A comparative study of the effect of the gradient term type on the plasticity solution behaviour
DOI:
https://doi.org/10.7242/1999-6691/2009.2.2.13Keywords:
gradient plasticity, correction functionsAbstract
The effect of the type of correction functions on the solution behavior is studied within the framework of the theory of gradient plasticity. Two ways of gradient term representation are considered, of which one uses a conventional form, and the other suggests application of space derivatives of the equivalent strain rate. Attention is mainly devoted to the difference in the qualitative behavior of the solutions of the boundary value problem on expansion of a sphere having an inner cavity of small radius acting as a stress concentrator. It is shown that the solution based on the new correction function better corresponds to physical expectations concerning the effect of the gradient term on the solution behavior.
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Novopasin M.D., Suknev S.V., Ivanov A.M. Uprugoplasticeskoe deformirovanie i predel’noe sostoanie elementov konstrukcij s koncentratorami naprazenij. - Novosibirsk: Nauka, 1995. - 111s.
Fleck N.A., Muller G.M, Ashby M.F., Hutchinson J.W. A reformulation of strain gradient plasticity // J. Mech. Phys. Solids. - 2001. - V. 49. - P. 2245-2271. DOI
Aifantis E.C. Update on a class of gradient theories // Mech. Mater. - 2003. - V. 35. - P. 259-280. DOI
Zervos A., Papanastasiou P., Vardoulakis I. Modelling of localization and scale effect in thick-walled cylinders with gradient elastoplasticity // Int. J. Solids Struct. - 2001. - V. 38. - P. 5081-5095. DOI
Gao X.-L. Analytical solution of a borehole problem using strain gradient plasticity // Trans. ASME. J. Engng Mater. Technol. - 2002. - V. 124, N. 2. - P. 365-370. DOI
Tsagrakis I., Aifantis E.C. Recent development in gradient plasticity. Part 1: Formulation and size effects // Trans. ASME. J. Engng Mater. Technol. - 2002. - V. 124, N. 2. - P. 352-357. DOI
Gao X.-L. An expanding cavity model incorporating strain-hardening and indentation size effects // Int. J. Solids Struct. - 2006. - V. 43. - P. 6615-6629. DOI
Marciniak Z., Duncan J. Mechanics of sheet metal forming. - London: Edwards Arnold, 1992. - 166 p.
Aukrust T., LaZghab S. Thin shear boundary layers in flow of hot aluminium // Int. J. Plast. - 2000. - V. 16, N. 1. - P. 59-71. DOI
Assempour A., Safikhani A.R., Hashemi R. An improved strain gradient approach for determination of deformation localization and forming limit diagram // J. Mater. Process. Technol. - 2009. - V. 209. - P. 1758-1769. DOI
Yuan H., Chen J. Identification of the intrinsic material length in gradient plasticity theory from micro-indentation tests // Int. J. Solids Struct. - 2001. - V. 38. - P. 8171-8187. DOI
Mosolov P.P., Masnikov V.P. Variacionnye metody v teorii tecenij zestko-vazko-plasticeskih sred. - M.: Izd-vo Moskovskogo universiteta, 1971. - 114 s.
Rees D.W.A. Basic engineering plasticity. - Oxford: Butterworth-Heinemann, 2006. - 511 p.
Hill R. Matematiceskaa teoria plasticnosti. - Moskva: Gostehteoretizdat, 1956 - 408 s.
Li M.-L., Fu M.-F. Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory // Appl. Math. Mech. - 2008. - V. 29, N. 12. - P. 1553-1559. DOI
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