Acta Mechanica Sinica

, Volume 28, Issue 4, pp 1115–1124 | Cite as

Deformation of plastically compressible hardening-softening-hardening solids

  • A. Needleman
  • S. B. Hutchens
  • N. Mohan
  • J. R. Greer
Research Paper


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.


Plasticity Localization Indentation Finite Element Analysis 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. Needleman
    • 1
  • S. B. Hutchens
    • 2
  • N. Mohan
    • 3
  • J. R. Greer
    • 3
  1. 1.Department of Materials Science and EngineeringUniversity of North TexasDentonUSA
  2. 2.Department of Polymer Science and EngineeringUniversity of Massachsetts AmherstAmherstUSA
  3. 3.Materials ScienceCalifornia Institute of TechnologyPasadenaUSA

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