2018
DOI: 10.1007/s12289-018-1436-1
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On the study of mystical materials identified by indentation on power law and Voce hardening solids

Abstract: We conduct an incisive investigation of the existence of a one-toone correspondence between a material's elastoplastic properties and its indentation responses, with particular emphasis on the residual imprint. We first unravel a so-called "mystical material" pair reported by Chen et al. ( 2007) by examining the specimens' post-indentation morphologies, despite using a single self-similar indenter. Next, using Metric Multidimensional Scaling (MDS), we mitigate the mystical material issue for materials hardenin… Show more

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Cited by 39 publications
(19 citation statements)
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“…(3) substituting the above-obtained parameters into Equations (14) and (16) to calculate the equibiaxial and shear stress part; (4) identifying the direction of the maximum principal residual stress from the direction of the major axis of residual indentation imprint and calculating the principal residual stresses according to the definition of the equibiaxial and shear stress parts. Generally, the sample's plastic properties could be identified using spherical indentation methods [36][37][38][39][40][41][42] or uniaxial tensile tests. The relative change in loading curvature could be obtained by fitting the load-depth curves of stressed and unstressed samples with Equation (2).…”
Section: Of 19mentioning
confidence: 99%
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“…(3) substituting the above-obtained parameters into Equations (14) and (16) to calculate the equibiaxial and shear stress part; (4) identifying the direction of the maximum principal residual stress from the direction of the major axis of residual indentation imprint and calculating the principal residual stresses according to the definition of the equibiaxial and shear stress parts. Generally, the sample's plastic properties could be identified using spherical indentation methods [36][37][38][39][40][41][42] or uniaxial tensile tests. The relative change in loading curvature could be obtained by fitting the load-depth curves of stressed and unstressed samples with Equation (2).…”
Section: Of 19mentioning
confidence: 99%
“…Since the plastic parameters (i.e., yield strain, ε y , and strain-hardening exponent, n) of the tested materials are also involved in the established correlations, to calculate residual stresses, these plastic parameters must be known a priori. Fortunately, either uniaxial tensile/compressive tests or spherical indentation tests [36][37][38][39][40][41][42] could be utilized to determine the plastic parameters. Patel et al [39] established a protocol to obtain the uniaxial stress-strain curve directly from the spherical indentation stress-strain curve by introducing a scaling factor.…”
mentioning
confidence: 99%
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“…Principal components analysis (PCA) (Amsallem et al 2015;Pearson 1901), proper generalized decomposition (PGD) (Chinesta et al 2011), hyper-reduction (Ryckelynck et al 2006), and reduced basis methods (Hoang et al 2016) are the three prominent schools of this field today. Of these, PCA, also called proper orthogonal decomposition or POD (Berkooz et al 1993;Xiao et al 2009;Dulong et al 2007;Raghavan and Breitkopf 2013;Raghavan et al 2013a;Raghavan et al 2013b;Meng et al 2018;Madra et al 2018;Xiao et al 2018;Meng et al 2019a), is an a posteriori statistical method that learns the covariance structure of complex multivariate data.…”
Section: Introductionmentioning
confidence: 99%
“…The Proper Orthogonal Decomposition (POD) [1], originating from statistical data analysis [2], post-processes training data gathered from Full Order Model (FOM) runs to build RBs used 'online' in reduced simulations. POD has found extensive applications in turbulent flow modeling [3][4][5][6] and computer graphics [7][8][9][10] as well as in a variety of scientific fields such as modeling of composites [11], inverse problems [12,13] and shape optimization [14][15][16]. However, when applied to explicit nonlinear dynamics [17,18], POD does not reduce the complexity of evaluating internal variables and entails a computational overhead in the 'online' reduction phase due to the necessity of computing internal forces over all elements.…”
Section: Introductionmentioning
confidence: 99%