Deformation of plastically compressible hardening-softening-hardening solids

Needleman, A.; Hutchens, Shelby B.; Mohan, Nisha; Greer, Julia R.

doi:10.1007/s10409-012-0117-4

Cited by 17 publications

(37 citation statements)

References 19 publications

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“…3 did not satisfy plastic normality and (ii) the overall stress-strain curve obtained with corrected code could contain numerically induced high frequency oscillations. 1,4 The error and its consequences are described in detail in Refs. 2 and 4.…”

mentioning

confidence: 99%

Erratum: “A microstructurally motivated description of the deformation of vertically aligned carbon nanotube structures” [Appl. Phys. Lett. 100, 121910 (2012)]

Hutchens

Needleman

Greer

2012

Applied Physics Letters

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mentioning

confidence: 99%

Erratum: “A microstructurally motivated description of the deformation of vertically aligned carbon nanotube structures” [Appl. Phys. Lett. 100, 121910 (2012)]

Hutchens

Needleman

Greer

2012

Applied Physics Letters

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“…Hence, it is useful to develop a predictive framework for the mechanical behavior of VACNTs under a wide range of loadings, which requires the knowledge of their intrinsic material properties. A key finding in [22,23] was that the response in compression is a structural response, i.e., the observed overall compressive stress-strain relation does not directly reflect the intrinsic material properties. Extraction of material properties from the overall stress-strain response is complex and not unique.…”

Section: Introductionmentioning

confidence: 99%

“…Rather, we focus on assessing the relation between material parameters characterizing the hardening-softening-hardening hardness function in the constitutive formulation of Refs. [22,23] and the qualitative nature of the predicted response in uniaxial tension. We first use a one-dimensional analysis to set the stage and then carry out finite deformation axisymmetric finite element calculations using the constitutive framework in [22,23] for compressible elasticviscoplastic solids with plastic non-normality.…”

Section: Introductionmentioning

confidence: 99%

“…[22,23] and the qualitative nature of the predicted response in uniaxial tension. We first use a one-dimensional analysis to set the stage and then carry out finite deformation axisymmetric finite element calculations using the constitutive framework in [22,23] for compressible elasticviscoplastic solids with plastic non-normality. We restrict consideration to the variation of three constitutive parameters and explore their influence on the deformation mode and the overall stress-strain response.…”

Section: Introductionmentioning

confidence: 99%

“…In uniaxial compression, VACNTs have been observed to deform in a progressive buckling-like deformation mode [1,[11][12][13][14][17][18][19][20][21]. A phenomenological elastic-viscoplastic constitutive relation, which incorporated plastic compressibility, plastic non-normality, and a hardening-softening-hardening hardness function [22,23] qualitatively reproduced the deformation mode and overall stress-strain behavior seen in the experiments in [13,24]. Additional calculations in [22] revealed a variety of deformation modes depending on material parameters and enabled the identification of the parameter regime that gives rise to progressive buckling type of deformation.…”

Section: Introductionmentioning

confidence: 99%

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Uniaxial Tension of a Class of Compressible Solids With Plastic Non-Normality

Mohan

Cheng

Greer

et al. 2013

Journal of Applied Mechanics

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Motivated by a model that qualitatively captured the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In Hutchens et al. ["Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes," J. Mech. Phys. Solids, 59, pp. 2227-2237), Erratum 60, 1753-1756] an elastic viscoplastic constitutive relation with plastic compressibility, plastic non-normality, and a hardening-softeninghardening hardness function was used to model experimentally obtained uniaxial compression data of cylindrical VACNT micropillars. Complex deformation modes were found in uniaxial compression, which include a sequential buckling-like collapse of the type seen in experiments. These complex deformation modes led to the overall stress-strain signature of the pillar not being of the same form as the input material hardness function. A fundamental question that motivates exploring the deformation of this class of materials-both experimentally and theoretically-is how to extract the intrinsic material response from simple tests. In this study we explore the relation between the input material response and the overall stress strain behavior in uniaxial tension using the constitutive framework of Hutchens et al. A simple one-dimensional analysis reveals the types of instability modes to be expected. Dynamic, finite deformation finite element calculations are carried out to explore the dependence of diffuse necking, localized necking, and propagating band deformation modes on characteristics of the hardness function. Attention is devoted to uncovering implications for obtaining intrinsic material properties of complex hierarchical structures; for example, vertically aligned carbon nanotubes (VACNTs), from uniaxial tension experiments.

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Indentation of elastically soft and plastically compressible solids

2015

Self Cite

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The effect of soft elasticity, i.e., a relatively small value of the ratio of Young's modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking rigid sharp indenter into a cylinder modeling indentation of a half space. The material is characterized by a finite strain elastic-viscoplastic constitutive relation that allows for plastic as well as elastic compressibility. Both soft elasticity and plastic compressibility significantly reduce the ratio of nominal indentation hardness to yield strength. A linear relation is found between the nominal indentation hardness and the logarithm of the ratio of Young's modulus to yield strength, but with a different coefficient than reported in previous studies. The nominal indentation hardness decreases rapidly for small deviations from plastic incompressibility and then decreases rather slowly for values of the plastic Poisson's ratio less than 0.25. For both soft elasticity and plastic compressibility, the main reason for the lower values of indentation hardness is related to the reduction in the hydrostatic stress level in the material below the indenter.

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Deformation of plastically compressible hardening-softening-hardening solids

Cited by 17 publications

References 19 publications

Erratum: “A microstructurally motivated description of the deformation of vertically aligned carbon nanotube structures” [Appl. Phys. Lett. 100, 121910 (2012)]

Erratum: “A microstructurally motivated description of the deformation of vertically aligned carbon nanotube structures” [Appl. Phys. Lett. 100, 121910 (2012)]

Uniaxial Tension of a Class of Compressible Solids With Plastic Non-Normality

Indentation of elastically soft and plastically compressible solids

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