A self-optimizing inverse analysis method for estimation of cyclic elasto-plasticity model parameters

Abstract In this paper, a novel inverse analysis methodology call a Self - Opt imizing I nverse M ethod (Self-OPTIM) has been presented, which inversely estimates cyclic elasto-plastic constitutive model parameters using global forces and displacement on the same partial boundaries and full-(or partial-) field displacement data. A novelty of the methodology is that it automatically self-estimates material parameters by updating “full-field” reference stresses and strains through two parallel nonlinear finite element simulations. Although a well-known classical cyclic plasticity model is chosen in this paper, it must be emphasized that the proposed Self-OPTIM method is a model-independent method, which means that any advanced model can be naturally integrated with the proposed methodology. Thus, using numerically generated test data of low-carbon steel specimens (AISI 1010), the proposed Self-OPTIM method has been verified showing its successful performance to estimate nonlinear isotropic and kinematic hardening parameters, yield stress, Young’s modulus and Poisson ratio. The effects of experimental noises from CCD camera and measurement errors of the boundary forces are also investigated for the Self-OPTIM method.

[1]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[2]  Edmundo Corona,et al.  Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure , 2008 .

[3]  A. Hauet,et al.  Multiscale experimental investigations about the cyclic behavior of the 304L SS , 2009 .

[4]  M. Abdel-Karim,et al.  Modified kinematic hardening rules for simulations of ratchetting , 2009 .

[5]  Fusahito Yoshida,et al.  Inverse approach to identification of material parameters of cyclic elasto-plasticity for component layers of a bimetallic sheet , 2003 .

[6]  A. Fatemi,et al.  Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths , 2010 .

[7]  Jd Jan Janssen,et al.  Determination of the elasto-plastic properties of aluminium using a mixed numerical–experimental method , 1998 .

[8]  Jean-Louis Chaboche,et al.  On some modifications of kinematic hardening to improve the description of ratchetting effects , 1991 .

[9]  B. Svendsen,et al.  Modeling and simulation of directional hardening in metals during non-proportional loading , 2006 .

[10]  K. S. Kim,et al.  Modeling of ratcheting behavior under multiaxial cyclic loading , 2003 .

[11]  Georges Cailletaud,et al.  Multi-mechanism models for the description of ratchetting: Effect of the scale transition rule and of the coupling between hardening variables , 2007 .

[12]  Stéphane Pagano,et al.  Identification of Mechanical Properties by Displacement Field Measurement: A Variational Approach , 2003 .

[13]  D. McDowell,et al.  On a Class of Kinematic Hardening Rules for Nonproportional Cyclic Plasticity , 1989 .

[14]  Peter Kurath,et al.  An Investigation of Cyclic Transient Behavior and Implications on Fatigue Life Estimates , 1997 .

[15]  Xu Chen,et al.  Modified kinematic hardening rule for multiaxial ratcheting prediction , 2004 .

[16]  Yanyao Jiang,et al.  Benchmark experiments and characteristic cyclic plasticity deformation , 2008 .

[17]  Atef F. Saleeb,et al.  An anisotropic viscoelastoplastic model for composites—sensitivity analysis and parameter estimation , 2003 .

[18]  Chung-Souk Han,et al.  Modeling multi-axial deformation of planar anisotropic elasto-plastic materials, part I: Theory , 2006 .

[19]  Issam Doghri,et al.  Fully implicit integration and consistent tangent modulus in elasto‐plasticity , 1993 .

[20]  Michael R Wisnom,et al.  Identification of the Orthotropic Elastic Stiffnesses of Composites with the Virtual Fields Method: Sensitivity Study and Experimental Validation , 2007 .

[21]  Fabrice Pierron,et al.  Applying the Virtual Fields Method to the identification of elasto-plastic constitutive parameters , 2006 .

[22]  K. Sasaki,et al.  Biaxial ratcheting deformation of type 304 stainless steel: Effect of memorization of back stress , 2004 .

[23]  Stéphane Roux,et al.  Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches , 2006 .

[24]  J. Chaboche,et al.  Modeling of the cylic response and ratchetting effects on inconel-718 alloy , 1991 .

[25]  Dimitri Debruyne,et al.  Elasto-plastic material parameter identification by inverse methods: Calculation of the sensitivity matrix , 2007 .

[26]  Xu Chen,et al.  On the Ohno–Wang kinematic hardening rules for multiaxial ratcheting modeling of medium carbon steel , 2005 .

[27]  K. Nakane,et al.  Thermal ratcheting of solder-bonded elastic and elastoplastic layers , 2008 .

[28]  J. Chaboche.  Time-independent constitutive theories for cyclic plasticity , 1986 .

[29]  S. Roux,et al.  “Finite-Element” Displacement Fields Analysis from Digital Images: Application to Portevin–Le Châtelier Bands , 2006 .

[30]  N. Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior , 1993 .

[31]  N. Ohno,et al.  Nonlinear Kinematic Hardening Rule with Critical State for Activation of Dynamic Recovery , 1991 .

[32]  E. Tanaka,et al.  A nonproportionality parameter and a cyclic viscoplastic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening. , 1994 .

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

[34]  Tasnim Hassan,et al.  Anatomy of coupled constitutive models for ratcheting simulation , 2000 .

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

[36]  Lakhdar Taleb,et al.  Numerical simulation of complex ratcheting tests with a multi-mechanism model type , 2006 .

[37]  M. Kuna,et al.  Identification of material parameters of the Rousselier model by non-linear optimization , 2003 .

[38]  Michael Wolff,et al.  Consistency for two multi-mechanism models in isothermal plasticity , 2008 .

[39]  Atef F. Saleeb,et al.  Parameter-Estimation Algorithms for Characterizing a Class of Isotropic and Anisotropic Viscoplastic Material Models , 2002 .

[40]  Fusahito Yoshida,et al.  A constitutive model of cyclic plasticity , 2000 .

[41]  P. Cheng,et al.  An anisotropic elastic-plastic constitutive model for single and polycrystalline metals. I-theoretical developments , 1996 .

[42]  J. Kajberg,et al.  Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling – Speckle measurements and high-speed photography , 2007 .

[43]  David L. McDowell,et al.  Modeling and experiments in plasticity , 2000 .

[44]  Stéphane Avril,et al.  Stress Reconstruction and Constitutive Parameter Identification in Plane-Stress Elasto-plastic Problems Using Surface Measurements of Deformation Fields , 2008 .

[45]  Karl-Gustaf Sundin,et al.  High strain-rate tensile testing and viscoplastic parameter identification using microscopic high-speed photography , 2004 .

[46]  K. Runesson,et al.  Computational modeling of inelastic large ratcheting strains , 2005 .

[47]  Stéphane Avril,et al.  The Virtual Fields Method for Extracting Constitutive Parameters From Full‐Field Measurements: a Review , 2006 .

[48]  Yanyao Jiang,et al.  Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper , 2008 .

[49]  Peter Kurath,et al.  Nonproportional cyclic deformation: critical experiments and analytical modeling , 1997 .

[50]  Bertrand Wattrisse,et al.  Elastoplastic Behavior Identification for Heterogeneous Loadings and Materials , 2008 .

[51]  Georges Cailletaud,et al.  Macro versus micro-scale constitutive models in simulating proportional and nonproportional cyclic and ratcheting responses of stainless steel 304 , 2009 .

[52]  Michael Vormwald,et al.  A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading , 2003 .

[53]  J. Chaboche.  Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[54]  François Hild,et al.  Inverse strategy from displacement field measurement and distributed forces using FEA , 2005 .

[55]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[56]  Franccois Hild,et al.  Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties – a Review , 2006 .

[57]  N. R. Batane,et al.  Modeling aspects of low plastic strain amplitude multiaxial cyclic plasticity in conventional and ultrafine grain nickel , 2008 .