EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 57 / No 3 (May-June 2023) ESAIM: M2AN, 57 3 (2023) 1195-1223 References
Open Access
Issue
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
Page(s) 1195 - 1223
DOI https://doi.org/10.1051/m2an/2023001
Published online 08 May 2023
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Vol. 140 of Pure and Applied Mathematics. Academic Press (2003). [Google Scholar]
  2. T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations. Vol. 252 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York (1982). [CrossRef] [Google Scholar]
  3. I. Babuška and A. Miller, The post-processing approach in the finite element method – Part 1: Calculation of displacements, stresses and other higher derivatives of the displacements. Int. J. Numer. Methods Eng. 20 (1984) 1085–1109. [CrossRef] [Google Scholar]
  4. I. Babuška and A. Miller, The post-processing approach in the finite element method – Part 2: the calculation of stress intensity factors. Int. J. Numer. Methods Eng. 20 (1984) 1111–1129. [CrossRef] [Google Scholar]
  5. J.R. Barber, Elasticity, 3 edition. Vol. 172 of Solid Mechanics and Its Applications. Springer, Dordrecht (2010). [CrossRef] [Google Scholar]
  6. S. Brenner and R. Scott, The Mathematical Theory of Finite Element Methods. Vol. 15 of Texts in Applied Mathematics. Springer-Verlag, New York (2008). [CrossRef] [Google Scholar]
  7. S.K. Chan, I.S. Tuba and W.K. Wilson, On the finite element method in linear fracture mechanics. Eng. Fract. Mech. 2 (1970) 1–17. [CrossRef] [Google Scholar]
  8. G.P. Cherepanov, The propagation of cracks in a continuous medium. J. Appl. Math. Mech. 31 (1967) 503–512. [CrossRef] [Google Scholar]
  9. M.M. Chiaramonte, Y.X. Shen, L.M. Keer and A.J. Lew, Computing stress intensity factors for curvilinear cracks. Int. J. Numer. Methods Eng. 104 (2015) 260–296. [CrossRef] [Google Scholar]
  10. M.M. Chiaramonte, Y.X. Shen and A.J. Lew, Mapped finite element methods: high-order approximations of problems on domains with cracks and corners. Int. J. Numer. Methods Eng. 111 (2017) 864–900. [CrossRef] [Google Scholar]
  11. M. Costabel, M. Dauge and R. Duduchava, Asymptotics without logarithmic terms for crack problems. Commun. Part. Differ. Equ. 28 (2003) 869–926. [CrossRef] [Google Scholar]
  12. M. Costabel, M. Dauge and Z. Yosibash, A quasi-dual function method for extracting edge stress intensity functions. SIAM J. Math. Anal. 35 (2004) 1177–1202. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Vol. 159 Applied Mathematical Sciences. Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  14. M. Feistauer, On the finite element approximation of functions with noninteger derivatives. Numer. Funct. Anal. Optim. 10 (1989) 91–110. [CrossRef] [MathSciNet] [Google Scholar]
  15. H. Gao and J.R. Rice, A first-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 56 (1989) 828–836. [CrossRef] [Google Scholar]
  16. M. Gosz and B. Moran, An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. Eng. Fract. Mech. 69 (2002) 299–319. [CrossRef] [Google Scholar]
  17. B.E. Grossman-Ponemon, L.M. Keer and A.J. Lew, A method to compute mixed-mode stress intensity factors for nonplanar cracks in three dimensions. Int. J. Numer. Methods Eng. 121 (2020) 4292–4328. [CrossRef] [Google Scholar]
  18. T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Courier Corporation, New York (2000). [Google Scholar]
  19. J.-H. Kim and G.H. Paulino, Finite element evaluation of mixed mode stress intensity factors in functionally graded materials. Int. J. Numer. Methods Eng. 53 (2002) 1903–1935. [CrossRef] [Google Scholar]
  20. A.A. Kosinski, Differential Manifolds. Vol. 138 of Pure and Applied Mathematics. Academic Press (1993). [Google Scholar]
  21. S.G. Krantz and H.R. Parks, The Implicit Function Theorem: History, Theory, and Applications. Modern Birkhäuser Classics. Birkhäuser, New York (2013). [CrossRef] [Google Scholar]
  22. J.-B. Leblond and O. Torlai, The stress field near the front of an arbitrarily shaped crack in a three-dimensional elastic body. J. Elasticity 29 (1992) 97–131. [CrossRef] [Google Scholar]
  23. J.-B. Leblond, A. Karma and V. Lazarus, Theoretical analysis of crack front instability in mode I+III. J. Mech. Phys. Solids 59 (2011) 1872–1887. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Liu and B. Joe, Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision. Math. Comput. Am. Math. Soc. 65 (1996) 1183–1200. [CrossRef] [Google Scholar]
  25. J.N. Lyness, An error functional expansion for N-dimensional quadrature with an integrand function singular at a point. Math. Comput. 30 (1976) 1–23. [Google Scholar]
  26. N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46 (1999) 131–150. [Google Scholar]
  27. G.P. Nikishkov and S.N. Atluri, Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the “equivalent domain integral” method. Int. J. Numer. Methods Eng. 24 (1987) 1801–1821. [CrossRef] [Google Scholar]
  28. J.R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35 (1968) 379–386. [CrossRef] [Google Scholar]
  29. Y.X. Shen and A. Lew, An optimally convergent discontinuous Galerkin-based extended finite element method for fracture mechanics. Int. J. Numer. Methods Eng. 82 (2010) 716–755. [CrossRef] [Google Scholar]
  30. L. Shunn and F. Ham, Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement. J. Comput. Appl. Math. 236 (2012) 4348–4364. [CrossRef] [MathSciNet] [Google Scholar]
  31. B.A. Szabó and I. Babuška, Finite Element Analysis. John Wiley & Sons Inc, New York (1991). [Google Scholar]
  32. B.A. Szabó and I. Babuška, Computation of the amplitude of stress singular terms for cracks and reentrant corners, in Fracture Mechanics: Nineteenth Symposium. ASTM International (1988). [Google Scholar]
  33. D.M. Tracey, Finite elements for determination of crack tip elastic stress intensity factors. Eng. Fract. Mech. 3 (1971) 255–265. [CrossRef] [Google Scholar]
  34. J.F. Yau, S.S. Wang and H.T. Corten, A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J. Appl. Mech. 47 (1980) 335–341. [CrossRef] [Google Scholar]
  35. Z. Yosibash, Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation. Vol. 37 of Interdisciplinary Applied Mathematics, Springer-Verlag, New York (2012). [CrossRef] [Google Scholar]
  36. Z. Yosibash, S. Shannon, M. Dauge and M. Costabel, Circular edge singularities for the laplace equation and the elasticity system in 3-D domains. Int. J. Fract. 168 (2011) 31–52. [CrossRef] [Google Scholar]
  37. A.T. Zehnder, Fracture Mechanics. Vol. 62 of Lecture Notes in Applied and Computational Mechanics. Springer, Netherlands (2012). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you