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

This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

[1]  Frédéric Barlat,et al.  Linear transfomation-based anisotropic yield functions , 2005 .

[2]  A. P. Karafillis,et al.  A general anisotropic yield criterion using bounds and a transformation weighting tensor , 1993 .

[3]  Wei Liu,et al.  Identification of sheet metal hardening for large strains with an in-plane biaxial tensile test and a dedicated cross specimen , 2015 .

[4]  Amit K. Ghosh.  Tensile instability and necking in materials with strain hardening and strain-rate hardening , 1977 .

[5]  J. Kajberg,et al.  Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields , 2004 .

[6]  Fusahito Yoshida,et al.  A Model of Large-Strain Cyclic Plasticity and its Application to Springback Simulation , 2002 .

[7]  Toshihiko Kuwabara,et al.  Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations , 2007 .

[8]  S. Thuillier,et al.  Potential of the Cross Biaxial Test for Anisotropy Characterization Based on Heterogeneous Strain Field , 2015 .

[9]  Kjell Mattiasson,et al.  On the modelling of the bending–unbending behaviour for accurate springback predictions , 2009 .

[10]  William Prager,et al.  Recent Developments in the Mathematical Theory of Plasticity , 1949 .

[11]  Weilong Hu,et al.  An orthotropic yield criterion in a 3-D general stress state , 2005 .

[12]  Sami Chatti,et al.  The effect of non-linear recovery on springback prediction , 2011 .

[13]  Alexander Brosius,et al.  A cyclic twin bridge shear test for the identification of kinematic hardening parameters , 2012 .

[14]  Xiao-qiang Li,et al.  Identification of material parameters from punch stretch test , 2013 .

[15]  O. Sherby,et al.  Large strain deformation of polycrystalline metals at low homologous temperatures , 1975 .

[16]  M. Oliveira,et al.  Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy , 2015, International Journal of Material Forming.

[17]  A. H. van den Boogaard,et al.  A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states , 2006 .

[18]  R. H. Wagoner,et al.  Anisotropic hardening equations derived from reverse-bend testing , 2002 .

[19]  Alexander Brosius,et al.  Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld2000-2D yield function , 2012 .

[20]  P. Prates,et al.  Inverse identification of the Swift law parameters using the bulge test , 2017 .

[21]  Hans-Werner Ziegler.  A Modification of Prager's Hardening Rule , 1959 .

[22]  H. Sol,et al.  Identification of Mechanical Material Behavior Through Inverse Modeling and DIC , 2008 .

[23]  Frédéric Barlat,et al.  Orthotropic yield criterion for hexagonal closed packed metals , 2006 .

[24]  E. Voce,et al.  The relationship between stress and strain for homogeneous deformations , 1948 .

[25]  E. Pagnacco,et al.  Identification from measurements of mechanical fields by finite element model updating strategies , 2009 .

[26]  D. C. Ludwigson,et al.  Modified stress-strain relation for FCC metals and alloys , 1971 .

[27]  Jeong Whan Yoon,et al.  On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming , 2008 .

[28]  P. Manach,et al.  Material parameters identification: Gradient-based, genetic and hybrid optimization algorithms , 2008 .

[29]  Marta Cristina Oliveira,et al.  On the identification of kinematic hardening with reverse shear test , 2014, Engineering with Computers.

[30]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[31]  Frédéric Barlat,et al.  Generalization of Drucker's Yield Criterion to Orthotropy , 2001 .

[32]  H. W. Swift.  Plastic instability under plane stress , 1952 .

[33]  L. Menezes,et al.  A modified swift law for prestrained materials , 1998 .

[34]  Fusahito Yoshida,et al.  A model of large-strain cyclic plasticity and its application to springback simulation , 2003 .

[35]  F. Barlat,et al.  A six-component yield function for anisotropic materials , 1991 .

[36]  Jian Cao,et al.  A study on formulation of objective functions for determining material models , 2008 .

[37]  Marta Oliveira,et al.  A new strategy for the simultaneous identification of constitutive laws parameters of metal sheets using a single test , 2014 .

[38]  Frédéric Barlat,et al.  Determination of Anisotropic Plastic Constitutive Parameters Using the Virtual Fields Method , 2014 .

[39]  Stéphane Avril,et al.  Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening , 2010 .

[40]  H. Belhadjsalah,et al.  Inverse identification using the bulge test and artificial neural networks , 2006 .

[41]  Alexander Brosius,et al.  A New Shear Test for Sheet Metal Characterization , 2011 .

[42]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[43]  Jacques Besson,et al.  A yield function for anisotropic materials Application to aluminum alloys , 2004 .

[44]  M. Bonnet,et al.  Overview of Identification Methods of Mechanical Parameters Based on Full-field Measurements , 2008 .

[45]  Dominique Guines,et al.  Development of an in-plane biaxial test for forming limit curve (FLC) characterization of metallic sheets , 2010 .

[46]  Jean-Louis Chaboche,et al.  A review of some plasticity and viscoplasticity constitutive theories , 2008 .

[47]  António Andrade-Campos,et al.  Novel criteria for determination of material model parameters , 2012 .

[48]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[49]  H. Haddadi,et al.  Improving the characterization of a hardening law using digital image correlation over an enhanced heterogeneous tensile test , 2012 .

[50]  L. Robert,et al.  Identification of hardening parameters using finite element models and full-field measurements: some case studies , 2012 .

[51]  J. Ponthot,et al.  A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation , 2006 .

[52]  N. Deng,et al.  Cruciform Specimen Design and Verification for Constitutive Identification of Anisotropic Sheets , 2015 .

[53]  D. Raabe,et al.  Strain rate sensitivity of automotive sheet steels : influence of plastic strain, strain rate, temperature, microstructure, bake hardening and pre-strain , 2010 .

[54]  Kjell Mattiasson,et al.  An evaluation of some recent yield criteria for industrial simulations of sheet forming processes , 2008 .

[55]  F. Barlat,et al.  Parameter identification of the homogeneous anisotropic hardening model using the virtual fields method , 2016 .

[56]  P.-A. Eggertsen,et al.  An efficient inverse approach for material hardening parameter identification from a three-point bending test , 2010, Engineering with Computers.

[57]  Frédéric Barlat,et al.  Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals , 2008 .

[58]  Kai Willner,et al.  Comparison of Different Biaxial Tests for the Inverse Identification of Sheet Steel Material Parameters , 2014 .

[59]  Sandrine Thuillier,et al.  Calibration of anisotropic yield criterion with conventional tests or biaxial test , 2014 .

[60]  Pierre Vacher,et al.  Contribution of heterogeneous strain field measurements and boundary conditions modelling in inverse identification of material parameters , 2011 .

[61]  Hiroshi Hamasaki,et al.  A user-friendly 3D yield function to describe anisotropy of steel sheets , 2013 .

[62]  Abdelwaheb Dogui,et al.  Anisotropic parameter identification using inhomogeneous tensile test , 2002 .

[63]  Frédéric Barlat,et al.  Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction , 2009 .

[64]  Luís Menezes,et al.  Study on the influence of work-hardening modeling in springback prediction , 2007 .

[65]  Stéphane Avril,et al.  Identification of Elasto-Plastic Constitutive Parameters from Statically Undetermined Tests Using the Virtual Fields Method , 2006 .

[66]  Frédéric Barlat,et al.  An alternative to kinematic hardening in classical plasticity , 2011 .

[67]  R. Hambli,et al.  Inverse technique identification of material parameters using finite element and neural network computation , 2009 .

[68]  C. O. Frederick,et al.  A mathematical representation of the multiaxial Bauschinger effect , 2007 .

[69]  Pierre Vacher,et al.  Out-of-plane Testing Procedure for Inverse Identification Purpose: Application in Sheet Metal Plasticity , 2012 .

[70]  Mhh Marcel Meuwissen,et al.  An inverse method for the mechanical characterisation of metals , 1998 .