An efficient numerical method for quasi-static crack propagation in heterogeneous media
Source abstract
Abstract
The paper is devoted to the problem of slow crack growth in heterogeneous media. The crack is subjected to arbitrary pressure distribution on the crack surface. The problem relates to construction of the so-called equilibrium crack. For such a crack, stress intensity factors are equal to the material fracture toughness at each point of the crack contour. The crack shape and size depend on spatial distributions of the elastic properties and fracture toughness of the medium, and the type of loading. In the paper, attention is focused on the case of layered elastic media when a planar crack propagates orthogonally to the layers. The problem is reduced to a system of surface integral equations for the crack opening vector and volume integral equations for stresses in the medium. For discretization of these equations, a regular node grid and Gaussian approximating functions are used. For iterative solution of the discretized equations, fast Fourier transform technique is employed. An iteration process is proposed for the construction of the crack shape in the process of crack growth. Examples of crack evolution for various properties of medium and types of loading are presented.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Contact Mechanics and Variational Inequalities · Elasticity and Wave Propagation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (28)
Show source-provided references
1. Duarte C, Hamzeh O, Liszka T, Tworzydlo W (2001) A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Comput Methods Appl Mech Eng 190(15):2227–226210.1016/S0045-7825(00)00233-4 ↗
2. Fries T, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84(3):253–30410.1002/nme.2914 ↗
3. Gao H, Rice J (1989) A first-order perturbation analysis of crack trapping by arrays of obstacles. J Appl Mech 56:828–83610.1115/1.3176178 ↗
4. Golub G, van Loan C (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, London
5. Kanaun S (1981) Elastic problem for 3D-anisotropic medium with a crack. Appl Math Mech (PMM) 45:361–37010.1016/0021-8928(81)90045-9 ↗
6. Kanaun S (2007) Fast solution of the 3D elasticity problem for a planar crack of arbitrary shape. Int J Fract 148:435–44210.1007/s10704-008-9208-4 ↗
7. Kanaun S (2017) Hydraulic fracture crack propagation in an elastic medium with varying fracture toughness. Int J Eng Sci 120:15–3010.1016/j.ijengsci.2017.06.009 ↗
8. Kanaun S, Levin V (2008) Self-consistent methods for composites I, static problems. Springer, Dordrecht
9. Kanaun S, Markov A (2017) Discrete and three-parameter models of hydraulic fracture crack growth. WSEAS Trans Appl Theor Mech 12:147–156
10. Kanaun S, Pervago E (2011) Combining self-consistent and numerical methods for the calculation of elastic fields and effective properties of 3D-matrix composites with periodic and random microstructures. Int J Eng Sci 49(5):420–44210.1016/j.ijengsci.2011.01.001 ↗
11. Kanaun S, Markov A, Babaii S (2013) An efficient numerical method for the solution of the second boundary problem of elasticity for 3D-bodies with cracks. Int J Fract 183(2):169–18610.1007/s10704-013-9885-5 ↗
12. Knight M, Wrobel L, Henshall J, De Lacerda L (2002) A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. Int J Fract 114(1):47–6110.1023/A:1014837509347 ↗
13. Kunin I (1983) The theory of elastic media with microstructure II. Springer, Berlin
14. Lei J, Wang Y, Huang Y, Yang Q, Zhang C (2012) Dynamic crack propagation in matrix involving inclusions by a time-domain BEM. Eng Anal Bound Elem 36(5):651–65710.1016/j.enganabound.2011.12.005 ↗
15. Markov A, Kanaun S (2017) Interactions of cracks and inclusions in homogeneous elastic media. Int J Fract 206(1):35–4810.1007/s10704-017-0199-x ↗
16. Maz’ya V, Schmidt G (2007) Approximate approximation, mathematical surveys and monographs, vol 141. American Math Society, Providence10.1090/surv/141 ↗
17. Mi Y, Aliabadi M (1994) Three-dimensional crack growth simulation using BEM. Comput Struct 52(5):871–87810.1016/0045-7949(94)90072-8 ↗
18. Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69(7):813–83310.1016/S0013-7944(01)00128-X ↗
19. Moes N, Dolbow J, Belytschko T (1999) Elastic crack growth in finite elements without remeshing. Int J Numer Methods Eng 46:131–15010.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J ↗
20. Movchan A, Gao H, Willis J (1998) On perturbations of plane cracks. Int J Solids Struct 35(26–27):3419–345310.1016/S0020-7683(97)00231-X ↗
21. Press W, Flannery B, Teukolsky S, Wetterling W (1992) Numerical recipes in FORTRAN: the art of scientific computing. Cambridge University Press, Cambridge
22. Ramanathan S, Ertas D, Fisher D (1997) Quasistatic crack propagation in heterogeneous media. Phys Rev Lett 79(5):873–87710.1103/PhysRevLett.79.873 ↗
23. Remmers J, de Borst R, Needleman A (2003) A cohesive segments method for the simulation of crack growth. Comput Mech 31(1):69–7710.1007/s00466-002-0394-z ↗
24. Sneddon I (1946) The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc R Soc Lond 187(1009):229–26010.1098/rspa.1946.0077 ↗
25. Sukumar N, Moes N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Methods Eng 48(11):1549–157010.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A ↗
26. Williams R, Phan A, Tippur H, Kaplan T, Gray L (2007) SGBEM analysis of crack-particle(s) interactions due to elastic constants mismatch. Eng Fract Mech 74(3):314–33110.1016/j.engfracmech.2006.06.004 ↗
27. Yang B, Ravi-Chandar K (1998) A single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks. In: Recent advances in fracture mechanics, pp 115–144. Springer, Netherlands10.1007/978-94-017-2854-6_7 ↗
28. Zhuang Z, Cheng B (2011) Equilibrium state of mode-I sub-interfacial crack growth in bi-materials. Int J Fract 170(1):27–3610.1007/s10704-011-9599-5 ↗