Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T09:03:36.687Z Has data issue: false hasContentIssue false
  • English
  • Français

XFEM for Fracture Analysis in 2D Anisotropic Elasticity

Part of: Generalities, axiomatics, foundations of continuum mechanics of solids Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  11 October 2016

Honggang Jia ,
Yufeng Nie  and
Junlin Li
Honggang Jia
Affiliation:
School of Mathematics and Statistics, Xuchang University, Xuchang, Henan 461000, China Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, China
Yufeng Nie*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, China
Junlin Li
Affiliation:
School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, Shanxi 030024, China
*
*Corresponding author. Email:yfnie@nwpu.edu.cn (Y. F. Nie)
Get access

Abstract

In this paper, a method is proposed for extracting fracture parameters in anisotropic thermoelasticity cracking via interaction integral method within the framework of extended finite element method (XFEM). The proposed method is applied to linear thermoelastic crack problems. The numerical results of the stress intensity factors (SIFs) are presented and compared with those reported in related references. The good agreement of the results obtained by the developed method with those obtained by other numerical solutions proves the applicability of the proposed approach and confirms its capability of efficiently extracting thermoelasticity fracture parameters in anisotropic materials.

Keywords

Anisotropic materialsthermoelasticitycrackXFEMstress intensity factors

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 74A45: Theories of fracture and damage
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 125 - 143
Copyright
Copyright © Global-Science Press 2017 

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

[1] Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, 2nd edn, Noordhoff, Leiden, 1953.Google Scholar
[2] Sih, G. C., Paris, P. and Irwin, G., On cracks in rectilinearly anisotropic bodies, Int. J. Fract. Mech., 1 (1965), pp. 189–203.Google Scholar
[3] Suo, Z., Singularities, interfaces and cracks in dissimilar anisotropic media, Proc. R. Soc. Lond. A, 427 (1990), pp. 331–358.Google Scholar
[4] Nobile, L. and Carloni, C., Fracture analysis for orthotropic cracked plates, Compos. Struct, 68 (2005), pp. 285–293.Google Scholar
[5] Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body, Science Press, Beijing, 1963.Google Scholar
[6] Zhang, S. Q. and Yang, W. Y., Prediction of mode I crack propagation direction in carbon-fiber reinforced composite plate, Appl. Math. Mech., 25 (2004), pp. 714–721.Google Scholar
[7] Jia, H. G., Nie, Y. F. and Li, J. L., Fracture analysis in orthotropic thermoelasticity using extended finite element method, Adv. Appl. Math. Mech., 7 (2015), pp. 780–795.Google Scholar
[8] Chang, J. H. and Liao, G. J., Nonhomogenized displacement discontinuity dethod for calculation of stree intensity factors for cracks in anisotropic FGMs, J. Eng. Mech., 140 (2014).CrossRefGoogle Scholar
[9] Cetisli, F. K. and Mete, O., Numerical analysis of interface crack prooblem in composite plates jointed with composite patch, Steel. Compos. Struct., 16 (2014), pp. 203–220.Google Scholar
[10] Prasad, N. N. V., Aliabadi, M. H. and Rooke, D. P., The dual boundary element method for thermoelastic crack problems, Int. J. Fract., 47 (2009), pp. 1926–1938.Google Scholar
[11] Tafreshi, A., Fracture mechanics analysis of composite structures using the boundary element shape sensitivities, AIAA. J., 23 (1999), pp. 87–96.Google Scholar
[12] Pasternak, I., Boundary integral equations and the boundary element method for fracture mechanics analysis in 2D anisotropic thermoelasticity, Eng. Anal. Bound. Elem., 36 (2012), pp. 1931–1941.Google Scholar
[13] Shiah, Y. C. and Tan, C. L., Fracture mechanics analysis in 2-D anisotropic thermoelasticity using BEM, Comp. Model. Eng., 3 (2000), pp. 91–99.Google Scholar
[14] Rajesh, K. N. and Rao, B. N., Two-dimensional analysis of anisotropic crack problems using coupled meshless and fractal finite element method, Int. J. Fract., 164 (2010), pp. 285–318.CrossRefGoogle Scholar
[15] Belinha, J. and Dinis, L. M. J. S., Nonlinear analysis of plates and laminates using the element free Galerkin method, Compos. Struct., 78 (2007), pp. 337–350.Google Scholar
[16] Bouhala, L., Makradi, A. and Belouettar, S., Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method, Eng. Fract. Mech., 88 (2012), pp. 35–48.Google Scholar
[17] Asadpoure, A. and Mohammadi, S., Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method, Int. J. Numer. Meth. Eng., 69 (2007), pp. 2150–2172.Google Scholar
[18] Hattori, G., Rojas-Díaz, R., Sáez, A., Sukumar, N. and García-Sánchez, F., New anisotropic crack-tip enrichment functions for the extended finite element method, Comput. Mech., 50 (2012), pp. 591–601.Google Scholar
[19] Duflot, M., The extended finite element method in thermoelastic fracture mechanics, Int. J. Numer. Meth. Eng., 74 (2008), pp. 827–847.CrossRefGoogle Scholar
[20] Hosseini, S., Bayesteh, H. and Mohammadi, S., Thermo-mechanical xfem crack propagation analysis of functionally graded materials, Math. Sci. Eng. A, 561 (2013), pp. 285–302.Google Scholar
[21] Ozkan, U., Nied, H. F. and Kaya, A. C., Fracture analysis of anisotropic materials using enriched crack tip elements, Eng. Fract. Mech., 77 (2010), pp. 1191–1202.Google Scholar
[22] Bayesteh, H., Afshar, A. and Mohammadi, S., Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method, Euro. J. Mech. A-Solid, 51 (2015), pp. 123–139.Google Scholar
[23] Mohammadi, S., Extended Finite Element Method for Fracture Analysis of Structures, Blackwell, UK, 2008.CrossRefGoogle Scholar
[24] Chen, J., Determination of thermal stress intensity factors for an interface crack in a graded orthotropic coating substrate structure, Int. J. Fract., 133 (2005), pp. 302–328.CrossRefGoogle Scholar
[25] Moës, N., Dolbow, J. and Belytschko, T., A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng., 46 (1999), pp. 131–150.3.0.CO;2-J>CrossRefGoogle Scholar
[26] Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35 (1968), pp. 379–386.CrossRefGoogle Scholar
[27] Stroh, A., Dislocation and cracks in anisotrpic elasticity, Philos. Mag., 3 (1958), pp. 625–646.Google Scholar
[28] Ting, T. C. T., Anisotropic Elasticity, Oxford University Press, New York, 1996.CrossRefGoogle Scholar
[29] Hwu, C., Anisotropic Elastic Plates, Springer, London, 2010.Google Scholar
[30] Bordas, S., Nguyen, P. V., Dunant, C., Guidoum, A. and Nguyen-Dang, H., An extended finite element library, Int. J. Numer. Meth. Eng., 71 (2007), pp. 703–732.Google Scholar