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Theoretical Foundations of Plasticity

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Theoretical foundation for large-scale computations for nonlinear material behavior

Part of the book series: Mechanics of elastic and inelastic solids 6 ((MEIS,volume 6))

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Abstract

The fundamental continuum aspects of the rate-independent elastic-plastic behavior of materials are discussed. First the general structure of the corresponding rate constitutive relations at finite strains and rotations is examined, bringing into focus the effect of plastically-induced material spin. The choice of stress and strain measures is then reviewed, and it is emphasized that all objective stress-rates equal the Jaumann rate plus terms linear in stress and deformation rate, when the current state is used as the reference state. The induced anisotropy due to stressing is shown to preclude an isotropic relation between the Jaumann rate of Cauchy (or Kirchhoff) stress and the deformation rate. The equations of the classical plasticity theory at finite strains and rotations are presented next, and questions of associative and non-associative flow rules, dilatancy and pressure-sensitivity, plastic anisotropy, Drucker’s postulate and its relation to normality and convexity, and finally the non-coaxiality of the plastic strain rate tensor and the stress tensor are discussed. Then some thermodynamic bases of both rate-dependent and rate-independent inelasticity are considered, emphasizing conditions under which flow potentials for inelastic strain-rates exist. Finally, the problem of strain-softening is briefly discussed, and it is pointed out that both for metals and geo-materials, such softening may often be the result of highly localized damage within the test specimen which no longer remains macroscopically homogeneous, and, hence, should not be regarded as a “representative sample.”

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Authors and Affiliations

  1. Northwestern University, Evanston, Illinois, USA

    S. Nemat-Nasser

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  1. S. Nemat-Nasser
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Editors and Affiliations

  1. Northwestern University, Evanston, Illinois, USA

    Siavouche Nemat-Nasser

  2. Brown University, Providence, Rhode Island, USA

    Robert J. Asaro

  3. University of California, San Diego, La Jolla, California, USA

    Gilbert A. Hegemier

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© 1984 Martinus Nijhoff Publishers, Dordrecht.

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Nemat-Nasser, S. (1984). Theoretical Foundations of Plasticity. In: Nemat-Nasser, S., Asaro, R.J., Hegemier, G.A. (eds) Theoretical foundation for large-scale computations for nonlinear material behavior. Mechanics of elastic and inelastic solids 6, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6213-2_2

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  • DOI: https://doi.org/10.1007/978-94-009-6213-2_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6215-6

  • Online ISBN: 978-94-009-6213-2

  • eBook Packages: Springer Book Archive

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