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Theory of Material Instability in Incrementally Nonlinear Plasticity

  • Conference paper
Material Instabilities in Elastic and Plastic Solids

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 414))

Abstract

Material instability in time-independent elastic-plastic solids is studied as a phenomenon strictly related to qualitative properties of an incremental constitutive law. A broad class of incrementally nonlinear material models is considered which encompasses classical elastoplasticity with a single smooth yield surface, as well as multi-mode plasticity with many internal mechanisms of inelastic deformation which give the yield-surface vertex effect. Three types of instability are investigated: with respect to internal microstructural rearrangements, for deviations from uniform deformation under boundary displacement control, and under flexible constraints corresponding to deformation-sensitive loading. It is shown that the respective instability criteria are different and, moreover, dependent on whether the instability concerns a single equilibrium state or a process of quasi-static deformation. Instability of equilibrium is of dynamic type, while instability of a process going through stable equilibrium states is related to a continuous spectrum of quasi-static bifurcation points along the deformation path. Basic concepts are outlined by the example of a one-dimensional discretized tensile bar and extended to incipient localization of deformation in a three-dimensional continuum. Under symmetry restrictions imposed on an incrementally nonlinear constitutive law, a unified approach to material instabilities of various types is presented which is based on the single energy criterion. By specifying the incremental energy consumption to second-order terms and determining the circumstances in which it fails to be minimized along a fundamental deformation path, the onset of material instability of a selected type can be estimated.

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  1. Polish Academy of Sciences, Warsaw, Poland

    H. Petryk

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  1. Polish Academy of Sciences, Poland

    Henryk Petryk

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Petryk, H. (2000). Theory of Material Instability in Incrementally Nonlinear Plasticity. In: Petryk, H. (eds) Material Instabilities in Elastic and Plastic Solids. CISM International Centre for Mechanical Sciences, vol 414. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2562-5_5

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  • DOI: https://doi.org/10.1007/978-3-7091-2562-5_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83328-5

  • Online ISBN: 978-3-7091-2562-5

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