An inversion method for identification of elastoplastic properties for engineering materials from limited spherical indentation measurements

Hasanov, Alemdar

doi:10.1080/17415970600903899

Cited by 13 publications

(4 citation statements)

References 18 publications

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“…In this context, for a given function g ¼ g ( 2 ), satisfying conditions (2), the nonlinear problem (1) is referred to the direct problem. The inverse problem (5) has first been considered in [9] and is also studied in [10,12,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Numerical solution of the nonlinear parabolic problem related to inverse elastoplastic torsional problem

Tatar

2012

Inverse Problems in Science and Engineering

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In this article, we study a class of direct and inverse coefficient problems defined for a nonlinear parabolic equation. An existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. Direct problem is solved numerically by using semi-implicit finite difference scheme and then some examples are presented related to steady-state solution of the nonlinear direct problem and ill-posedness of the inverse problem. IntroductionThe determination of unknown coefficients in partial differential equations from measured output data are well-known in the literature as inverse coefficient problems (ICPs). Especially, the nonlinear ICPs have been investigated by many authors in the past years. Among these, the torsion problems in linear elasticity have been well-studied in the classical literature [1][2][3][4]. In the case of elastoplastic torsion, the problems related to qualitative properties and an existence of a weak solution of the nonlinear direct problem are also well-studied in mathematical literature [5,6]. Within the range of monotone potential operator theory, the solvability of the nonlinear direct problem has been proved in [7], in the class of admissible coefficients. Many analytical and computational methods are given in the scientific literature, especially when small amounts of twisting are reversible and the beam returns to its original shape after releasing the twisting force. This is called the elastic behaviour. However, inverse problems in torsional deformation are less well-known and have received relatively little attention in the mathematical as well as in engineering literature [8][9][10]. The quasi-static mathematical model of torsional creep within J 2 -deformation theory of plasticity is given in [11]. In this model, one seeks the solution u(x, y), (x, y) 2 & R 2 , of the following nonlinear boundary-value problem:

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Section: Introductionmentioning

confidence: 99%

“…G, 2 0 , , the ICP intends reconstruction of the function g ¼ g( 2 ) by determining these unknowns approximately. As it seen in [18][19][20], some methods have been improved to determine the unknowns such as the parametrization algorithm and the fast algorithm.…”

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confidence: 99%

Numerical solution of the nonlinear parabolic problem related to inverse elastoplastic torsional problem

Tatar

2012

Inverse Problems in Science and Engineering

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“…A number of theoretical and semi-theoretical methods have been developed. [1][2][3][4][5][6][7][8][9][10] In most of these studies, the linear elastic power-law hardening constitutive model was generally adopted. In fact, however, the stress-strain behaviors of many metals are better described by the linear elastic and perfectly plastic constitutive model or the linear elastic linear hardening constitutive model (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test

Zhang

Peng

et al. 2017

MRS Communications

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“…One category of previous studies aimed to obtain the stress-strain curve from a load-depth curve. [1] In another category of studies, many fitting parameters were involved. [2] In this case, it was easy to determine the relationship between the mechanical parameters and the measurement parameters tested.…”

Section: Introductionmentioning

confidence: 99%

Relationships between the work recovery ratio of indentation and plastic parameters for instrumented spherical indentation

Yang

Feng

et al. 2015

MRS Communications

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This paper aims to obtain an analytical expression for the ratio of unloading work of indentation (W u ) to total loading work of indentation (W t ) (work recovery ratio of indentation) in instrumented spherical indentation. The expanding cavity model and Lamé solution are used. Three typical stress-strain relations (elastic-perfectly plastic, linear hardening, and power-law hardening) are analyzed. The results of finite-element method coincide with the expressions. The expressions show that the work recovery ratio of indentation is just related to plastic parameters. Furthermore, elastic work (W e ) are obtained, and it is proved that W e should be distinguished from W u in spherical indentation.

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An inversion method for identification of elastoplastic properties for engineering materials from limited spherical indentation measurements

Cited by 13 publications

References 18 publications

Numerical solution of the nonlinear parabolic problem related to inverse elastoplastic torsional problem

Numerical solution of the nonlinear parabolic problem related to inverse elastoplastic torsional problem

Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test

Relationships between the work recovery ratio of indentation and plastic parameters for instrumented spherical indentation

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