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On a proposal for a continuum with microstructure

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Summary

A recently proposed model for a continuum with microstructure is further substantiated by identifying the microstructure with dislocations. In particular, the continuum is viewed as a superimposed state composed of a perfect lattice state, an immobile dislocation state, and a mobile dislocation state. It is assumed that each state evolves continuously in space-time and transitions from one state to another take place spontaneously according to the balance laws of effective mass and momentum. When the constitutive equations are subjected to the requirements of invariance, familiar statements from dislocation dynamics are deduced. When plastic strain and yield are identified in terms of the parameters characterizing the dislocation states, familiar flow rules and yield surfaces are produced. The capability of the model to predict not only Tresca and Von-Mises plastic behavior but also phenomena such as kinematic hardening, different responses in tension and compression, latent hardening, and the Bauschinger effect, is shown. Finally, the appropriateness of our equations to model creep, cyclic plasticity, and fatigue, is illustrated.

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Author notes

  1. D. J. Bammann

    Present address: Sandia National Laboratories, 94550, Livermore, CA, USA

  2. E. C. Aifantis

    Present address: Department of Chemical Engineering and Material Science, University of Minnesota, 55455, Minneapolis, MN, USA

Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, University of Illinois, 61801, Urbana, IL, USA

    D. J. Bammann &  E. C. Aifantis

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Bammann, D.J., Aifantis, E.C. On a proposal for a continuum with microstructure. Acta Mechanica 45, 91–121 (1982). https://doi.org/10.1007/BF01295573

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