Abstract
The present paper shows the applicability of the Dual Boundary Element Method to analyze plastic, visco-plastic and creep behavior in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate are analyzed. Special attention is taken when the discretization of the domain is done. In Fact, for the plasticity and viscoplasticity cases only the region susceptible to yielding was discretized, whereas, the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study this kind of non-linear problems. Results from the present formulation are compared to those of the well-established Finite Element Technique, and they are in good agreement. Important fracture mechanic parameters such as KI, KII, J- and C- integrals are also included. In general, the results, for the plastic, visco-plastic and creep cases, show that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M.H. Aliabadi, in The Boundary Element Method 2, Applications in Solids and Structures, (John Wiley & Sons, UK, 2002).
M.H. Aliabadi, Int. J. Fract. 86, 91–125 (1997).
M.H. Aliabadi, Appl. Mech. Review 50, 83–96 (1997).
M.H. Aliabadi and A. Portela, in Boundary Element Technology VII, (Computational Mechanics Publications, Southampton, 1992) pp. 607–616.
J.L. Bassani and F.A. McClintock, Int. J. Solids Struct. 17, 479–492 (1981).
A.A. Becker and T.H. Hyde, NAFEMS Report R0027, 1993.
Y.J. Chao, X.K. Zhu and L. Zhang, Int. J. Solids Struct. 38, 3853–3875 (2001).
A.P. Cisilino and M.H. Aliabadi, Int. J. Pres. Ves. Pip. 70, 135–144 (1997).
A.P. Cisilino, M.H. Aliabadi and J.L. Otegui, Int. J. Numer. Meth. Eng. 42, 237–256 (1998).
A.P. Cisilino and M.H. Aliabadi, Eng. Fract. Mech. 63, 713–733 (1999).
R. Ehlers and H. Riedel, in A Finite Element Analysis of Creep Deformation in a Specimen Containing a Microscopic Crack, edited by D. Francois, (Advances in Fracture Research, Proc. Fifth. Int. Conf. on Fracture 2, Pergamon, New York, 1981) pp. 691–698.
J.W. Hutchinson, J. Mech. Phys. Solids 16, 13–31 (1968).
V. Leitao, M.H. Aliabadi, D.P. Rooke, Int. J. Numer. Meth. Eng. 38, 315–333 (1995).
F.Z. Li, A. Needlemen and C.F. Shih, Int. J. Fract. 36, 163–186 (1988).
A. Mendelson, NASA Report No. TN D-7418, 1973.
Y. Mi and M.H. Aliabadi, Eng. Anal. Bound. Elem. 10, 161–171 (1992).
J.T. Oden, in Finite Elements of Nonlinear Continua, (McGraw-Hill, New York, 1972).
K. Ohji, K. Ogura and S. Kubo, JSME 790, 18–20 (1979).
A. Portela, M.H. Aliabadi and D.P. Rooke, Int. J. Numer. Meth. Eng. 33, 1269–1287 (1992).
C.P. Providakis and S.G. Kourtakis, Comput. Mech. 29, 298–306 (2002).
P. Riccardella, PhD Thesis, Carnegie Mellon University, 1973.
J.R. Rice and G.F. Rosengren, J. Mech. Phys. Solids 16, 1–12 (1968).
H. Riedel and J.R. Rice, in Fracture Mechanics: 12th Conference, (ASTM STP 700, Philadelphia, PA, 1980) pp. 112–130.
J.L. Swedlow and T.A. Cruse, Int. J. Solids Struct. 7, 1673–1681 (1971).
J.C.F. Telles and C.A. Brebbia, Int. J. Mech. Sci. 24, 605–618 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
León, E.P., Rodríguez-Castellanos, A. & Aliabadi, M. Numerical Analysis Applied to Nonlinear Problems. MRS Online Proceedings Library 1765, 51–57 (2015). https://doi.org/10.1557/opl.2015.806
Published:
Issue Date:
DOI: https://doi.org/10.1557/opl.2015.806