Surface instability in gradient elasticity with surface energy

International Journal of Solids and Structures

Volumn 35, Issue 18, 1998, Pages 2251-2281

  Exadaktylos, G E ^a   Vardoulakis, I ^b  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

BUCKLING; CRACKS; ELASTICITY; INTERFACIAL ENERGY; STABILITY; STRESSES; SURFACE WAVES;

ANISOTROPIC GRADIENT ELASTICITY THEORY; BIOT THEORY; STRAIN GRADIENT; SURFACE INSTABILITY;

STRAIN;

EID: 0032083716     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)89945-3     Document Type: Article

References (45)

1. Aifantis, E. C. (1987) The physics of plastic deformation. International Journal of Plasticity 3, 211-247.
2. Barenblatt, G. I. (1962) Mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7, 55.
3. Beatty, M. F. (1966) Some static and dynamic implications of the general theory of elastic stability. Archives of Rational Mechanical Analysis 19, 167-188.
4. Benallal, A. and Tvergaard, V. (1995) Nonlocal continuum effects on bifurcation in the plane strain tension-compression test. Journal of the Mechanics and Physics of Solids 43(5), 741-770.
5. Benallal, A., Billardon, R. and Geymonat, G. (1988) Some mathematical aspects of the damage softening problem. Cracking and Damage (Edited by J. Mazars and Z. P. Bazant), pp. 247-258. Elsevier, Amsterdam.
6. Biot, M. A. (1963) Internal buckling under initial stress in finite elasticity. Proceedings of the Royal Society A, A273, 306-328.
7. Biot, M. A. (1965) Mechanics of Incremental Deformations. Wiley, New York.
8. Biot, M. A. (1966) Fundamental skin effect in anisotropic solid mechanics. International Journal of Solids and Structures 2, 645-663.
9. Casal, P. (1961) La capillarite interne. Cahier du Groupe Francais d'Etudes de Rheologie C.N.R.S. VI, 31-37.
10. Cole, J. D. (1968) Perturbation Methods in Applied Mathematics. Blaisdell, Waltham, Mass.
11. Deere, D. U. and Miller, R. P. (1966) Engineering classification and index properties for intact rock. Tech. Rept No. AFWL-TR-G5-116. Air Force Weapons Lab., Kirtland Air Force Base, New Mexico, USA.
12. Eshelby, J. D. (1951) The force on an elastic singularity. Philosophical Transactions of the Royal Society of London, Series A 244, 87-112.
13. Exadaktylos, G. E. (1997) Gradient elasticity with surface energy : Mode-I crack problem. International Journal of Solids and Structures (in press).
14. Exadaktylos, G. E., Vardoulakis, I and Aifantis, E. C. (1996) Cracks in gradient elastic bodies with surface energy. International Journal of Fracture 79, 107-119.
15. Fairhurst, C. and Cook, N. G. W. (1966) The phenomenon of rock splitting parallel to the direction of maximum compression in the neighbourhood of a surface. Proceedings of the 1st International Congress of Rock Mechanics, pp. 687-692.
16. Frantziskonis, G. and Vardoulakis, I. (1992) On the micro-structure of surface effects and related instabilities. European Journal of Mechanics, A/Solids 11(1), 21-34.
17. Gazis, D. C. and Wallis, R. F. (1965) Surface tension and surface modes in semi-infinite lattices. Surface Science 3, 19-32.
18. Germain, P. (1973a) La methode des puissances vituelles en mecanique des milieux continus. Premiere Partie: Theorie due second gradient. Journal de Mecanique 12, 235-274.
19. Germain, P. (1973b) The method of virtual power in continuum mechanics. Part 2. Microstructure. SIAM, Journal of Applied Mathematics 25, 556-575.
20. Germer, L. H., Macrae, A. U. and Hartman, C. D. (1961) (110) Nickel surface. Journal of Applied Physics 32, 2432-2439.
21. Handin, J., Friedman, M., Logan, J. M., Pattison, L. J. and Swolfs, H. S. (1972) Experimental folding of rocks under confining pressure : Buckling and single-layer rock beams. In : Flow and Fracture of Rocks (Edited by H. C. Heard, I. Y. Borg, et al.), pp. 1-28. Geophysical monograph 16, American Geophysical Union, Washington DC.
22. Handin, J., Friedman, M., Logan, J. M., Pattison, L. J. and Swolfs, H. S. (1972) Experimental folding of rocks under confining pressure : Buckling and single-layer rock beams. In : Flow and Fracture of Rocks (Edited by H. C. Heard, I. Y. Borg, et al.), pp. 1-28. Geophysical monograph 16, American Geophysical Union, Washington DC.
23. Hill, R. and Hutchinson, J. W. (1975) Bifurcation phenomena in the plane strain tension test. Journal of Mechanics and Physics of Solids 23, 239-264.
24. Hutchinson, J. W. and Tvergaard, V. (1980) Surface instabilities on statically strained plastic solids. International Journal of Mechanical Science 22, 339-354.
25. Iliadis, J. (1996) Study of Propagation of Rayleigh Waves in a Half-space with Microstructure. Diploma Dissertation Thesis. National Technical University of Athens (in Greek).
26. Keer, L. M., Nemat-Nasser, S. and Oranratnachai, S. (1982) Surface instability and splitting in compressed brittle elastic solids containing crack arrays. Journal of Applied Mechanics 49, 761-767.
27. Love, A. E. H. (1927) A Treatise on the Mathematical Theory of Elasticity. Fourth Edition, Cambridge University Press, Cambridge.
28. Mindlin, R. D. (1964) Micro-structure in linear elasticity. Archives of Rational Mechanical Analysis 16, 51-78.
29. Mindlin, R. D. (1965) Second gradient of strain and surface-tension in linear elasticity. International Journal of Solids and Structures 1, 417-438.
30. Mindlin, R. D. and Eshel, N. N. (1968) On first strain-gradient theories in linear elasticity. International Journal of Solids and Structures 4, 109-124.
31. Nazarenko, V. M. (1986) Theory of fracture of materials in compression along near surface cracks under plane-strain conditions. Soviet Applied Mechanics 22, 1192-1199.
32. Papamichos, E., Vardoulakis, I. and Muhlhaus, H. B. (1990) Buckling of layered elastic media: A Cosserat-continuum approach and its validation. International Journal of Numerical and Analytical Methods in Geomechanics 14, 473-498.
33. Papamichos, E., Labuz, J. F. and Vardoulakis, I. (1994) A surface instability detection apparatus. Rock Mechanics and Rock Engineering 27(1), 37-56.
34. Toupin, R. A. (1962) Elastic materials and couple-stresses. Archives of Rational Mechanical Analysis 11, 385-414.
35. Toupin, R. A. and Gazis, D. C. (1964) Surface effects and initial stress in continuum and lattice models of elastic crystals. Proceedings of the International Conference on Lattice Dynamics, Copenhagen, August, 1963 (Edited by R. F. Wallis), pp. 597-602.
36. Truesdell, C. and Toupin, R. A. (1960) Classical field theories of mechanics. Handbook of Physics, Vol. III/1. Springer, New York.
37. Usmani, S. A. and Beatty, M. F. (1974) On the surface instability of a highly elastic half-space. Journal of Elasticity 4(4), 249-263.
38. Wu, C. H. (1992) Cohesive elasticity and surface phenomena. Quarterly Applied Mathematics L(1), 73-103.
39. Vardoulakis, I. (1984) Rock bursting as a surface instability phenomenon. International Journal of Rock Mechanics and Minimal Science & Geomechanical Abstracts 21, 137-144.
40. Vardoulakis, I. and Papamichos, E. (1991) Surface instabilities in elastic anisotropic media with surface-parallel Griffith cracks. International Journal of Rock Mechanics and Minimum Science & Geomechanical Abstracts 28, 163-173.
41. Vardoulakis, I. and Aifantis, E. C. (1991) A gradient flow theory of plasticity for granular materials. Acta Mechanics 87, 197-217.
42. Vardoulakis, I. and Frantziskonis, G. (1992) Micro-structure in kinematic-hardening plasticity. European Journal of Mechanics, A/Solids 11(4), 467-486.
43. Vardoulakis, I. and Sulem, J. (1995) Bifurcation Analysis in Geomechanics. Blackie Academic and Professional, Glasgow.
44. Vardoulakis, I., Exadaktylos, G. and Aifantis, E. (1996) Gradient elasticity with surface energy : Mode-III crack problem. International Journal of Solids and Structures 33(30), 4531-4559.
45. Vardoulakis, I. and Exadaktylos, G. (1997) The asymptotic solution of anisotropic gradient elasticity with surface energy. In: Non-Linear Singularities in Deformation and Flow (Edited by D. Durban and J. R. A. Pearson), IUTAM Symposium, Haifa, Israel, 1997.