Deformation of plastically compressible hardening-softening-hardening solids

作     者：A. Needleman S. B. Hutchens N. Mohan J. R. Greer 

作者机构：Department of Materials Science and Engineering University of North Texas Department of Polymer Science and Engineering University of Massachsetts Amherst Materials Science California Institute of Technology 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2012年第28卷第4期

页      面：1115-1124页

核心收录：

学科分类：08[工学] 080104[工学-工程力学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S.Army Research Office 

主　　题：Plasticity Localization Indentation . Finite Element Analysis 

摘      要：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 hardening- softening-hardening. The same material characterization gives rise to a Lfiders band-like deformation mode in ten- sion. 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.