Anisotropic linear elastic parameter estimation using error in the constitutive equation functional

A modified error in the constitutive equation-based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored. Following an alternating minimization procedure associated with the underlying optimization problem, the new strategy results in an explicit material parameter update formula for general anisotropic material. This immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction. We consider a few common materials to derive such conditions. Then, we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space-dependent material orientations. Finally, we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest.

[1]  Jung-Ryul Lee,et al.  Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test , 2005 .

[2]  Yi Liu,et al.  Tomography-based 3-D anisotropic elastography using boundary measurements , 2005, IEEE Transactions on Medical Imaging.

[3]  Guillermo Rus-Carlborg,et al.  A New Convex Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location , 2014, SIAM J. Appl. Math..

[4]  Zubaidah Ismail,et al.  Determination of material properties of orthotropic plates with general boundary conditions using Inverse method and Fourier series , 2013 .

[5]  Assad A. Oberai,et al.  INVERSE PROBLEMS PII: S0266-5611(03)54272-1 Solution of inverse problems in elasticity imaging using the adjoint method , 2003 .

[6]  Charles R. Farrar,et al.  The fundamental axioms of structural health monitoring , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Gilles Lubineau,et al.  A Dissipation Gap Method for full‐field measurement‐based identification of elasto‐plastic material parameters , 2012 .

[8]  Eric Florentin,et al.  Identification of the parameters of an elastic material model using the constitutive equation gap method , 2010 .

[9]  Wenfeng Hao,et al.  Inversion and decoupling of thermo-mechanical deformation in anisotropic materials using the virtual fields method , 2013, Proceedings of the Royal Society A.

[10]  I. Villemure,et al.  Regularized virtual fields method for mechanical properties identification of composite materials , 2014 .

[11]  Andrea Poggialini,et al.  Elastic characterization of anisotropic materials by speckle interferometry , 2005 .

[12]  Joel Spruck,et al.  A variational approach to image fusion , 2000 .

[13]  Jia Lu,et al.  Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Luigi Bruno,et al.  A full-field approach for the elastic characterization of anisotropic materials , 2002 .

[15]  Marc Bonnet,et al.  Inverse problems in elasticity , 2005 .

[16]  Stéphane Avril,et al.  The Virtual Fields Method , 2012 .

[17]  Ramesh Raghupathy,et al.  Generalized anisotropic inverse mechanics for soft tissues. , 2010, Journal of biomechanical engineering.

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

[19]  Pauli Pedersen,et al.  Optimal Orientation of Anisotropic Materials Optimal Distribution of Anisotropic Materials Optimal Shape Design with Anisotropic Materials Optimal Design for a Class of Non-Linear Elasticity , 1993 .

[20]  N. J. Pagano,et al.  INVARIANT PROPERTIES OF COMPOSITE MATERIALS. , 1968 .

[21]  Benoît Blaysat,et al.  The constitutive compatibility method for identification of material parameters based on full-field measurements , 2013 .

[22]  Fabrice Pierron,et al.  Special virtual fields for the direct determination of material parameters with the virtual fields method. 2––Application to in-plane properties , 2002 .

[23]  Marc Bonnet,et al.  Large Scale Parameter Estimation Problems in Frequency-Domain Elastodynamics Using an Error in Constitutive Equation Functional. , 2013, Computer methods in applied mechanics and engineering.

[24]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[25]  Debasish Roy,et al.  A pseudo-dynamical systems approach to a class of inverse problems in engineering , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  Thouraya Baranger,et al.  An energy error-based method for the resolution of the Cauchy problem in 3D linear elasticity , 2008 .

[27]  Michel Grédiac,et al.  The Virtual Fields Method: Extracting Constitutive Mechanical Parameters from Full-field Deformation Measurements , 2012 .

[28]  Hugo Sol,et al.  Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens , 2007 .

[29]  Paolo Vannucci,et al.  Plane Anisotropy by the Polar Method* , 2005 .

[30]  Sankara J. Subramanian,et al.  Identification of orthotropic elastic constants using the Eigenfunction Virtual Fields Method , 2014 .

[31]  G. Holzapfel,et al.  Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[32]  GUILLAUME BAL,et al.  Reconstruction of a Fully Anisotropic Elasticity Tensor from Knowledge of Displacement Fields , 2015, SIAM J. Appl. Math..

[33]  M. Grédiac,et al.  On the direct determination of invariant parameters governing anisotropic plate bending problems , 1996 .

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

[35]  C. M. Mota Soares,et al.  Identification of material properties of composite plate specimens , 1993 .

[36]  K. Turner,et al.  General Anisotropy Identification of Paperboard with Virtual Fields Method , 2014 .

[37]  L. Lamberti,et al.  A new hybrid technique for in-plane characterization of orthotropic materials , 2004 .

[38]  Pierre Feissel,et al.  Modified constitutive relation error identification strategy for transient dynamics with corrupted data : the elastic case , 2007 .

[39]  Guillaume Bal,et al.  Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements , 2013, 1310.5131.

[40]  Pierre Ladevèze,et al.  Error Estimate Procedure in the Finite Element Method and Applications , 1983 .

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

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

[43]  Pierre Ladevèze,et al.  Application of a posteriori error estimation for structural model updating , 1999 .

[44]  A. Oberai,et al.  Uniqueness of inverse problems of isotropic incompressible three-dimensional elasticity , 2014 .

[45]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[46]  Pizhong Qiao,et al.  Vibration-based Damage Identification Methods: A Review and Comparative Study , 2011 .

[47]  Pierre Villon,et al.  Robust identification of elastic properties using the Modified Constitutive Relation Error , 2015 .

[48]  Assad A Oberai,et al.  Transversely isotropic elasticity imaging of cancellous bone. , 2011, Journal of biomechanical engineering.

[49]  M. Reynier,et al.  Updating of finite element models using vibration tests , 1994 .

[50]  B. Banerjee.  Elastic Parameter Identification of Plate Structures Using Modal Response: An ECE Based Approach , 2016 .