Computational Mechanics

, Volume 3, Issue 5, pp 331–342 | Cite as

Computational studies on path independent integrals for non-linear dynamic crack problems

  • T. Nishioka
  • M. Kobashi
  • S. N. Atluri
Article

Abstract

Recently the authors have derived various new types of path independent integrals in which the theoretical limitations of the so-calledJ integral are overcome. First, for elastodynamic crack problems, a path independent integralJ′ which has the physical meaning of energy release rate was derived. Later, more general forms of path independent integralsT* andT were derived, which are valid for any constitutive relation under quasi-static as well as dynamic conditions.

This paper presents the theoretical and computational aspects of these integrals, of relevance in non-linear dynamic fracture mechanics. An efficient solution technique is also presented for non-linear dynamic finite element method in which a factorization of the assembled stiffness matrix is done only once throughout the computation for a given mesh pattern. Finite element analyses were carried out for an example problem of a center-cracked plate subject to a uniaxial impact loading. The material behavior was modeled by three different constitutive relations such as linear-elastic, elastic-plastic, elastic-viscoplastic cases. The applicability of theT* integral to non-linear dynamic fracture mechanics was shown with the numerical results.

Keywords

Finite Element Method Finite Element Analysis Stiffness Matrix Constitutive Relation Energy Release Rate 

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References

  1. Atluri, S. N. (1982): Path indpendent integrals in finite elasticity and inelasticity with body forces, inertia and arbitrary crack-face conditions. Eng. Fract. Mech. 16, 341–364Google Scholar
  2. Atluri, S. N.; Nishioka, T.; Nakagaki, M. (1984): Incremental path independent integrals in inelastic and dynamic fracture mechanics. Eng. Fract. Mech. 20, 209–244Google Scholar
  3. Atluri, S. N.; Nakagaki, M.; Nishioka, T.; Kuang, Z. B. (1986): Crack-tip parameters and temperature rise in dynamic crack propagation. Eng. Fract. Mech. 23, 167–182Google Scholar
  4. Baker, R. B. (1962): Dynamic stresses created by a moving crack. J. Appl. Mech. 29, 449–545Google Scholar
  5. Bodner, S. R.; Symonds, P. S. (1962): Experimental and theoretical investigation of the plastic deformation of cantilever beams subjected to impulse loading. J. Appl. Mech. 29, 719–728Google Scholar
  6. Brust, F. W.; Nishioka, T.; Atluri, S. N.; Nakagaki, M. (1985): Further studies on elastic-plastic stable fracture utilizing theT * integral. Eng. Fract. Mech. 20, 1079–1103Google Scholar
  7. Budiansky, B.; Rice, J. R. (1973): Conservation laws and energy release rates. J. Appl. Mech. 40, 201–203Google Scholar
  8. Kishiomoto, K.; Aoki, S.; Sakata, M. (1980): On the path independent integral J. Eng. Fract. Mech. 13, 841–850Google Scholar
  9. Mondkar, D. P.; Powell, G. H. (1974): Large capacity equation solver for structural analysis. Compt. Structures 4, 699–728Google Scholar
  10. Nishioka, T.; Atluri, S. N. (1980a): Numerical modeling of dynamic crack propagation in finite bodies, by moving singular elements, Part 1: formulation. J. Appl. Mech. 47, 570–576Google Scholar
  11. Nishioka, T.; Atluri, S. N. (1980b): Numerical modeling of dynamic crack propagation in finite bodies, by moving singular elements, Part II: results. J. Appl. Mech. 47, 577–582Google Scholar
  12. Nishioka, T.; Atluri, S. N. (1983a): Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng. Fract. Mech. 18, 1–22Google Scholar
  13. Nishioka, T.; Atluri, S. N. (1983b): A numerical study of the use of path-independent integrals in elasto-dynamic crack propagation. Eng. Fract. Mech. 18, 23–33Google Scholar
  14. Nishioka, T.; Atluri, S.N. (1984a): On the computation of mixed-mode K-factors for a dynamically propagating crack, using path-independent integralJ′. Eng. Fract. Mech. 20, 193–203Google Scholar
  15. Nishioka, T.; Atluri, S. N. (1984b): A path-independent integral and moving isoparametric elements for dynamic crack propagation. AIAA J. 22, 409–414Google Scholar
  16. Nishioka, T.; Fujihara, H.; Yagami, H. (1986): Finite element analyses of stress intensity factors in dynamic crack propagation using path independentJ′ integral. In: Sih, G. C.; Nishitani, H.; Ishihara, T. (eds.): Role of Fracture Mechanics in Modern Technology, pp. 561–573. North-HollandGoogle Scholar
  17. Perzyna, P. (1963): The constitutive equations for rate sensitive plastic materials. Quarterly of Appl. Mech. 20, 321.Google Scholar
  18. Rice, J. R. (1968): A path-independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379–386Google Scholar
  19. Sih, G. C.; Embley, G. T.; Ravera, R. S. (1972): Impact response of a finite crack in plane extension. Int. J. Solids & Struct. 8, 977–993Google Scholar
  20. Thau, S.A.; Lu, T.H. (1971): Transient stress intensity factors for finite crack in an elastic solid caused by a dilatational wave. Int. J. Solids & Struct. 7, 731–750Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • T. Nishioka
    • 1
  • M. Kobashi
    • 1
  • S. N. Atluri
    • 2
  1. 1.Department of Ocean Mechanical EngineeringKobe University of Mercantile MarineKobeJapan
  2. 2.Center for the Advancement of Computational MechanicsGeorgia Institute of TechnologyAtlantaUSA

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