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Deformation of plastically compressible hardening-softening-hardening solids

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Abstract

Motivated by a model of the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the deformation of a class of compressible elastic-viscoplastic solids with a hardeningsoftening-hardening variation of flow strength with plastic strain. In previous work (Hutchens et al. 2011) a constitutive relation was presented and used to model the response of VACNT pillars in axisymmetric compression. Subsequently, it was found that due to a programming error the constitutive relation presented in the paper (Hutchens et al. 2011) was not the one actually implemented. In particular, the plastic flow rule actually used did not satisfy plastic normality. Here, we present the constitutive formulation actually implemented in the previous work (Hutchens et al. 2011). Dynamic, finite deformation, finite element calculations are carried out for uniaxial compression, uniaxial tension and for indentation of a “half-space” by a conical indenter tip. A sequential buckling-like deformation mode is found in compression when there is plastic non-normality and hardeningsoftening-hardening. The same material characterization gives rise to a Lüders band-like deformation mode in tension. When there is a deformation mode with a sharp front along mesh boundaries, the overall stress-strain response contains high frequency oscillations that are a mesh artifact. The responses of non-softening solids are also analyzed and their overall stress-strain behavior and deformation modes are compared with those of hardening-softening-hardening solids. We find that indentation with a sharp indenter tip gives a qualitatively equivalent response for hardening and hardening-softening-hardening solids.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, University of North Texas, 1155 Union Circle 305310, Denton, TX, 76203-5017, USA

    A. Needleman

  2. Department of Polymer Science and Engineering, University of Massachsetts Amherst, 120 Governors Drive, Amherst, MA, 01003, USA

    S. B. Hutchens

  3. Materials Science, California Institute of Technology, 1200 E. California Blvd, MC 210-41, Pasadena, CA, 91106, USA

    N. Mohan & J. R. Greer

Authors
  1. A. Needleman
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  2. S. B. Hutchens
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  3. N. Mohan
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  4. J. R. Greer
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Correspondence to A. Needleman.

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Needleman, A., Hutchens, S.B., Mohan, N. et al. Deformation of plastically compressible hardening-softening-hardening solids. Acta Mech Sin 28, 1115–1124 (2012). https://doi.org/10.1007/s10409-012-0117-4

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  • DOI: https://doi.org/10.1007/s10409-012-0117-4

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