Asymptotic path-independent integrals for the evaluation of crack-tip parameters in a neo-Hookean material
Source abstract
Abstract
In this paper, we develop new asymptotic path-independent integrals for the evaluation of the crack tip parameters in a 2D neo-Hookean material. The new integrals are of both J-integral and interaction energy integral type and rely on the separation of the asymptotic boundary value problem into independent problems for each of the deformed coordinates. Both the plane stress and plane strain cases are considered. The integrals developed are used to compute the amplitude parameters of the asymptotic crack tip fields, which allows for direct extraction of these parameters from numerical results. A long strip with an edge crack under mixed loading modes is considered for both homogeneous and biomaterial cases. It is found that the asymptotic J-integrals produce good results for the first-order parameters while the interactions integrals produce good results for both the first and second-order parameters.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Fatigue and fracture mechanics · Ultrasonics and Acoustic Wave Propagation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (32)
Show source-provided references
1. Arfaoui M, Trifa M, Mansouri K et al (2018) Three-dimensional singular elastostatic fields in a cracked neo-Hookean hyperelastic solid. Int J Eng Sci 128:1–11. https://doi.org/10.1016/j.ijengsci.2018.03.00610.1016/j.ijengsci.2018.03.006 ↗
2. Ayatollahi MR, Nejati M (2011) An over-deterministic method for calculation of coefficients of crack tip asymptotic field from finite element analysis. Fatigue Fract Eng Mater Struct 34:159–176. https://doi.org/10.1111/j.1460-2695.2010.01504.x10.1111/j.1460-2695.2010.01504.x ↗
3. Begley MR, Creton C, McMeeking RM (2015) The elastostatic plane strain mode I crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer. J Mech Phys Solids 84:21–38. https://doi.org/10.1016/j.jmps.2015.07.00510.1016/j.jmps.2015.07.005 ↗
4. Belytschko T, Liu WK, Moran B, Elkhodary K (2013) Nonlinear finite elements for continua and structures. John wiley & sons, New York
5. Chang JH, Li JF (2004) Evaluation of asymptotic stress field around a crack tip for Neo-Hookean hyperelastic materials. Int J Eng Sci 42:1675–1692. https://doi.org/10.1016/j.ijengsci.2004.03.00910.1016/j.ijengsci.2004.03.009 ↗
6. Geubelle PH, Knauss WG (1994a) Finite strains at the tip of a crack in a sheet of hyperelastic material: I. Homogeneous case. J Elast 35:61–98. https://doi.org/10.1007/BF0011553910.1007/BF00115539 ↗
7. Geubelle PH, Knauss WG (1994b) Finite strains at the tip of a crack in a sheet of hyperelastic material: III. General bimaterial case. J Elast 35:139–174. https://doi.org/10.1007/BF0011554110.1007/BF00115541 ↗
8. Gong JP (2010) Why are double network hydrogels so tough? Soft Matter 6:2583–2590. https://doi.org/10.1039/B924290B10.1039/B924290B ↗
9. Herrmann JM (1989) An asymptotic analysis of finite deformations near the tip of an interface-crack. J Elast 21:227–269. https://doi.org/10.1007/BF0004577910.1007/BF00045779 ↗
10. Knowles JK (1977) The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Int J Fract 13:611–639. https://doi.org/10.1007/BF0001729610.1007/BF00017296 ↗
11. Knowles JK, Sternberg E (1973) An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack. J Elast 3:67–107. https://doi.org/10.1007/BF0004581610.1007/BF00045816 ↗
12. Knowles JK, Sternberg E (1974) Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration and higher-order results. J Elast 4:201–233. https://doi.org/10.1007/BF0004926510.1007/BF00049265 ↗
13. Knowles JK, Sternberg E (1983) Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. J Elast 13:257–293. https://doi.org/10.1007/BF0004299710.1007/BF00042997 ↗
14. Lengyel TH, Qi Y, Schiavone P, Long R (2016) Interface crack between a compressible elastomer and a rigid substrate with finite slippage. J Mech Phys Solids 90:142–159. https://doi.org/10.1016/j.jmps.2016.02.00610.1016/j.jmps.2016.02.006 ↗
15. Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21:405–421. https://doi.org/10.1016/0013-7944(85)90029-310.1016/0013-7944(85)90029-3 ↗
16. Liu Y, Zhang H, Zheng Y (2015) A multiplicative finite element algorithm for the inhomogeneous swelling of polymeric gels. Comput Methods Appl Mech Eng 283:517–550. https://doi.org/10.1016/j.cma.2014.08.02910.1016/j.cma.2014.08.029 ↗
17. Long R, Hui C-Y (2015) Crack tip fields in soft elastic solids subjected to large quasi-static deformation—a review. Extreme Mech Lett 4:131–155. https://doi.org/10.1016/j.eml.2015.06.00210.1016/j.eml.2015.06.002 ↗
18. Long R, Krishnan VR, Hui C-Y (2011) Finite strain analysis of crack tip fields in incompressible hyperelastic solids loaded in plane stress. J Mech Phys Solids 59:672–695. https://doi.org/10.1016/j.jmps.2010.12.00510.1016/j.jmps.2010.12.005 ↗
19. Mirzaei AM, Ayatollahi MR, Bahrami B (2019) Asymptotic stress field and the coefficients of singular and higher order terms for V-notches with end holes under mixed-mode loading. Int J Solids Struct 172–173:51–69. https://doi.org/10.1016/j.ijsolstr.2019.05.01110.1016/j.ijsolstr.2019.05.011 ↗
20. Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Eng Fract Mech 27:615–642. https://doi.org/10.1016/0013-7944(87)90155-X10.1016/0013-7944(87)90155-X ↗
21. Nakamura T, Parks DM (1989) Antisymmetrical 3-D stress field near the crack front of a thin elastic plate. Int J Solids Struct 25:1411–1426. https://doi.org/10.1016/0020-7683(89)90109-110.1016/0020-7683(89)90109-1 ↗
22. Nakamura T, Parks DM (1992) Determination of elastic T-stress along three-dimensional crack fronts using an interaction integral. Int J Solids Struct 29:1597–1611. https://doi.org/10.1016/0020-7683(92)90011-H10.1016/0020-7683(92)90011-H ↗
23. Ravichandran G, Knauss WG (1989) A finite elastostatic analysis of bimaterial interface cracks. Int J Fract 39:235–253. https://doi.org/10.1007/BF0004745210.1007/BF00047452 ↗
24. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386. https://doi.org/10.1115/1.360120610.1115/1.3601206 ↗
25. Rivlin RS, Thomas AG (1953) Rupture of rubber. I. Characteristic energy for tearing. J Polym Sci 10:291–318. https://doi.org/10.1002/pol.1953.12010030310.1002/pol.1953.120100303 ↗
26. Shih CF, Moran B, Nakamura T (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int J Fract 30:79–102. https://doi.org/10.1007/BF0003401910.1007/BF00034019 ↗
27. Stephenson RA (1982) The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials. J Elast 12:65–99. https://doi.org/10.1007/BF0004370610.1007/BF00043706 ↗
28. Su RKL, Feng WJ (2005) Accurate determination of mode I and II leading coefficients of the Williams expansion by finite element analysis. Finite Elem Anal Des 41:1175–1186. https://doi.org/10.1016/j.finel.2004.11.00610.1016/j.finel.2004.11.006 ↗
29. Sun J-Y, Zhao X, Illeperuma WRK et al (2012) Highly stretchable and tough hydrogels. Nature 489:133–136. https://doi.org/10.1038/nature1140910.1038/nature11409 ↗
30. Wong FS, Shield RT (1969) Large plane deformations of thin elastic sheets of neo-Hookean material. Z Für Angew Math Phys ZAMP 20:176–199. https://doi.org/10.1007/BF0159555910.1007/BF01595559 ↗
31. Wriggers P (2008) Nonlinear finite element methods. Springer Science & Business Media, Berlin
32. Wu MS (2017) Anti-plane crack solutions in higher-order elasticity. Int J Eng Sci 121:60–79. https://doi.org/10.1016/j.ijengsci.2017.08.01410.1016/j.ijengsci.2017.08.014 ↗