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Extending the Bodner–Partom model to simulate the response of materials with extreme kinematic hardening

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Abstract

This paper demonstrates that, at extreme levels of kinematic hardening, the traditional formulation of the Bodner–Partom model can produce anomalous results. The reasons for this anomalous behaviour are explained, and a reformulated version of the model is presented. This reformulation extends the range of the model to include levels of kinematic hardening that may be problematic in the traditional formulation. The formulation of the model is adjusted so as to retain the rate dependency of the original Bodner–Partom model; and to permit the values of the material parameters used with the traditional formulation to be re-used with the extended model—with the exception only of the hardening coefficients which become dimensionless constants holding different numerical values. This revised formulation also imposes associated flow, thereby ensuring phase consistency between stress and plastic strain during non-proportional loading. In this way, the anomalies are removed, the range and stability of the model is increased, and all the advantages and important features of the Bodner–Partom model are retained.

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Authors and Affiliations

  1. Centre for Micro- and Nanomechanics, School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, Scotland, UK

    C. M. Sands & I. A. Guz

  2. School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, Scotland, UK

    H. W. Chandler

  3. Timoshenko Institute of Mechanics, 3, Nesterov Street, 03057, Kiev, Ukraine

    Y. A. Zhuk

Authors
  1. C. M. Sands
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  2. H. W. Chandler
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  3. I. A. Guz
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  4. Y. A. Zhuk
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Correspondence to C. M. Sands.

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Supported by EPSRC: EP/E30351/1.

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Sands, C.M., Chandler, H.W., Guz, I.A. et al. Extending the Bodner–Partom model to simulate the response of materials with extreme kinematic hardening. Arch Appl Mech 80, 161–173 (2010). https://doi.org/10.1007/s00419-009-0307-0

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