Analysis of finite strain anisotropic elastoplastic fracture in thin plates and shells

Journal of Aerospace Engineering

Volumn 19, Issue 4, 2006, Pages 259-270

  Areias, Pedro M A ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

Anisotropic materials; Ductility; Elastoplasticity; Fractures; Plates; Shells

Indexed keywords

ANISOTROPIC MATERIALS; KIRCHHOFF-LOVE SHELL MODEL; PLASTIC ANISOTROPY; THIN PLATES;

ANISOTROPY; CRACKS; DUCTILITY; ELASTOPLASTICITY; FINITE ELEMENT METHOD; FRACTURE; PLATES (STRUCTURAL COMPONENTS);

SHELLS (STRUCTURES);

EID: 33748764950     PISSN: 08931321     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0893-1321(2006)19:4(259)     Document Type: Article

References (31)

1. Anand, L. (1979). "On Hencky's, H. approximate strain-energy function for moderate deformations." ASME Trans. J. Appl. Mech., 46, 78-82.
2. Areias, P., and Belytschko, T. (2005a). "Analysis of three-dimensional crack initiation and propagation using the extended finite element method." Int. J. Numer. Methods Eng., 63, 760-788.
3. Areias, P., and Belytschko, T. (2005b). "Non-linear analysis of shells with arbitrary evolving cracks using XFEM." Int. J. Numer. Methods Eng., 62, 384-415.
4. Areias, P., César de Sá, J., Conceição António, C., Carneiro, J., and Teixeira, V. (2004). "Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems." Comput. Mech., 35, 54-71.
5. Areias, P., Song, J.-H., and Belytschko, T. (2005a). "Analysis of fracture in thin shells by overlapping paired elements." Comput. Methods Appl. Mech. Eng.
6. Areias, P., Song, J.-H., and Belytschko, T. (2005b). "A finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints." Int. J. Numer. Methods Eng., 64, 1166-1206.
7. Atkins, A. (1996). "Fracture in forming." J. Mater. Process. Technol., 56, 609-618.
8. Barlat, F., Brem, J., Yoon, J., Chung, K., Dick, R., Lege, D., Pourgoghrat, F., Choi, S.-H., and Chu, E. (2003). "Plane stress yield function for aluminum alloy sheets. Part I: Theory." Int. J. Plast., 19, 1297-1319.
9. Bažant, Z., and Belytschko, T. (1985). "Wave propagation in a strain-softening bar: Exact solution." J. Eng. Mech., 111(3), 381-389.
10. Belytschko, T., and Black, T. (1999). "Elastic crack growth in finite elements with minimal remeshing." Int. J. Numer. Methods Eng., 45, 601-620.
11. Belytschko, T., Liu, W., and Moran, B. (2000). Nonlinear finite elements for continua and structures, Wiley, New York.
12. Belytschko, T., Moës, N., Usui, S., and Parimi, C. (2001). "Arbitrary discontinuities in finite elements." Int. J. Numer. Methods Eng., 50, 993-1013.
13. Deuflhard, P. (2004). "Newton methods for nonlinear problems." Affine invariance and adaptive algorithms, Springer, New York.
14. Gurtin, M. (1981). Topics infinite elasticity, SIAM.
15. Han, C.-S., Chung, K., Wagoner, R., and Oh, S.-I. (2003). "A multiplicative finite elastoplastic formulation with anisotropic yield functions." Int. J. Plast., 19, 197-211.
16. Hansbo, A., and Hansbo, P. (2004). "A finite element method for the simulation of strong and weak discontinuities in solid mechanics." Comput. Methods Appl. Mech. Eng., 193, 3523-3540.
17. Hartmann, S. (2003). "Computational aspects of the symmetric eigen-value problem of second order tensors." Technische Mechanik, 23, 283-294.
18. Irons, B. (1976). "The semiloof shell element." Finite elements for thin shells and curved members, Wiley, New York, 197-222.
19. Lee, Y.-W., Woertz, J., and Wierzbicki, T. (2004). "Fracture prediction of thin plates under hemi-spherical punch with calibration and experimental verification." Int. J. Mech. Sci., 46, 751-781.
20. Lin, R. (2002). "Numerical study of consistency of rate constitutive equations with elasticity at finite deformations." Int. J. Numer. Methods Eng., 55, 1053-1077.
21. Lubliner, J. (1990). Plasticity theory, Macmillan, New York.
22. Mergheim, J., Kuhl, E., and Steinmann, P. (2005). "A finite element method for the computational modeling of cohesive cracks." Int. J. Numer. Methods Eng., 63, 276-289.
23. Moës, N., and Belytschko, T. (2002). "Extended finite element method for cohesive crack growth." Eng. Fract. Mech., 69, 813-833.
24. Moës, N., Dolbow, J., and Belytschko, T. (1999). "A finite element method for crack growth without remeshing." Int. J. Numer. Methods Eng., 46, 131-150.
25. Moës, N., Gravouil, A., and Belytschko, T. (2002). "Non-planar 3D crack growth by the extended finite element and level sets. Part I: Mechanical model." Int. J. Numer. Methods Eng., 53, 2549-2568.
26. Montáns, F., and Bathe, K.-J. (2005). "Computational issues in large-strain elasto-plasticity: An algorithm for mixed hardening and plastic spin." Int. J. Numer. Methods Eng.. 63, 159-196.
27. Noor, A. (1999). "Computational structures technology: Leap frogging into the twenty-first century." Comput. Struct., 73, 1-31.
28. Simo, J. (1992). "Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory." Comput. Methods Appl. Mech. Eng., 99, 61-112.
29. Tugcu, P., and Neale, K. (1999). "On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming." Int. J. Plast., 15, 1021-1040.
30. Tugcu, P., Wu, P., and Neale, K. (1999). "Finite strain analysis of simple shear using recent anisotropic yield criteria." Int. J. Plast., 15, 939-962.
31. Wierzbicki, T., Bao, Y., Lee, Y.-W., and Bai, Y. (2005). "Calibration and evaluation of seven fracture models." Int. J. Mech. Sci., 47, 719-743.