Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T20:10:43.270Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Analysis Applied to Nonlinear Problems

Published online by Cambridge University Press:  01 October 2015

E. Pineda León ,
A. Rodríguez-Castellanos  and
M.H. Aliabadi
E. Pineda León
Affiliation:
Escuela Superior de Ingeniería y Arquitectura, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos s/n, México D.F.
A. Rodríguez-Castellanos
Affiliation:
Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A Madero, México D.F.
M.H. Aliabadi
Affiliation:
Department of Aeronautical Engineering, Imperial College London, South Kensington campus, London SW72AZ
Get access

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.

Keywords

Non-linear analysisboundary element methodfracture mechanics
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1765: Symposium 4A – Advanced Structural Materials—2014 , 2015 , pp. 51 - 57
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aliabadi, M.H., in The Boundary Element Method 2, Applications in Solids and Structures, (John Wiley & Sons, UK, 2002).Google Scholar
Aliabadi, M.H., Int. J. Fract. 86, 91–125 (1997).CrossRefGoogle Scholar
Aliabadi, M.H., Appl. Mech. Review 50, 83–96 (1997).CrossRefGoogle Scholar
Aliabadi, M.H. and Portela, A., in Boundary Element Technology VII, (Computational Mechanics Publications, Southampton, 1992) pp. 607–616.CrossRefGoogle Scholar
Bassani, J.L. and McClintock, F.A., Int. J. Solids Struct. 17, 479–492 (1981).CrossRefGoogle Scholar
Becker, A.A. and Hyde, T.H., NAFEMS Report R0027, 1993.Google Scholar
Chao, Y.J., Zhu, X.K. and Zhang, L., Int. J. Solids Struct. 38, 3853–3875 (2001).CrossRefGoogle Scholar
Cisilino, A.P. and Aliabadi, M.H., Int. J. Pres. Ves. Pip. 70, 135–144 (1997).CrossRefGoogle Scholar
Cisilino, A.P., Aliabadi, M.H. and Otegui, J.L., Int. J. Numer. Meth. Eng. 42, 237–256 (1998).3.0.CO;2-6>CrossRefGoogle Scholar
Cisilino, A.P. and Aliabadi, M.H., Eng. Fract. Mech. 63, 713–733 (1999).CrossRefGoogle Scholar
Ehlers, R. and Riedel, H., in A Finite Element Analysis of Creep Deformation in a Specimen Containing a Microscopic Crack, edited by Francois, D., (Advances in Fracture Research, Proc. Fifth. Int. Conf. on Fracture 2, Pergamon, New York, 1981) pp. 691–698.Google Scholar
Hutchinson, J.W., J. Mech. Phys. Solids 16, 13–31 (1968).CrossRefGoogle Scholar
Leitao, V., Aliabadi, M.H., Rooke, D.P., Int. J. Numer. Meth. Eng. 38, 315–333 (1995).CrossRefGoogle Scholar
Li, F.Z., Needlemen, A. and Shih, C.F., Int. J. Fract. 36, 163–186 (1988).Google Scholar
Mendelson, A., NASA Report No. TN D-7418, 1973.Google Scholar
Mi, Y. and Aliabadi, M.H., Eng. Anal. Bound. Elem. 10, 161–171 (1992).CrossRefGoogle Scholar
Oden, J.T., in Finite Elements of Nonlinear Continua, (McGraw-Hill, New York, 1972).Google Scholar
Ohji, K., Ogura, K. and Kubo, S., JSME 790, 18–20 (1979).Google Scholar
Portela, A., Aliabadi, M.H. and Rooke, D.P., Int. J. Numer. Meth. Eng. 33, 1269–1287 (1992).CrossRefGoogle Scholar
Providakis, C.P. and Kourtakis, S.G., Comput. Mech. 29, 298–306 (2002).CrossRefGoogle Scholar
Riccardella, P., PhD Thesis, Carnegie Mellon University, 1973.Google Scholar
Rice, J.R. and Rosengren, G.F., J. Mech. Phys. Solids 16, 1–12 (1968).CrossRefGoogle Scholar
Riedel, H. and Rice, J.R., in Fracture Mechanics: 12th Conference, (ASTM STP 700, Philadelphia, PA, 1980) pp. 112–130.CrossRefGoogle Scholar
Swedlow, J.L. and Cruse, T.A., Int. J. Solids Struct. 7, 1673–1681 (1971).CrossRefGoogle Scholar
Telles, J.C.F. and Brebbia, C.A., Int. J. Mech. Sci. 24, 605–618 (1982).CrossRefGoogle Scholar