Liu Y, Murakami S (1996) Creep crack growth analysis by use of a local approach incorporating perfect plasticity. In: Townley H, Asada Y, Tseng A (eds) Proceedings of 6th international conference on creep and fatigue. Mechanical Engineering Publications, London, pp 331–340

    Google Scholar 

  • Liu Y, Murakami S, Kanagawa Y (1994) Mesh-dependence and stress singularity in finite element analysis of creep crack growth by continuum damage mechanics approach. Eur J Mech A/Solids 13:395–418

    MATH  Google Scholar 

  • Mühlhaus HB, Vardoulakis I (1987) The thickness of shear bands in granular materials. Geotechnique 37:271–283

    Article  Google Scholar 

  • Murakami S, Liu Y (1995) Mesh-dependence in local approach to creep fracture. Int J Damage Mech 4:230–250

    Article  Google Scholar 

  • Murakami S, Liu Y (1996) Local approach of fracture based on continuum damage mechanics and the related problems. Mater Sci Res Int 2:131–142

    Google Scholar 

  • Pietruszczak S, Mróz Z (1981) Finite element analysis of deformation of strain-softening materials. Int J Numer Methods Eng 17:327–334

    Article  MATH  Google Scholar 

  • Pijaudier-Cabot G, Bažant ZP (1987) Nonlocal damage theory. J Eng Mech Trans ASCE 113:1512–1533

    Article  Google Scholar 

  • Saanouni K, Chaboche JL, Lesne PM (1989) On the creep crack-growth prediction by a nonlocal damage formulation. Eur J Mech A/Solids 8:437–459

    MATH  Google Scholar 

  • Simo JC (1989) Strain softening and dissipation: a unification of approaches. In: Mazars J, Bažant ZP (eds) Cracking and damage – strain localization and size effect. Elsevier, London, pp 440–461

    Google Scholar 

  • Triantafyllidis N, Aifantis EC (1986) A gradient approach to localization of deformation, I. Hyperelastic materials. J Elasticity 16:225–237

    Article  MathSciNet  MATH  Google Scholar 

  • Bažant ZP, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. J Appl Mech Trans ASME 55:287–293

    Article  MATH  Google Scholar 

  • Tvergaard V, Needleman A (1995) Effects of nonlocal damage in porous plastic solids. Int J Solids Struct 32:1063–1077

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nagoya University, 3-63-3 Hinata-cho, Mizuho-ku, 467-0047, Nagoya, Japan

    Sumio Murakami (Professor Emeritus)

Authors
  1. Sumio Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sumio Murakami .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Murakami, S. (2012). Local Approach to Damage and Fracture Analysis. In: Continuum Damage Mechanics. Solid Mechanics and Its Applications, vol 185. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2666-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-2666-6_11

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-2665-9

  • Online ISBN: 978-94-007-2666-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation