Relationships between the admissible range of surface material parameters and stability of linearly elastic bodies

Philosophical Magazine

Volumn 92, Issue 28-30, 2012, Pages 3540-3563

  Javili, A ^a   McBride, A ^a   Steinmann, P ^a   Reddy, B D ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF CAPE TOWN   (South Africa)

Author keywords

bifurcation; mesh dependency; stability; surface elasticity

Indexed keywords

ATOMISTIC MODELS; BALANCE EQUATIONS; CONTINUUM FORMULATION; DISCRETISATION; ELASTIC BODY; ELASTIC SURFACES; ENERGETIC SURFACE; GOVERNING EQUATIONS; LENGTH SCALE; LOCAL BIFURCATIONS; MATERIAL PROPERTY; MESH-DEPENDENCY; MODEL SURFACE; NONLOCAL; NUMERICAL EXAMPLE; STATIONARY WAVES; SURFACE ELASTICITIES; SURFACE MATERIALS; SURFACE PARAMETER;

BIFURCATION (MATHEMATICS); CONTINUUM MECHANICS; CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; FINITE ELEMENT METHOD; TENSORS;

STABILITY;

EID: 84867805325     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786435.2012.682175     Document Type: Conference Paper

References (47)

1. J.W. Gibbs, The Scientific Papers, Dover Publications, New York, 1961.
2. M.E. Gurtin and A.I. Murdoch, Arch. Rat. Mech. Anal. 57 (1975) p.291.
3. D.J. Steigmann and R.W. Ogden, Roy. Soc. London Proc. Series A 455 (1999) p.437.
4. N. Daher and G.A. Maugin, Acta Mechanica 60 (1986) p.217.
5. E. Fried and M.E. Gurtin, Adv. Appl. Mech. 40 (2004) p.1.
6. F.D. Fischer, T. Waitz, D. Vollath and N.K. Simha, Prog. Mater. Sci. 53 (2008) p.481.
7. W.C. Johnson, Acta Materialia 48 (2000) p.433.
8. V.B. Shenoy, Phys. Rev. B 71 (2005) p.1.
9. H.L. Duan, J. Wang and B.L. Karihaloo, Adv. Appl. Mech. 42 (2009) p.1.
10. P. Steinmann, J. Mech. Phys. Solids 56 (2008) p.772.
11. J. Yvonnet, A. Mitrushchenkov, G. Chambaud and Q.C. He, Comp. Meth. Appl. Mech. Eng. 200 (2011) p.614.
12. A. Javili and P. Steinmann, Int. J. Solids Struct. 47 (2010) p.3245.
13. J. Choi, M. Cho and W. Kim, J. Mech. Mater. Struct. 5 (2010) p.161.
14. H.S. Park and P.A. Klein, Comp. Meth. Appl. Mech. Eng. 197 (2008) p.3249.
15. R.C. Cammarata, K. Sieradzki and F. Spaepen, J. Appl. Phys. 87 (2000) p.1227.
16. H.C. Simpson and S.J. Spector, J. Elasticity 15 (1985) p.229.
17. A. Benallal, R. Billardon and G. Geymonat, Bifurcation and localization in rateindependent materials. Some general considerations, in Bifurcation and Stability of Dissipative Systems, Q.S. Nguyen Ed., CISM Courses and Lectures, Vol. 327, Springer- Verlag, Austria, 1993, p.1.
18. A. Benallal and C. Comi, Comptes Rendus Me'canique 333 (2005) p.319.
19. R. Hill, J. Mech. Phys. Solids 6 (1958) p.236.
20. A.I. Murdoch, J. Mech. Physi. Solids 24 (1976) p.137.
21. D.S. Chandrasekharaiah, Acta Mechanica 41 (1981) p.283.
22. M.A. Dowaikh and R.W. Ogden, IMA J. Appl. Math. 44 (1990) p.261.
23. D.J. Steigmann and R.W. Ogden, Proc. Roy. Soc. A 453 (1997) p.853.
24. R. Ogden and D.J. Steigmann, J. Mech. Phys. Solids 50 (2002) p.1869.
25. B.D. Reddy, Math. Proc. Cambridge Phil. Soc. 91 (1982) p.491.
26. B.D. Reddy, Quart. J. Mech. Appl. Math. 36 (1983) p.337.
27. Z. Suo, M. Ortiz and A. Needleman, J. Mech. Phys. Solids 40 (1992) p.613.
28. D. Bigoni, M. Ortiz and A. Needleman, Int. J. Solids Struct. 34 (1997) p.4305.
29. D. Bigoni and M. Gei, Int. J. Solids Struct. 38 (2001) p.5117.
30. D.J. Steigmann, Int. J. Eng. Sci. 48 (2010) p.1604.
31. D.J. Steigmann, Math. Mech. Solids (2011). doi: 10.1177/108128651141997.
32. A. Benallal, T. Berstad, T. Borvik and O.S. Hopperstad, Int. J. Numer. Meth. Eng. 84 (2010) p.864.
33. T.C.T. Ting, Math. Mech. Solids 14 (2009) p.52.
34. J.K. Djoko, F. Ebobisse, A.T. McBride and B.D. Reddy, Comp. Meth. Appl. Mech. Eng. 196 (2007) p.3881.
35. E. Bittencourt, A. Needleman, M.E. Gurtin and E. van der Giessen, J. Mech. Phys. Solids 51 (2003) p.281.
36. S. Forest, N.M. Cordero and E.P. Busso, Comp. Mater. Sci. 50 (2011) p.1299.
37. P.G. Ciarlet, An Introduction to Differential Geometry with Applications to Elasticity, Vol. 78-79, Springer, Berlin, 2005.
38. A. Javili and P. Steinmann, Comp. Meth. Appl. Mech. Eng. 199 (2010) p.755.
39. J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity, Dover Publications, New York, 1994.
40. R.C. Cammarata, Prog. Surf. Sci. 46 (1994) p.1.
41. Z.P. Huang and J. Wang, Acta Mechanica 182 (2006) p.195.
42. R.E. Miller and V.B. Shenoy, Nanotechnology 11 (2000) p.139.
43. P. Sharma, S. Ganti and N. Bhate, Appl. Phys. Lett. 82 (2003) p.535.
44. D.J. Steigmann and R.W. Ogden, IMA J. Appl. Math. 72 (2007) p.730.
45. J. Utzinger, A. Menzel, P. Steinmann and A. Benallal, Eur. J. Mech. A Solids 27 (2008) p.532.
46. A. Javili and P. Steinmann, Comp. Meth. Appl. Mech. Eng. 198 (2009) p.2198.
47. T.J.R. Hughes The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Vol. 65, Prentice Hall, Englewood Cliffs, NJ, 1987.