Skip to main content Accessibility help
×
Home

Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

  • Bin Chen (a1), Wen Chen (a1) and Xing Wei (a2)

Abstract

This article addresses the resolution of the inverse problem for the parameter identification in orthotropic materials with a number of measurements merely on the boundaries. The inverse problem is formulated as an optimization problem of a residual functional which evaluates the differences between the experimental and predicted displacements. The singular boundary method, an integration-free, mathematically simple and boundary-only meshless method, is employed to numerically determine the predicted displacements. The residual functional is minimized by the Levenberg-Marquardt method. Three numerical examples are carried out to illustrate the robustness, efficiency, and accuracy of the proposed scheme. In addition, different levels of noise are added into the boundary conditions to verify the stability of the present methodology.

Copyright

Corresponding author

*Corresponding author. Email:chenwen@hhu.edu.cn (W. Chen)

References

Hide All
[1]Hematiyan, M. R., Khosravifard, A., Shiah, Y. C. and Tan, C. L., Identification of material parameters of two-dimensional anisotropic bodies using an inverse multi-loading boundary element technique, CMES-Comput. Model. Eng., 87 (2012), pp. 5576.
[2]Meuwissen, M., An Inverse Method for the Mechanical Characterization of Metals, Eindhoven University of Technology, 1998.
[3]Huang, L. X., Sun, X. S., Liu, Y. H. and Cen, Z. Z., Parameter identification for two-dimensional orthotropic material bodies by the boundary element method, Eng. Anal. Bound. Elem., 28 (2004), pp. 109121.
[4]Lecompte, D., Smits, A., Sol, H., Vantomme, J. and Van Hemelrijck, D., Mixed numericalCexperimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens, Int. J. Solids. Struct., 44 (2007), pp. 16431656.
[5]Sol, H., Hua, H., De Visscher, J., Vantomme, J. and De Wilde, W., A mixed numerical/experimental technique for the nondestructive identification of the stiffness properties of fibre reinforced composite materials, NDT. E. Int., 30 (1997), pp. 8591.
[6]De Wilde, W. P., Identification of the rigidities of composite systems by mixed numerical/experimental methods, Mechanical Identification of Composites, Springer, 1991, pp. 115.
[7]Rikards, R., Chate, A. and Gailis, G., Identification of elastic properties of laminates based on experiment design, Int. J. Solids. Struct., 38 (2001), pp. 50975115.
[8]Wang, W. T. and Kam, T. Y., Material characterization of laminated composite plates via static testing, Comput. Struct., 50 (2000), pp. 347352.
[9]Grédiac, M., The use of full-field measurement methods in composite material characterization: interest and limitations, Compos. Part A Appl. S., 35 (2004), pp. 751761.
[10]Geymonat, G. and Pagano, S., Identification of mechanical properties by displacement field measurement: a variational approach, Meccanica., 38 (2003), pp. 535545.
[11]Eric, F. and Gilles, L., Using constitutive equation gap method for identification of elastic material parameters: technical insights and illustrations, IJIDeM., 5 (2011), pp. 227234.
[12]Meuwissen, M. H. H., Oomens, C. W. J., Baaijens, F. P. T., Petterson, R. and Janssen, J. D., Determination of the elasto-plastic properties of aluminium using a mixed numerical-experimental method, J. Mater. Process. Tech., 75 (1998), pp. 204211.
[13]Le Magorou, L., Bos, F. and Rouger, F., Identification of constitutive laws for wood-based panels by means of an inverse method, Compos. Sci. Technol., 62 (2002), pp. 591596.
[14]Chen, S. S., Li, Q. H., Liu, Y. H. and Chen, H. T., Identification of elastic orthotropic material parameters by the scaled boundary finite element method, Eng. Anal. Bound. Elem., 37 (2013), pp. 781787.
[15]Kavanagh, K. T. and Clough, R. W., Finite element applications in the characterization of elastic solids, Int. J. Solids. Struct., 7 (1971), pp. 1123.
[16]Grédiac, M., Toussaint, E. and Pierron, F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 1–Principle and definition, Int. J. Solids. Struct., 39 (2002), pp. 26912705.
[17]Grédiac, M., Toussaint, E. and Pierron, F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 2–Application to in-plane properties, Int. J. Solids. Struct., 39 (2002), pp. 27072730.
[18]Grédiac, M., Toussaint, E. and Pierron, F., Special virtual fields for the direct determination of material parameters with the virtual fields method. 3–Application to the bending rigidities of anisotropic plates, Int. J. Solids. Struct., 40 (2003), pp. 24012419.
[19]Pierron, F., Zhavoronok, S. and Grédiac, M., Identification of the through-thickness properties of thick laminated tubes using the virtual fields method, Int. J. Solids. Struct., 37 (2000), pp. 44374453.
[20]Ohkami, T., Ichikawa, Y. and Kawamoto, T., A boundary element method for identifying orthotropic material parameters, Int. J. Numer. Anal. Met., 15 (1991), pp. 609625.
[21]Huang, L. X., Xiang, Z. H., Sun, X. S., Liu, Y. H. and Cen, Z. Z., A study of the optimal measurement placement for parameter identification of orthotropic composites by the boundary element method, Comput. Mech., 38 (2006), pp. 201209.
[22]Sun, X., Huang, L., Liu, Y. and Cen, Z., Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration, Acta. Mech. Sinica., 21 (2005), pp. 472484.
[23]Masaru, I., Inversion Formulas for the linearized problem for an inverse boundary value problem in elastic prospection, Soc. Ind. Appl. Math., 50 (1990), pp. 16351644.
[24]Damien, C., François, H. and Stéphane, R., Identification of damage fields using kinematic measurements, Comptes Rendus Mécanique, 330 (2002), pp. 729734.
[25]Damien, C., François, H. and Stéphane, R., Identification of a damage law by using full-field displacement measurements, Int. J. Damage. Mech., 16 (2007), pp. 179197.
[26]Fioralba, C., Michele, D. C. and Sun, J. G., A multistep reciprocity gap functional method for the inverse problem in a multilayered medium, Complex. Var. Elliptic., 57 (2012), pp. 261276.
[27]Avril, S., Bonnet, M., Bretelle, A.-S., Grédiac, M., Hild, F., Ienny, P., Latourte, F., Lemosse, D., Pagano, S., Pagnacco, E. and Pierron, F., Overview of identification methods of mechanical parameters based on full-field measurements, Exp. Mech., 48 (2008), pp. 381402.
[28]Avril, S. and Pierron, F., General framework for the identification of constitutive parameters from full-field measurements in linear elasticity, Int. J. Solids. Struct., 44 (2007), pp. 49785002.
[29]Golberg, M. A. and Chen, C. S., The method of fundamental solutions for potential, Helmholtz and diffusion problems, Bound. Integr. Meth. Numer. Math. Aspects., (1998), pp. 103176.
[30]Wei, X., Chen, W. and Chen, B., An ACA accelerated MFS for potential problems, Eng. Anal. Bound. Elem., 41 (2014), pp. 9097.
[31]Chen, W., Singular boundary method: a novel, simple, meshfree, boundary collocation numerical method, Chinese. J. Solid. Mech., 30 (2009), pp. 592599.
[32]Gu, Y., Chen, W. and Zhang, C. Z., Singular boundary method for solving plane strain elastostatic problems, Int. J. Solids. Struct., 48 (2011), pp. 25492556.
[33]Gu, Y., Chen, W. and Zhang, C., Stress analysis for thin multilayered coating systems using a sinh transformed boundary element method, Int. J. Solids. Struct., 50 (2013), pp. 34603471.
[34]Wei, X., Chen, W. and Fu, Z. J., Solving inhomogeneous problems by singular boundary method, J. Marine Sci. Tech., 21 (2013), pp. 814.
[35]Gu, Y., Chen, W., Fu, Z.-J. and Zhang, B., The singular boundary method: Mathematical background and application in orthotropic elastic problems, Eng. Anal. Bound. Elem., 44 (2014), pp. 152160.
[36]Wei, X., Chen, W., Chen, B. and Sun, L. L., Singular boundary method for heat conduction problems with certain spatially varying conductivity, Comput. Math. Appl., 69 (2015), pp. 206222.
[37]Wei, X., Chen, W., Sun, L. L. and Chen, B., A simple accurate formula evaluating origin intensity factor in singular boundary method for two-dimensional potential problems with Dirichlet boundary, Eng. Anal. Bound. Elem., 58 (2015), pp. 151165.
[38]Rizzo, F. J. and Shippy, D. J., A method for stress determination in plane anisotropic elastic bodies, J. Compos. Mater., 4 (1970), pp. 3661.
[39]Moré, J. J., The Levenberg-Marquardt Algorithm: Implementation and Theory, in: Numerical Analysis, Springer, 1978, pp. 105116.
[40]Sun, W. Y. and Yuan, Y. X., Optimization Theory and Methods: Nonlinear Programming, Springer, 2006.
[41]Rhee, J. and Rowlands, R. E., Stresses around extremely large or interacting multiple holes in orthotropic composites, Comput. Struct., 61 (1996), pp. 935950.
[42]Shanno, D. F., Conditioning of quasi-Newton methods for function minimization, Math. Comput., 24 (1970), pp. 647656.
[43]Conn, A. R., Gould, N. and Toint, P. L., A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds, Math. Comput. Am. Math. Soc., 66 (1997), pp. 261288.

Keywords

MSC classification

Identification of Elastic Orthotropic Material Parameters by the Singular Boundary Method

  • Bin Chen (a1), Wen Chen (a1) and Xing Wei (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed