A boundary element method for solving 3D static gradient elastic problems with surface energy

Computational Mechanics

Volumn 29, Issue 4-5, 2002, Pages 361-381

  Tsepoara, K G ^a,b   Papargyri Beskou, S ^c   Polyzos, D ^a,b  

^a UNIVERSITY OF PATRAS   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

^c ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

Boundary Element Method; Fundamental solutions; Gradient elasticity; Materials with microstructure; Non classical boundary conditions; Surface energy

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; ELASTICITY; INTEGRAL EQUATIONS; MICROSTRUCTURE;

LINEAR ELASTIC MATERIALS;

INTERFACIAL ENERGY;

EID: 0036814242     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0348-5     Document Type: Article

References (32)

1. Aifantis E.C. (1984) On the microstructural origin of certain inelastic models. ASME J. Engng. Mat. Tech. 106: 326-330.
2. Aifantis E.C. (1992) On the role of gradients in the localization of deformation and fracture. Int. J. Engng. Sci. 30: 1279-1299.
3. Altan B.S., Evensen H., Aifantis E.C. (1996) Longitudinal vibrations of a beam: a gradient elasticity approach. Mech. Res. Comm. 23: 35-40.
4. Altan S., Aifantis E.C. (1992) On the structure of the mode III crack-tip in gradient elasticity. Scripta Metall. Mater. 26: 319-324.
5. Amanatidou E., Aravas N. (2002) Mixed finite element formulations of strain-gradient elasticity problems. Comp. Meth. Appl. Mech. Engng. 191: 1723-1751.
6. Brand L. (ed) (1966) Vector and Tensor Analysis. John Wiley: New York.
7. Brebbia C.A., Domingnez J. (1992) Boundary Elements, An Introductory Course. CMP & McGraw Hill, Southampton & New York.
8. Chang C.S., Gao J. (1997) Wave propagation in granular rod using high-gradient theory. ASCE J. Engng. Mech. 123: 52-59.
9. Cosserat E., Cosserat F. (1909) Theorie des Corps Deformables. A. Hermann et Cie, Paris.
10. Dassios G., Lindell I.V. (2001) On the Helmholtz Decomposition for Polyadics. Quarterly of Applied Mathematics LIX 4: 787-796.
11. Dragos L. (1984) Fundamental solutions in micropolar elasticity. Int. J. Engng. Sci. 22: 265-275.
12. Eringen A.C. (1968) Theory of micropolar elasticity. In: Liebowitz H. (ed) Fracture, Vol. II, pp. 621-729. New York: Academic Press.
13. Exadaktylos G.E., Vardoulakis I. (2001) Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics. Tectonophysics 335: 81-109.
14. Exadaktylos G.E., Vardoulakis I. (1998) Surface instability in gradient elasticity with surface energy. Int. J. Solids Struct. 35: 2251-2281.
15. Exadaktylos G., Vardoulakis I., Aifantis E.C. (1996) Cracks in gradient elastic bodies with surface energy. Int. J. Fracture 79: 107-119.
16. Georgiadis H.G., Vardoulakis I., Lykotrafitis G. (2000) Torsional surface waves in a gradient-elastic half-space. Wave Motion 31: 333-348.
17. Guiggiani M., Gigante A. (1990) A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. ASME J. of Applied Mechanics 57: 906-915.
18. Huang F.Y., Liang K.Z. (1997) Boundary element analysis of stress concentration in micropolar elastic plate. Int. J. Num. Meth. Engng 40: 1611-1622.
19. Huang F.Y., Liang K.Z. (1994) Torsional analysis of micropolar elasticity using the finite element method. Int. J. Engng. Sci. 32: 347-358.
20. Huber O., Lang A., Kuhn G. (1993) Evaluation of the stress tensor in 3D elastostatics by direct solving of hypersingular integrals. Computational Mechanics 12:39-50.
21. Koiter W.T. (1964) Couple stresses in the theory of elasticity, I. & II. In: Proc. K. Ned. Akad. Wet., Vol. B 67, pp. 17-44.
22. Liang K.Z., Huang F.Y. (1996) Boundary element method for micropolar elasticity. Int. J. Engng. Sci. 34: 509-521.
23. Mindlin R.D., Tiersten H.F. (1962) Effects of couple-stresses in linear elasticity. Arch. Rat. Mech. Anal. 11: 415-448.
24. Mindlin R.D. (1964) Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 10: 51-78.
25. Mindlin R.D. (1965) Second gradient of strain and surface tension in linear elasticity. Int. J. Solids Struct. 1: 417-438.
26. Nakamura S., Benedict R., Lakes R. (1984) Finite element method for orthotropic micropolar elasticity. Int. J. Engng Sci. 22: 319-330.
27. Papargyri-Beskou S., Tsepoura K.G., Polyzos D., Beskos D.E. (2002) Bending and stability analysis of gradient elastic beams. Int. J. Solids Struct. (In press).
28. Ru C.Q., Aifantis E.C. (1993) A simple approach to solve boundary value problems in gradient elasticity. Acta Mechanica 101: 59-68.
29. Shn J.Y., King W.E., Fleck N.A. (1999) Finite elements for materials with strain gradient effects. Int. J. Num. Meth. Engng. 44, 373-391.
30. Toupin R.A. (1965) Theories of elasticity with couple-stresses, Arch. Rat. Mech. Anal. 17: 85-112.
31. Tsepoura K.G., Papargyri-Beskou S., Polyzos D., Beskos D.E. (2002) Static and dynamic analysis of gradient elastic bars in tension. Arch. Appl. Mechanics (In press).
32. Vardoulakis I., Sulem J. (1995) Bifurcation Analysis in Geomechanics. Blackie/Chapman and Hall, London.