Technical Papers
Jul 17, 2020

Multiple Crack Propagation and Coalescence in Finite Elements with Minimal Local Remeshing Using the Subregion Generalized Variational Principle

Publication: Journal of Engineering Mechanics
Volume 146, Issue 10

Abstract

Multiple crack propagation and coalescence in two-dimensional linear elastic media were modeled using the finite-element method (FEM) in conjunction with the subregion generalized variational principle. The proposed approach computes the stress intensity factor (SIF) accurately, as proved in a previous work. The approach results in regular geometric meshes. A multiple crack propagation scheme was developed in this study. The scheme follows the crack propagation by moving just the complementary energy subregion on the basis of the regular mesh. Consequently, it requires only minimal local remeshing without affecting most of the existing mesh. The scheme can handle crack coalescence easily. These advantages simplify the modeling and thus improve the efficiency. Four numerical examples, including a structure containing 10 cracks, were investigated to demonstrate the accuracy and efficiency of the proposed approach.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request, including computer codes of all the numerical examples.

References

Agathos, K., S. P. A. Bordas, and E. Chatzi. 2019. “Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization.” Comput. Methods Appl. Mech. Eng. 346 (Apr): 1051–1073. https://doi.org/10.1016/j.cma.2018.08.007.
Andrade, H. C., and E. D. Leonel. 2019. “The multiple fatigue crack propagation modelling in nonhomogeneous structures using the DBEM.” Eng. Anal. Boundary Elem. 98 (Jan): 296–309. https://doi.org/10.1016/j.enganabound.2018.10.026.
Areias, P., T. Rabczuk, and P. P. Camanho. 2014. “Finite strain fracture of 2D problems with injected anisotropic softening elements.” Theor. Appl. Fract. Mech. 72 (Aug): 50–63. https://doi.org/10.1016/j.tafmec.2014.06.006.
Azadi, H., and A. R. Khoei. 2011. “Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing.” Int. J. Numer. Methods Eng. 85 (8): 1017–1048. https://doi.org/10.1002/nme.3002.
Belytschko, T., D. Organ, and Y. Krongauz. 1995. “A coupled finite element-element-free Galerkin method.” Comput. Mech. 17 (3): 186–195. https://doi.org/10.1007/BF00364080.
Bittencourt, T. N., P. A. Wawrzynek, A. R. Ingraffea, and J. L. Sousa. 1996. “Quasi-automatic simulation of crack propagation for 2D LEFM problems.” Eng. Fract. Mech. 55 (2): 321–334. https://doi.org/10.1016/0013-7944(95)00247-2.
Bouchard, P. O., F. Bay, and Y. Chastel. 2003. “Numerical modelling of crack propagation: Automatic remeshing and comparison of different criteria.” Comput. Methods Appl. Mech. Eng. 192 (35–36): 3887–3908. https://doi.org/10.1016/S0045-7825(03)00391-8.
Budyn, É., G. Zi, N. Moës, and T. Belytschko. 2004. “A method for multiple crack growth in brittle materials without remeshing.” Int. J. Numer. Methods Eng. 61 (10): 1741–1770. https://doi.org/10.1002/nme.1130.
Chevaugeon, N., N. Moës, and H. Minnebo. 2013. “Improved crack tip enrichment functions and integration for crack modeling using the extended finite element method.” Int. J. Multiscale Comput. Eng. 11 (6): 597–631. https://doi.org/10.1615/IntJMultCompEng.2013006523.
Davis, P. J., and P. Rabinowitz. 2007. Methods of numerical integration. New York: Dover.
De Luycker, E., D. J. Benson, T. Belytschko, Y. Bazilevs, and M. C. Hsu. 2011. “X-FEM in isogeometric analysis for linear fracture mechanics.” Int. J. Numer. Methods Eng. 87 (6): 541–565. https://doi.org/10.1002/nme.3121.
Erdogan, F., and G. C. Sih. 1963. “On the crack extension in plates under plane loading and transverse shear.” J. Basic Eng. 85 (4): 519–525. https://doi.org/10.1115/1.3656897.
Garg, S., and M. Pant. 2018. “Meshfree methods: A comprehensive review of applications.” Int. J. Comput. Methods 15 (4): 1830001. https://doi.org/10.1142/S0219876218300015.
Ghorashi, S. S., N. Valizadeh, and S. Mohammadi. 2012. “Extended isogeometric analysis for simulation of stationary and propagating cracks.” Int. J. Numer. Methods Eng. 89 (9): 1069–1101. https://doi.org/10.1002/nme.3277.
Gupta, V., C. A. Duarte, I. Babuška, and U. Banerjee. 2015. “Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics.” Comput. Methods Appl. Mech. Eng. 289 (Jun): 355–386. https://doi.org/10.1016/j.cma.2015.01.014.
Karihaloo, B. L., and Q. Z. Xiao. 2003. “Modelling of stationary and growing cracks in FE framework without remeshing: A state-of-the-art review.” Comput. Struct. 81 (3): 119–129. https://doi.org/10.1016/S0045-7949(02)00431-5.
Khoei, A. R., R. Yasbolaghi, and S. O. R. Biabanaki. 2015. “A polygonal finite element method for modeling crack propagation with minimum remeshing.” Int. J. Fract. 194 (2): 123–148. https://doi.org/10.1007/s10704-015-0044-z.
Leonel, E. D., and W. S. Venturini. 2011. “Multiple random crack propagation using a boundary element formulation.” Eng. Fract. Mech. 78 (6): 1077–1090. https://doi.org/10.1016/j.engfracmech.2010.11.012.
Li, W., N. Nguyen-Thanh, J. Huang, and K. Zhou. 2020. “Adaptive analysis of crack propagation in thin-shell structures via an isogeometric-meshfree moving least-squares approach.” Comput. Methods Appl. Mech. Eng. 358 (Jan): 112613. https://doi.org/10.1016/j.cma.2019.112613.
Liao, M., X. Deng, and Z. Guo. 2018. “Crack propagation modelling using the weak form quadrature element method with minimal remeshing.” Theor. Appl. Fract. Mech. 93 (Feb): 293–301. https://doi.org/10.1016/j.tafmec.2017.09.012.
Liao, M., and D. Dong. 2018. “An accurate and efficient approach coupling quadrature element method and subregion generalized variational principle for fatigue crack growth modelling.” Theor. Appl. Fract. Mech. 96 (Aug): 452–460. https://doi.org/10.1016/j.tafmec.2018.06.008.
Liao, M., A. Tang, Y. G. Hu, and Z. Guo. 2015. “Computation of coefficients of crack-tip asymptotic fields using the weak form quadrature element method.” J. Eng. Mech. 141 (8): 04015018. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000904.
Liao, M., and P. Zhang. 2019. “An improved approach for computation of stress intensity factors using the finite element method.” Theor. Appl. Fract. Mech. 101 (Jun): 185–190. https://doi.org/10.1016/j.tafmec.2019.02.019.
Liu, Y. J., Y. X. Li, and W. Xie. 2017. “Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method.” Eng. Fract. Mech. 172 (Mar): 1–16. https://doi.org/10.1016/j.engfracmech.2017.01.010.
Long, Y. 1981. “Piecewise generalized variation principles in elasticity.” Chin. Q. Mech. 2: 1–9. https://doi.org/10.15959/j.cnki.0254-0053.1981.02.005.
Memari, A., and H. Mohebalizadeh. 2019. “Quasi-static analysis of mixed-mode crack propagation using the meshless local Petrov–Galerkin method.” Eng. Anal. Boundary Elem. 106 (Sep): 397–411. https://doi.org/10.1016/j.enganabound.2019.05.030.
Moës, N., J. Dolbow, and T. Belytschko. 1999. “A finite element method for crack growth without remeshing.” Int. J. Numer. Methods Eng. 46 (1): 131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1%3C131::AID-NME726%3E3.0.CO;2-J.
Nguyen-Thanh, N., and K. Zhou. 2017. “Extended isogeometric analysis based on PHT-splines for crack propagation near inclusions.” Int. J. Numer. Methods Eng. 112 (12): 1777–1800. https://doi.org/10.1002/nme.5581.
Ooi, E. T., C. Song, F. Tin-Loi, and Z. Yang. 2012. “Polygon scaled boundary finite elements for crack propagation modelling.” Int. J. Numer. Methods Eng. 91 (3): 319–342. https://doi.org/10.1002/nme.4284.
Ramalho, L. D. C., J. Belinha, and R. D. S. G. Campilho. 2019. “The numerical simulation of crack propagation using radial point interpolation meshless methods.” Eng. Anal. Boundary Elem. 109 (Dec): 187–198. https://doi.org/10.1016/j.enganabound.2019.10.001.
Rao, B. N., and S. Rahman. 2001. “A coupled meshless-finite element method for fracture analysis of cracks.” Int. J. Press. Vessels Pip. 78 (9): 647–657. https://doi.org/10.1016/S0308-0161(01)00076-X.
Williams, M. L. 1952. “Stress singularities resulting from various boundary conditions in angular corners of plates in extension.” J. Appl. Mech. 19 (4): 526–528.
Williams, M. L. 1957. “On the stress distribution at the base of a stationary crack.” J. Appl. Mech. 24 (1): 109–114. https://doi.org/10.1115/1.3640470.
Xiao, Q. Z., and B. L. Karihaloo. 2007. “Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM.” Comput. Methods Appl. Mech. Eng. 196 (13–16): 1864–1873. https://doi.org/10.1016/j.cma.2006.09.022.
Yang, Z. 2006. “Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method.” Eng. Fract. Mech. 73 (12): 1711–1731. https://doi.org/10.1016/j.engfracmech.2006.02.004.
Yang, Z. J., X. F. Wang, D. S. Yin, and C. Zhang. 2015. “A non-matching finite element-scaled boundary finite element coupled method for linear elastic crack propagation modelling.” Comput. Struct. 153 (Jun): 126–136. https://doi.org/10.1016/j.compstruc.2015.02.034.
Yau, J. F., S. S. Wang, and H. T. Corten. 1980. “A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity.” J. Appl. Mech. 47 (2): 335–341. https://doi.org/10.1115/1.3153665.
Zhu, H., P. Sun, and Y. Cai. 2017. “Independent cover meshless method for the simulation of multiple crack growth with arbitrary incremental steps and directions.” Eng. Anal. Boundary Elem. 83 (Oct): 242–255. https://doi.org/10.1016/j.enganabound.2017.08.005.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 146Issue 10October 2020

History

Received: Jan 4, 2020
Accepted: May 26, 2020
Published online: Jul 17, 2020
Published in print: Oct 1, 2020
Discussion open until: Dec 17, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

Associate Professor, School of Civil Engineering, Chongqing Univ., No. 83 Shapingba North St., Chongqing 400045, China (corresponding author). ORCID: https://orcid.org/0000-0002-8982-5994. Email: [email protected]
Pan Zhang
M.S. Graduate, School of Civil Engineering, Chongqing Univ., No. 83 Shapingba North St., Chongqing 400045, China.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share