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Isotropic hardening in micropolar plasticity

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Abstract

Experimental evidence for length scale effects in plasticity has been provided, e.g., by Fleck et al. (Acta Metall. Mater. 42:475–487, 1994). Results from torsional loadings on copper wires, when appropriately displayed, indicated that, for the same shear at the outer radius, the normalized torque increased with decreasing specimen radius. Modeling of the constitutive behavior in the framework of micropolar plasticity is a possibility to account for length scale effects. The present paper is concerned with this possibility and deals with the theory developed by Grammenoudis and Tsakmakis (Contin. Mech. Thermodyn. 13:325–363, 2001; Int. J. Numer. Methods Eng. 62:1691–1720, 2005; Proc. R. Soc. 461:189–205, 2005). Both isotropic and kinematic hardening are present in that theory, with isotropic hardening being captured in a unified manner. Here, we discuss isotropic hardening composed of two parts, responsible for strain and gradient effects, respectively.

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References

  1. Aifantis, E.: On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci. 20, 1279–1299 (1992)

    Article  Google Scholar 

  2. Aifantis, E.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)

    Article  Google Scholar 

  3. Aifantis, E.: Update on a class of gradient theories. Mech. Mater. 35, 259–280 (2003)

    Article  Google Scholar 

  4. Besdo, D.: Ein Beitrag zur nichtlinearen Theorie des Cosserat–Kontinuums. Acta Mech. 20, 105–131 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  5. de Borst, R.: Simulation of strain localization: a reappraisal of the Cosserat continuum. Eng. Comput. 8, 317–332 (1991)

    Article  Google Scholar 

  6. de Borst, R.: A generalization of J 2–flow theory for polar continua. Comput. Methods Appl. Mech. Eng. 103, 347–362 (1993)

    Article  MATH  Google Scholar 

  7. de Borst, R., Mühlhaus, H.: Finite deformation analysis of inelastic materials with micro-structure. In: Besdo D., Stein E. (eds.) Finite Inelastic Deformations—Theory and Applications, IUTAM Symposium Hannover/Germany 1991, pp. 313–322. Springer, Heidelberg (1992)

    Google Scholar 

  8. Chaboche, J.: Cyclic viscoplastic constitutive equations. Part I: A thermodynamically consistent formulation. J. Appl. Mech. 60, 813–821 (1993)

    Article  MATH  Google Scholar 

  9. Chaboche, J.: Cyclic viscoplastic constitutive equations. Part II: Stored energy-comparison between models and experiments. J. Appl. Mech. 60, 822–828 (1993)

    Article  Google Scholar 

  10. Cosserat, E., Cosserat, F.: Théorie des Corps Déformables. Herman et fils, Paris (1909)

    Google Scholar 

  11. Diepolder, W., Mannl, V., Lippmann, H.: The Cosserat continuum, a model for grain rotations in metals?. Int. J. Plast. 7, 313–328 (1991)

    Article  Google Scholar 

  12. Dietsche, A., Willam, K.: Boundary effects in elasto-plastic Cosserat continua. Int. J. Solids Struct. 7, 877–893 (1997)

    Article  Google Scholar 

  13. Ehlers, W., Volk, W.: On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials. Int. J. Solids Struct. 35, 4597–4617 (1998)

    Article  MATH  Google Scholar 

  14. Eringen, A.: Theory of micropolar elasticity. In: , (eds) Fracture, An Advanced Treatise, pp. 621–729. Academic, New York (1968)

    Google Scholar 

  15. Eringen, A., Suhubi, E.: Nonlinear theory of simple micro-elastic solids—I. Int. J. Eng. Sci. 2, 189–203 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  16. Eringen, A.: Microcontinuum field theories: I. Foundations and Solids. Springer, New York (1999)

    MATH  Google Scholar 

  17. Fleck, N., Huang, Y., Nix, W., Hutchinson, J.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475–487 (1994)

    Article  Google Scholar 

  18. Fleck, N., Hutchinson, J.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825–1857 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  19. Fleck, N., Hutchinson, J.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245–2271 (2001)

    Article  MATH  Google Scholar 

  20. Forest, S.: Modelling slip, kink and shear banding in classical and generalized single crystal plasticity. Acta Mater. 9, 3265–3281 (1998)

    Article  Google Scholar 

  21. Forest, S., Barbe, F., Cailletaud, G.: Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials. Int. J. Solids Struct. 37, 7105–7126 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Grammenoudis, P., Tsakmakis, Ch.: Hardening rules for finite deformation micropolar plasticity: restrictions imposed by the second law of thermodynamics and the postulate of Il’iushin. Contin. Mech. Thermodyn. 13, 325–363 (2001)

    MATH  MathSciNet  Google Scholar 

  23. Grammenoudis, P., Tsakmakis, Ch.: Finite Element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects. Int. J. Numer. Methods Eng. 62, 1691–1720 (2005)

    Article  MATH  Google Scholar 

  24. Grammenoudis, P., Tsakmakis, Ch.: Predictions of microtorsional experiments by micropolar plasticity. Proc. R. Soc. 461, 189–205 (2005)

    Article  Google Scholar 

  25. Lee, E., Liu, D.: Finite strain elastic–plastic theory with application to plane-wave analysis. J. Appl. Phys. 38, 19–27 (1967)

    Article  Google Scholar 

  26. Lee, E.: Elastic plastic deformation at finite strain. ASME Trans. J. Appl. Mech. 36, 1–6 (1969)

    MATH  Google Scholar 

  27. Lippmann, H.: Eine Cosserat–Theorie des plastischen Fließens. Acta Mech. 8, 255–284 (1969)

    Article  MATH  Google Scholar 

  28. Ma, Q., Clarke, D.: Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853–863 (1995)

    Article  Google Scholar 

  29. Mindlin, R., Tiersten, H.: Effects of couple-stresses in linear elasticity. Arch. Rat. Mech. Anal. 11, 415–448 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  30. Mindlin, R.: Influence of couple-stresses on stress concentrations. Exp. Mech. 3, 1–7 (1963)

    Article  Google Scholar 

  31. Mühlhaus, H., Vardoulakis, I.: The thickness of shear bands in granular materials. GèOtechnique 37, 271–283 (1987)

    Article  Google Scholar 

  32. Poole, W., Ashby, M., Fleck, N.: Micro-hardness of annealed and work-hardened copper polycrystals. Scr. Mater. 34, 559–564 (1996)

    Article  Google Scholar 

  33. Steinmann, P.: A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. Int. J. Solids Struct. 31, 1063–1084 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  34. Steinmann, P., Willam, K.: Localization within the framework of micropolar elasto-plasticity. In: Brüller O., Mannl, V., Najar, J.(eds) Advances in Continuum Mechanics., pp. 296–313. Springer, Berlin (1991)

    Google Scholar 

  35. Stelmashenko, A., Walls, M., Brown, L., Milman, Y.: Microindentations on W and Mo oriented single crystals: An STM study. Acta Metall. Mater. 41, 2855–2865 (1993)

    Article  Google Scholar 

  36. Stölken, J., Evans, A.: A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109–5115 (1998)

    Article  Google Scholar 

  37. Tejchman, J., Wu, W.: Numerical study on patterning of shear bands in Cosserat continuum. Acta Mech. 99, 61–74 (1993)

    Article  MATH  Google Scholar 

  38. Toupin, R.: Elastic materials with couple-stresses. Arch. Rat. Mech. Anal. 11, 385–414 (1962)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Darmstadt University of Technology, Department of Civil Engineering and Geodesy, Institute of Continuum Mechanics, Hochschulstraße 1, 64289, Darmstadt, Germany

    P. Grammenoudis & Ch. Tsakmakis

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  1. P. Grammenoudis
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  2. Ch. Tsakmakis
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Correspondence to Ch. Tsakmakis.

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Grammenoudis, P., Tsakmakis, C. Isotropic hardening in micropolar plasticity. Arch Appl Mech 79, 323–334 (2009). https://doi.org/10.1007/s00419-008-0236-3

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