Improving the Extended Finite Element Method in the Crack Problems via the Remeshing Process

Document Type : پژوهشی

Authors

• Hamid Moslemi
• Kamran Modabber

Shahed University

10.22067/civil.v32i1.60546

Abstract

Challenging and complex nature of the numerical analysis of crack problems have attracted the interest of many researchers in past decades and several techniques have been proposed for these problems. One of these techniques is the extended finite element method in which the crack tip field modeling is improved by enrichment of shape functions and the crack can intersect the elements. On the other hand, we have adaptive finite element method which aims to improve the accuracy of displacement and stress fields near the crack tip by remeshing process. Researchers have  reported the drawbacks of each of these two techniques. In this paper the drawbacks of the previous techniques are covered with proper combination of these two techniques. By this combination the crack can pass through the elements and there is no need for crack tracking by mesh. In addition the estimated error is limited to desirable bands and stress intensity factor can be computed numerically with acceptable accuracy.

Keywords

• Extended finite element method
• Crack problems
• Adaptive finite element method
• Enrichment functions, Remeshing

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References

1. Melenk, JM., Babuška, I, "The Partition of Unity Finite Element Method: Basic Theory and Applications", Comp Methods Appl Mech Eng. Vol. 139, No. 1, pp. 289-314, (1996).

2. Mohammadi, S., "Extended Finite Element, Method for Fracture Analysis of Structures", 1st edn. Black well Publishing Ltd. (2008).

3. Sundararajan, N., "Enriched Finite Element Methods: Advances & Applications", Cardiff University. (2011).

4. Moes, N., Dolbow, J., Belytschko, T., "A Finite Element Method for Crack Growth without Remeshing", Int. J. Numer. Methods Eng. Vol. 46, No. 1, pp. 133–150, (1999).

5. Dolbow, J., "An Extended Finite Element Method with Discontinuous Enrichment for Applied Mechanics", Northwestern university, (1999).

6. Babuška, I., Rheinboldt, W.C., "A‐posteriori Error estimates for the Finite Element Method", Int. J. Numer. Methods Eng. Vol. 12, No. 10, pp. 1597-1615, (1978).

7. Zienkiewicz, O.C., Boroomand, B., Zhu, J.Z., Recovery Procedures in Error Estimation and Adaptivity Part I: Adaptivity in linear problems. Comp Methods Appl Mech Eng. Vol. 176, No. 1, pp. 111-125, (1999).

8. Zienkiewicz, O.C., Taylor, R.L., "The Finite Element Method for Solid and Structural Mechanics", Butterworth-heinemann, (2005).

9. Sih, G., Paris, C.P., Irwin, G.R., "On Cracks in Rectilinearly Anisotropic Bodies", Int. J. of Fract Mech. Vol. 1, No. 3, pp. 189-203, (1965).

10. Paulino., GH., Kim, J.H., A New Approach to Compute T-stress in Functionally Graded Materials by means of the Ineraction Integral Method on Cracks in Rectilinearly Anisotropic Bodies, Eng. Fract Mech, Vol. 71, No. 1, pp. 1907-1950, (2004).

11. Unger, J.F., Eckardt, S., Könke, C., Modelling of Cohesive Crack Growth in Concrete Structures with the Extended Finite Element, Comp Methods Appl Mech Eng. Vol. 196, No. 4, pp. 4087-4100, (2007).