Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-05T14:00:32.467Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of the stiffness distribution in two and three dimensions using boundary deformations: a preliminary study

Published online by Cambridge University Press:  07 June 2018

Ping Luo ,
Yue Mei ,
Maulik Kotecha ,
Amirhossein Abbasszadehrad ,
Stephen Rabke ,
Geoffrey Garner  and
Sevan Goenezen
Ping Luo
Affiliation:
Texas A&M University, High Performance Research Computing, College Station, TX 77843, USA
Yue Mei*
Affiliation:
Swansea University, Zienkiewicz Centre for Computational Engineering, Swansea SA18EN, UK
Maulik Kotecha
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
Amirhossein Abbasszadehrad
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
Stephen Rabke
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
Geoffrey Garner
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
Sevan Goenezen
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Address all correspondence to Yue Mei at meiyue1989@gmail.com
Get access

Abstract

We present for the first time the feasibility to recover the stiffness (here shear modulus) distribution of a three-dimensional heterogeneous sample using measured surface displacements and inverse algorithms without making any assumptions about local homogeneities and the stiffness distribution. We simulate experiments to create measured displacements and augment them with noise, significantly higher than anticipated measurement noise. We also test two-dimensional problems in plane strain with multiple stiff inclusions. Our inverse strategy recovers the shear modulus values in the inclusions and background well, and reveals the shape of the inclusion clearly.

Type
Research Letters
Information
MRS Communications , Volume 8 , Issue 3 , September 2018 , pp. 893 - 902
Check for updates
Copyright
Copyright © Materials Research Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bruck, H.A., McNeill, S.R., Sutton, M.A., and Peters, W.H.: Digital image correlation using Newton–Raphson method of partial differential correction. Exp. Mech. 29, 261–267 (1989).Google Scholar
2.IIiopoulos, A., Michopoulos, J.G., Orifici, A.C., and Thomson, R.S.: Experimental validation of the 2D meshless random grid method. In Proc. ASME IDETC/CIE, 513–520 (2011).Google Scholar
3.Michopoulos, J.G. and IIiopoulos, A.: A computational workbench for remote full field 3D displacement and strain measurements. In Proc. ASME IDETC/CIE, 489–498 (2011).Google Scholar
4.IIiopoulos, A. and Michopoulos, J.G.: Meshless methods for full field displacement and strain measurement. Adv. Comput. Inf. Eng. Res. 1, 28 (2014).Google Scholar
5.Stamborska, M., Kvícala, M., and Losertova, M.: Identification of the mechanical properties of high strength steel using digital image correlation, advanced materials research. Adv. Mater. Res. 980, 122–126 (2014).Google Scholar
6.Kato, A.: Measurement of strain distribution in metals for tensile test using digital image correlation method and consideration of stress-strain relation. Mech. Eng. J. 3, 16-00141 (2016).Google Scholar
7.Mei, Y., Fulmer, R., Raja, V., Wang, S., and Goenezen, S.: Estimating the non-homogeneous elastic modulus distribution from surface deformations. Int. J. Solids Struct. 83, 73–80 (2016).Google Scholar
8.Mei, Y., Wang, S., Shen, X., Rabke, S., and Goenezen, S.: Mechanics based tomography: a preliminary feasibility study. Sensors 17, 1075 (2017).Google Scholar
9.Liu, H.T., Sun, L.Z., Wang, G., and Vannier, M.W.: Analytic modeling of breast elastography. Med. Phys. 30, 2340–2349 (2003).Google Scholar
10.Schnur, D.S. and Zabaras, N.: An inverse method for determining elastic material properties and material interface. Int. J. Numer. Methods Eng. 33, 2039–2057 (1992).Google Scholar
11.Elijah, E.W., Houten, V., Peters, A., and Chase, J.G.: Phantom elasticity reconstruction with digital image elasto-tomography. J. Mech. Behav. Biomed. Mater. 4, 1741–1754 (2011).Google Scholar
12.Reddy, J.N.: An Introduction to the Finite Element Method, 3rd ed. (McGraw-Hill Education, New York, USA, 2005).Google Scholar
13.Frick, K., Lorenz, D., and Resmerita, E.: Morozov's principle for the augmented Lagrangian method applied to linear inverse problems. Multiscale Model. Simul. 9, 1528–1548 (2011).Google Scholar
14.Zhu, C., Byrd, R.H., Lu, P., and Nocedal, J.: L-BFGS-B: a limited memory FORTRAN code for solving bound constrained optimization problems Technical Report, NAM-11, EECS Department, Northwestern University (1994).Google Scholar
15.Goenezen, S.: Inverse problems in finite elasticity: An application to imaging the nonlinear elastic properties of soft tissues. Ph.D. dissertation (Rensselaer Polytechnic Institute, Troy, NY, 2011).Google Scholar
16.Goenezen, S., Barbone, P., and Oberai, A.A.: Solution of the nonlinear elasticity imaging inverse problem: the incompressible case. Comput. Methods Appl. Mech. Eng. 200, 1406–1420 (2011).Google Scholar
17.Mei, Y., Stover, B., Kazerooni, N.A., Srinivasa, A., Hajhashemkhani, M., Hematiyan, M.R., and Goenezen, S.: A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials. Int. J. Mech. Sci. 140, 446–454 (2018).Google Scholar
18.Mei, Y., Tajderi, M., and Goenezen, S.: Regularizing biomechanical maps for partially known material properties. Int. J. Appl. Mech. 9, 1750020 (2017).Google Scholar