A new finite element method for strain gradient theories and applications to fracture analyses

European Journal of Mechanics, A/Solids

Volumn 25, Issue 6, 2006, Pages 897-913

  Wei, Yueguang ^a  

^a INSTITUTE OF MECHANICS   (China)

Author keywords

Crack tip fields; Finite element method; Strain gradient theory

Indexed keywords

CRACKS; DEFORMATION; FINITE ELEMENT METHOD; NUMERICAL METHODS; PLASTICITY; STRAIN;

CRACK TIP FIELDS; STRAIN GRADIENT PLASTICITY; STRAIN GRADIENT THEORY;

FRACTURE;

EID: 33750331945     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2006.03.001     Document Type: Article

References (27)

1. Aifantis E.C. On the microstructural origin of certain inelastic models. Trans. ASME J. Engrg. Mater. Tech. 106 (1984) 326-330
2. Bagchi A., and Evans A.G. The mechanics and physics of thin film decohesion and its measurement. Interface Sci. 3 (1996) 169-193
3. Begley M.R., and Hutchinson J.W. The mechanics of size-dependent indentation. J. Mech. Phys. Solids 46 (1998) 2049-2068
4. Chen S.H., and Wang T.C. Strain gradient theory with couple stress for crystalline solids. Eur. J. Mech. A Solids 20 (2001) 739-756
5. Engel G., Garikipati K., Hughes T.J.R., Larson M.G., Mazzei L., and Taylor R.L. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3669-3750
6. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiments. Acta Metall. Mater. 42 (1994) 475-487
7. Fleck N.A., and Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41 (1993) 1825-1857
8. Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. Adv. Appl. Mech. 33 (1997) 295-361
9. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity - I. Theory. J. Mech. Phys. Solids 47 (1999) 1239-1263
10. Huang Y., Chen J.Y., Guo T.F., Zhang L., and Hwang K.C. Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects. Int. J. Fracture 100 (1999) 1-27
11. Lipkin D.M., Clarke D.R., and Evans A.G. Effect of interfacial carbon on adhesion and toughness of gold-sapphire interface. Acta Mater. 46 (1998) 4835-4850
12. Ma Q., and Clarke D.R. Size dependent hardness of solver single crystals. J. Mater. Res. 10 (1995) 853-863
13. Matsushima T., Chambon R., and Caillerie D. Large strain finite element analysis of a local second gradient model: Application to localization. Inter. J. Numer. Methods Engrg. 54 (2002) 499-521
14. McElhaney K.W., Vlassak J.J., and Nix W.D. Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13 (1998) 1300-1306
15. Shi M.X., Huang Y., and Hwang K.C. Fracture in a higher-order elastic continuum. J. Mech. Phys. Solids 48 (2000) 2513-2538
16. Shu J.Y., and Fleck N.A. The prediction of a size effect in micro indentation. Int. J. Solids Struct. 35 (1998) 1363-1383
17. Shu J.Y., King W.E., and Fleck N.A. Finite elements for materials with strain gradient effects. Inter. J. Numer. Methods Engrg. 44 (1999) 373-391
18. Specht B. Modified shape functions for the three-node plate bending element passing the patch test. Inter. J. Numer. Methods Engrg. 26 (1988) 705-715
19. Stelmashenko N.A., Walls M.G., Brown L.M., and Milman Y.V. Microindentations on W and Mo oriented single crystals: An STM study. Acta Metall. Mater. 41 (1993) 2855-2865
20. Stolken J.S., and Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Mater. 46 (1998) 5109-5115
21. Wei Y. Particulate size effects in the particle-reinforced metal matrix composites. Acta Mech. Sinica 17 (2001) 45-58
22. Wei Y., and Hutchinson J.W. Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity. J. Mech. Phys. Solids 45 (1997) 1253-1273
23. Wei Y., Wang X., Wu X., and Bai Y. Theoretical and experimental researches of size effect in micro-indentation test. Sci. China Ser. A 44 (2001) 74-82
24. Xia Z.C., and Hutchinson J.W. Crack tip fields in strain gradient plasticity. J. Mech. Phys. Solids 44 (1996) 1621-1648
25. Zhang L., Huang Y., Chen J.Y., and Hwang K.C. The mode III full-field solution in elastic materials with strain gradient effects. Int. J. Fracture (1998) 325-348
26. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method, vol. 1. Basic Formulation and Linear Problems. fourth ed (1989), McGraw-Hill, London
27. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method, vol. 2: Solid and Fluid Mechanics, Dynamics and Non-Linearity. fourth ed (1989), McGraw-Hill, London