106
Views
0
CrossRef citations to date
0
Altmetric
Articles

Direct computation of stress intensity factors in finite element method

& ORCID Icon
Pages 309-335 | Received 08 Apr 2017, Accepted 10 Jul 2017, Published online: 19 Jul 2017

References

  • Akhondzadeh, Sh, Khoei, A. R., & Broumand, P. (2017). An efficient enrichment strategy for modeling stress singularities in isotropic composite materials with X-FEM technique. Engineering Fracture Mechanics, 169, 201–225.
  • Aliabadi, M. H. (1987). An enhanced boundary element method for determining fracture parameters. In Proceedings 4th International Conference on Numerical Methods in Fracture Mechanics, 27–39. San Antonio, TX: Pineridge Press.
  • Aliabadi, M. H., Rooke, D. P., & Cartwright, D. J. (1987). An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures. Journal of Strain Analysis, 22, 1–5.
  • Barsoum, R. S. (1976). On the use of isoparametric finite elements in linear fracture mechanics. International Journal for Numerical Methods in Engineering, 10, 25–37.
  • Bath, K. J., & Wilson, E. L. (1976). Numerical methods in finite element analysis. New Jersey, NJ: Prentice Hall.
  • Belytschko, T., & Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45, 601–620.
  • Belytschko, T., Krongauz, Y., & Organ, D. (1996). Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering, 139, 3–47.
  • Bethem, J. P. (1977). State of stress at vertex of a quarter-infinite crack in a half-space. International Journal of Solids and Structures, 13, 479–492.
  • Blandford, G. E., Ingraffea, A. R., & Liggett, J. A. (1981). Two-dimensional stress intensity factor computations using the boundary element method. International Journal for Numerical Methods in Engineering, 17, 387–404.
  • Bordas, S., & Duflot, M. (2007). Derivative recovery and a posteriori error estimate for extended finite elements. Computer Methods in Applied Mechanics and Engineering, 196, 3381–3399.
  • Bordas, S., Duflot, M., & Le, P. (2008). A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24, 961–971.
  • Bordas, S., Rabczuk, T., & Zi, G. (2008). Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 75, 943–960.
  • Brahtz, J. H. A. (1933). Stress distribution in a reentrant corner. Transactions of the American Society of Mechanical Engineers, 55, 31–37.
  • Caicedo, J., & Portela, A. (2015). Cracked plate analysis with the dual boundary element method and Williams’ eigen expansion. Journal of Engineering Analysis with Boundary Elements, 52, 16–23.
  • Carpinteri, A., Ferro, G., & Ventura, G. (2003). The partition of unity quadrature in element-free crack modeling. Computers and Structures, 81, 1783–1794.
  • Civelek, M. B., & Erdogan, F. (1982). International Journal of Fracture, 19, 139–159. Retrieved from https://link.springer.com/article/10.1007/BF00016570
  • Cruse, T. A., & Wilson, R. B. (1977). Boundary integral equation method for elastic fracture mechanics analysis, AFOSR-TR-780355, Pratt and Whitney Aircraft Group, Hartford, Connecticut.
  • Dong, L., & Atluri, S. N. (2013). Fracture and fatigue analyses: SGBEM-FEM or XFEM? Part 1: 2D structures. Computer Modeling in Engineering and Sciences, 90, 91–146.
  • Duflot, M., & Bordas, S. (2008). A posteriori error estimation for extended finite elements by an extended global recovery. International Journal for Numerical Methods in Engineering, 76, 1123–1138.
  • Estrada, O., Rdenas, J., Bordas, S., Duflot, M., Kerfriden, P., & Giner, E. (2012). On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods. Engineering Computations, 29, 814–841.
  • Felippa, C. A. (2013). Introduction to finite element methods. Boulder: University of Colorado. Retrieved from http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/
  • Fleming, M., Chu, Y., Moran, B., & Belytschko, T. (1997). Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, 40, 1483–504.
  • Folias, E. S. (1975). On the three-dimensinal theory of cracked plates. Journal of Applied Mechanics, 42, 663–674.
  • Gu, Y. T., & Zhang, L. C. (2008). Coupling of the meshfree and finite element methods for determination of the crack tip fields. Engineering Fracture Mechanics, 75, 986–1004.
  • Hedayati, E., & Vahedi, M. (2014). Using extended finite element method for computation of the stress intensity factor, crack growth simulation and predicting fatigue crack growth in a slant-cracked plate of 6061–T651 aluminum. World Journal of Mechanics, 4, 24–30.
  • Henshell, R. D., & Shaw, K. G. (1975). Crack tip elements are unnecessary. International Journal for Numerical Methods in Engineering, 9, 495–509.
  • Karihaloo, B. L., & Xiao, Q. Z. (2001). Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Engineering Fracture Mechanics, 68, 1609–1630.
  • Khoei, A. R. (2015). Extended finite element method: Theory and applications. London: Wiley.
  • Li, S., & Liu, W. K. (2002). Meshfree and particle methods and their applications. Applied Mechanics Reviews, 54, 1–34.
  • Liu, G. R., & Gu, Y. T. (2005). An introduction to meshfree methods and their programming. Berlin: Springer Press.
  • Liu, X. Y., Xiao, Q. Z., & Karihaloo, B. L. (2004). Xfem for direct evaluation of mixed mode stress intensity factors in homogeneous and bi-materials. International Journal for Numerical Methods in Engineering, 59, 1103–1118.
  • Lu, Y. Y., Belytschko, T., & Tabbara, M. (1995). Element-free Galerkin method for wave propagation and dynamic fracture. Computer Computer Methods in Applied Mechanics and Engineering, 126, 131–53.
  • Martinez, J., & Dominguez, J. (1984). On the use of quarter-point boundary elements for stress intensity factor computations. International Journal for Numerical Methods in Engineering, 20, 1941–1950.
  • Melenk, J. M., & Babuska, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139, 289–314.
  • Natarajana, S., Ooi, E., Chiong, I., & Song, C. (2014). Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation. Finite Elements in Analysis and Design, 85, 101–122.
  • Natarajana, S., Songa, C., & Belouettarb, S. (2014). Numerical evaluation of stress intensity factors and T-stress for interfacial cracks and cracks terminating at the interface without asymptotic enrichment. Computer Methods in Applied Mechanics and Engineering, 279, 86–112.
  • Nguyen, V. P., Rabczuk, T., Bordas, S., & Duflotd, M. (2008). Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation, 79, 763–813.
  • Ooi, E., Song, C., Loi, F., & Yang, Z. (2012). Polygon scaled boundary finite elements for crack propagation modelling. International Journal for Numerical Methods in Engineering, 91, 319–342.
  • Portela, A., & Aliabadi, M. H. (1993). Crack growth analysis using boundary elements -- Software. Southampton, Boston: Computational Mechanics Publications. Press (1987).
  • Portela, A., Aliabadi, M. H., & Rooke, D. P. (1991). Efficient boundary element analysis of sharp notched plates. International Journal for Numerical Methods in Engineering, 32, 445–470.
  • Portela, A., Aliabadi, M. H., & Rooke, D. P. (1992). The dual boundary element method: Effective implementation for crack problems. International Journal for Numerical Methods in Engineering, 33, 1269–1287.
  • Portela, A., Aliabadi, M. H., & Rooke, D. P. (1992). Dual boundary element analysis of cracked plates: Singularity subtraction technique. International Journal of Fracture, 55, 17–28.
  • Portela, A., Aliabadi, M. H., & Rooke, D. P. (1989). Boundary element analysis of V-notched plates. In C. A. Brebbia, Proceedings of the fourth International Conference on Boundary Element Technology, Windsor, Canada, Southampton: Computational Mechanics Publications.
  • Portela, A., & Charafi, A. (2002). Finite elements using maple -- A Symbolic programming approach. Berlin: Springer.
  • Prange, C., Loehnert, S., & Wriggers, P. (2012). Error estimation for crack simulations using the XFEM. International Journal for Numerical Methods in Engineering, 91, 1459–1474.
  • Rabczuk, T., & Belytschko, T. (2007). A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 196, 2777–2799.
  • Rdenas, J., Estrada, O., Tarancn, E., & Fuenmayor, F. (2008). A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. International Journal for Numerical Methods in Engineering, 76, 545–571.
  • Rodenas, J., Estrada, O., Diez, P., & Fuenmayor, F. (2010). Accurate recovery-based upper error bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering, 199, 2607–2621.
  • Shivakumar, K. N., & Raju, I. S. (1990). Treatment of singularities in cracked bodies. International Journal of Fracture, 45, 159–178.
  • Sladek, J., Sladek, V., Wunsche, M., & Zhang, C. (2009). Interface crack problems in anisotropic solids analyzed by the MLPG. Computer Modeling in Engineering and Sciences, 54, 223–252.
  • Smith, R. N. L., & Mason, J. C. (1987). A boundary element method for curved crack problems in two-dimensions. In C. A. Brebbia (Ed.), Proceedings of Fourth International Seminar on BEM. Berlin: Springer-Verlag.
  • Symm, G. T. (1963). Integral equation methods in potential theory II. Proceedings of Royal Society, A275, 33–46.
  • Tong, P., Pian, T. H. H., & Lasry, S. J. (1973). A hybrid element approach to crack problems in plane elasticity. International Journal for Numerical Methods in Engineering, 7, 297–308.
  • Wen, P. H., & Aliabadi, M. H. (2007). Applications of meshless method to fracture mechanics with enriched radial basis functions. Durability of Structures and Health Monitoring, 3, 107–119.
  • Williams, M. L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics, 526–528. ISSN: 0021-8936.
  • Xanthis, L. S., Bernal, M. J. M., & Atkinson, C. (1981). The treatment of the singularities in the calculation of stress intensity factors using the integral equation method. Computer Methods in Applied Mechanics and Engineering, 26, 285–304.
  • Xiao, Q. Z., Karihaloo, B. L., & Liu, X. Y. (2004). Direct determination of SIF and higher order terms of mixed-mode cracks by a hybrid crack element. International Journal of Fracture, 125, 207–225.
  • Zienkiewicz, O. C. (1977). The finite element method. New York, NY: Mc Graw-Hill.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.