Review Article

Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets

Table 1

Comparative overview of inverse identification strategies coupled with FE simulations.

AuthorType of testStrain paths Strain path reversalConstitutive modelOptimization stepsNumber of cost functionsAnalysed resultsMeasuring instants

Cooreman et al. [21]Cruciform biaxial tensile testUniaxial tension to biaxial stretchingNoHill’48 criterion
+
Swift isotropic law
OneOneStrain field (2D)Various
()
Schmaltz and Willner [24]Cruciform biaxial tensile testSimple shear to biaxial stretching (but depending on the test geometry)NoHill’48 criterion
+
Hockett-Sherby isotropic law
(only 2 of 4 parameters identified)
Two steps using
the same cost function
OneDisplacement field (2D)One
Prates et al. [25]Cruciform biaxial tensile testUniaxial tension to biaxial stretchingNoHill’48 criterion
+
Swift isotropic law
Five steps using
four cost functions
FourLoad
+
equivalent strain field (1D)
During the test
One
Prates et al. [26]Cruciform biaxial tensile testUniaxial tension to biaxial stretchingNoVarious criteria ()
+
Swift and Voce isotropic laws
Two (Hill’48 criterion) or three (other criteria)Two or threeLoad
+
equivalent strain
+
strain path fields (1D)
During the test
One
Zhang et al. [28]Cruciform biaxial tensile testUniaxial tension to biaxial stretchingNoBron and Besson criterionOneOneStrain field (1D)One
Liu et al. [29]Cruciform biaxial tensile testUniaxial tension to biaxial stretchingNoVoce-type isotropic lawOneOneStrain field (2D)During the test
Güner et al. [22]Uniaxial tensile test on a notched sampleNear uniaxial tensionNoYld2000 (2D) criterionOneOneStrain field (2D)
+
load
During the test
Pottier et al. [23]Out-of-plane testSimple shear to biaxial stretchingNoHill’48 Criterion
+
Ludwick isotropic law
OneOneLoad
+
displacement field (3D)
Various
()
Chamekh et al. [51]Circular and elliptical bulge testsBiaxial stretchingNoLudwick isotropic law
+
, , and
TwoOnePressureDuring the test
Bambach [52]Circular bulge testBiaxial stretchingNoVoce isotropic lawTwoFourPressure, pole strain, and pole thicknessDuring the test
Reis et al. [53]Circular bulge testBiaxial stretchingNoSwift isotropic lawFourOnePressureDuring the test
Eggertsen and Mattiasson [54]Three-point bending testTension-
compression
YesVarious kinematic laws ()OneOneLoadDuring the test
Yin et al. [55]Twin bridge shear testPure shear to uniaxial tensionYesArmstrong-Frederick kinematic law
+
Voce isotropic law (only 2 of 3 parameters identified)
OneOneAngular momentDuring the test
Pereira et al. [56]Shear testShear with reversalYesLemaître-Chaboche kinematic law
+
Swift isotropic law
OneOneLoadDuring the test

Note: 1D: in one direction in the sheet plane; 2D: on the surface of the sheet plane; 3D: three-dimensional.