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Non-singular stresses in gradient elasticity at bi-material interface with transverse crack. (English) Zbl 1273.74423

Summary: Bi-material interfaces are studied with cracks that end perpendicular to the interface. As is well-known, singularities in the stresses appear when classical elasticity is used. Moreover, the nature of the singularity depends on the difference in elastic constants of the two materials. In this paper, the gradient elasticity theory of Aifantis is used to remove these singularities. This is demonstrated for a range of ratios between the two Young’s moduli.

MSC:

74R10 Brittle fracture
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[1] Aifantis E.C. (1992) On the role of gradients in the localization of deformation and fracture. International Journal of Engineering Science 30: 1279–1299 · Zbl 0769.73058 · doi:10.1016/0020-7225(92)90141-3
[2] Altan S.B., Aifantis E.C. (1992) On the structure of the mode III crack-tip in gradient elasticity. Scripta Metallurgica et Materialia 26: 319–324 · doi:10.1016/0956-716X(92)90194-J
[3] Askes H., Aifantis E.C. (2002) Numerical modeling of size effect with gradient elasticity – formulation, meshless discretization and examples. International Journal of Fracture 117: 347–358 · doi:10.1023/A:1022225526483
[4] Askes H., Morata I., Aifantis E.C. (2008) Finite element analysis with staggered gradient elasticity. Computers & Structures 86: 1266–1279 · doi:10.1016/j.compstruc.2007.11.002
[5] Barut A., Guven I., Madenci E. (2001) Analysis of singular stress fields at junctions of multiple dissimilar materials under mechanical and thermal loading. International Journal of Solids and Structures 38: 9077–9109 · Zbl 1090.74681 · doi:10.1016/S0020-7683(01)00206-2
[6] Carpinteri A., Paggi M. (2007) Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems. Engineering Fracture Mechanics 74: 59–74 · doi:10.1016/j.engfracmech.2006.01.030
[7] Chang C.S., Gao J. (1995) Second-gradient constitutive theory for granular material with random packing structure. International Journal of Solids and Structures 32: 2279–2293 · Zbl 0869.73004 · doi:10.1016/0020-7683(94)00259-Y
[8] Erofeyev V.I. Wave processes in solids with microstructure. World Scientific (2003). · Zbl 1056.74001
[9] Fenner D.N. (1976) Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface. International Journal of Fracture 12: 705–721
[10] Gitman I.M., Askes H., Aifantis E.C. (2005) The Representative Volume size in static and dynamic micromacro transitions. International Journal of Fracture 135: L3–L9 · Zbl 1196.74167 · doi:10.1007/s10704-005-4389-6
[11] Jakata K., Every A.G. (2008) Determination of the dispersive elastic constants of the cubic crystals Ge, Si, GaAs, and InSb. Phyical Review B 77: 174301 · doi:10.1103/PhysRevB.77.174301
[12] Kunin I.A. Elastic media with microstructure. I – One-dimensional models. Springer (1982). · Zbl 0527.73002
[13] Kunin I.A. Elastic media with microstructure. II – Three-dimensional models. Springer (1983). · Zbl 0536.73003
[14] Maranganti R., Sharma P. (2007) A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir)relevance for nanotechnologies. Journal of the Mechanics and Physics of Solids 55: 1823–1852 · Zbl 1173.74003 · doi:10.1016/j.jmps.2007.02.011
[15] Mindlin R.D. (1964), Micro-structure in linear elasiticity, Archive for Rational Mechanics and Analysis 16, 51-78 · Zbl 0119.40302
[16] Muhlhaus H.-B., Oka F. (1996) Dispersion and wave propagation in discrete and continuous models for granular materials. International Journal of Solids and Structures 33: 2841–2858 · Zbl 0926.74052 · doi:10.1016/0020-7683(95)00178-6
[17] Papanicolopulos S.-A., Zervos A., Vardoulakis I. (2009) A three dimensional C1 finite element for gradient elasticity. Internation Journal for Numerical Methods in Engineering 77: 1396–1415 · Zbl 1156.74382 · doi:10.1002/nme.2449
[18] Ru C.Q., Aifantis E.C. (1993) A simple approach to solve boundary-value problems in gradient elasticity. Acta Mechanica 101: 59–68 · Zbl 0783.73015 · doi:10.1007/BF01175597
[19] Suiker A.S.J., de Borst R., Chang C.S. (2001) Micro-mechanical modelling of granular material. Part 1: Derivation of a second–gradient micropolar constitutive theory Acta Mechanica 149 161180 · Zbl 1135.74307
[20] Tang Z., Shen S., Atluri S.N. (2003) Analysis of materials with strain-gradient effects: a meshless local Petrov-Galerkin (MLPG) approach, with nodal displacements only. Computer Modeling in Engineering and Sciences 4: 177–196 · Zbl 1148.74346
[21] Tenek L.T., Aifantis E.C. (2002) A two-dimensional finite element implementation of a special form of gradient elasticity. Computer Modeling in Engineering and Sciences 3: 731–741 · Zbl 1143.74376
[22] Wang J., Karihaloo B.L. (1994) Mode II and mode III stress singularities and intensities at a crack tip terminating on a transversely isotropic-orthotropic bimaterial interface. Proceedings of the Royal Society A 444: 447–460 · Zbl 0869.73058 · doi:10.1098/rspa.1994.0031
[23] Zervos A. (2008) Finite elements for elasticity with microstructure and gradient elasticity. International Journal for Numerical Methods in Engineering 72: 564–595 · Zbl 1166.74043 · doi:10.1002/nme.2093
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