Analytical solution of a borehole problem using strain gradient plasticity

Journal of Engineering Materials and Technology

Volumn 124, Issue 3, 2002, Pages 365-370

  Gao, X L ^a  

^a Michigan Technological University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOREHOLES; CONTINUUM MECHANICS; DEFORMATION; ITERATIVE METHODS; PARAMETER ESTIMATION; STRAIN; STRESS CONCENTRATION;

INTERNAL LENGTH; MICRO-TORSION TESTS; SIZE EFFECTS; SPATIAL GRADIENTS;

PLASTICITY;

EID: 0042199277     PISSN: 00944289     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1480408     Document Type: Article

References (23)

1. Papanastasiou, P., and Vardoulakis, I. 1989, "Bifurcation Analysis of Deep Boreholes: II. Scale Effect," Int. J. Num. Anal. Meth. Geomech., 13, pp. 183-198.
2. Papanastasiou, P., and Vardoulakis, I., 1992, "Numerical Treatment of Progressive Localisation in Relation to Borehole Stability," Int. J. Num. Anal. Meth. Geomech., 16, pp. 389-424.
3. Zervos, A., Papanastasiou, P., and Vardoulakis, I., 2001, "Modeling of Localization and Scale Effect in Thick-Walled Cylinders With Gradient Elastoplasticity," Int. J. Solids Struct., 38, pp. 5081-5095.
4. Mendelson, A., 1968, Plasticity: Theory and Application, Macmillan, New York.
5. Gao, X.-L., and Rowlands, R. E., 1999, "Analytical Solution for the Plane Strain Inclusion Problem of an Elastic Power Law Hardening Matrix Containing an Elastic Cylindrical Inclusion," Int. J. Pressure Vessels Piping, 76, pp. 291-297.
6. Aifantis, E. C., 1996, "Higher Order Gradients and Size Effects," Size-Scale Effect in the Failure Mechansims of Materials and Structure, A. Carpinteri, ed., Chapman and Hall, London, pp. 231-242.
7. Aifantis, E. C., 1984, "On the Microstructural Origin of Certain Inelastic Models," ASME J. Eng. Mater. Technol., 106, pp. 326-330.
8. Aifantis, E. C., 1987, "The Physics of Plastic Deformation," Int. J. Plast., 3, pp. 211-247.
9. Zbib, H. M., and Aifantis, E. C., 1988, "On the Localization and Post-Localization Behavior of Plastic Deformation, I, II and III," Res. Mech., 23, pp. 261-305
10. Mühlhaus, H.-B., and Aifantis, E. C., 1991, "A Variational Principle for Gradient Plasticity," Int. J. Solids Struct., 28, pp. 845-857.
11. Zhu, H. T., Zbib, H. M., and Aifantis, E. C. 1997, "Strain Gradients and Continuum Modeling of Size Effect in Metal Matrix Composites," Acta Mech., 121, pp. 165-176.
12. Hutchinson, J. W., 2000, "Plasticity at the Micron Scale," Int. J. Solids Struct., 37, pp. 225-238.
13. Fleck, N. A., Müller, G. M., Ashby, M. F., and Hutchinson, J. W., 1994, "Strain Gradient Plasticity: Theory and Experiments," Acta Metall. Mater., 42, pp. 475-487.
14. Stolken, J. S., and Evans, A. G., 1998, "A Microbend Test Method for Measuring the Plasticity Length Scale," Acta Meter., 46, pp. 5109-5115.
15. Ma, Q., and Clarke, D. R., 1995, "Size Dependent Hardness of Silver Single Crystals," J. Mater Res., 10, pp. 853-863
16. Nan, C. W., and Clarke, D. R., 1996, "Influence of Particle Size and Particle Fracture on the Elastic/Plastic Deformation of Metal Matrix Composites," Acta Mater., 44, pp. 3801-3811.
17. Aifantis, E. C., 1999, "Strain Gradient Interpretation of Size Effects," Int. J. Fract., 95, pp. 299-314.
18. Vardoulakis, I., and Aifantis, E. C., 1995, "Heterogeneities and Size Effects in Geomaterials," Mechanics of Materials with Discontinuities and Heterogeneities, A. Misra and C. S. Chang, eds., AMD-Vol. 201, ASME Press, New York, pp. 27-30.
19. Gao, X.-L., 1994, "Finite Deformation Elasto-Plastic Solution for the Pure Bending Problem of a Wide Plate of Elastic Linear-Hardening Material," Int. J. Solids Struct., 31, pp. 1357-1376.
20. Gao, X.-L., 1998, "A Mathematical Analysis of the Elasto-Plastic Plane Stress Problem of a Power-Law Material," IMA J. Appl. Math., 60, pp. 139-149.
21. Gao, X.-L., 1999, "An Exact Elastoplastic Solution for the Plane Wedge Problem of an Elastic Linear-Hardening Material," Math. Mech. Solids, 4, pp. 289-306.
22. Little, R. W., 1973, Elasticity, Prentice Hall, Englewood Cliffs, NJ.
23. Aifantis, E. C., 1995, "Pattern Formation in Plasticity," Int. J. Eng. Sci., 33, pp. 2161-2178