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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 1-2/2018

08-05-2017 | SPECIAL

Identifiability of material parameters in solid mechanics

Authors: Stefan Hartmann, Rose Rogin Gilbert

Published in: Archive of Applied Mechanics | Issue 1-2/2018

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Abstract

Material parameter identification using constitutive models of elasticity, viscoelasticity, rate-independent plasticity and viscoplasticity has a long history with regard to homogeneous and inhomogeneous deformations. For example, uniaxial tensile tests, pure shear tests, torsion experiments of thin-walled tubes or biaxial tensile tests are used to obtain the material parameters by solving the inverse problem. Frequently, the parameters are determined by numerical optimization tools. In this paper, we investigate some very basic single- and two-layered examples regarding identifiability, because these tests are the basis for more complex geometrical and physical nonlinear problems. These simple examples are the uniaxial tensile/compression case, biaxial tensile tests of a cruciform specimen, torsion of a thin-walled tube, a thick-walled tube under internal pressure and the indentation test. For the thick-walled tube under internal and external pressure with an axial pre-strain with several layers, an analytical solution is provided directly suitable for programming. The aim is to get an understanding whether some problems lead to non-identifiable parameters.
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Appendix
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Literature
1.
Amin, A.F.M.S., Alam, M.S., Okui, Y.: An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification. Mech. Mater. 34, 75–95 (2002)CrossRef
2.
Andresen, K., Dannemeyer, S., Friebe, H., Mahnken, R., Ritter, R., Stein, E.: Parameteridentifikation für ein plastisches Stoffgesetz mit FE-Methoden und Rasterverfahren. Bauingenieur 71, 21–31 (1996)
3.
Bai, Y., Igland, T.R., Moan, T.: Tube collapse under combined external pressure, tension and bending. Mar. Struct. 10(5), 389–410 (1997)CrossRef
4.
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming. Wiley, New York (1993)MATH
5.
Beck, J.V., Arnold, K.J.: Parameter Estimation in Engineering and Science. Wiley, New York (1977)MATH
6.
Benedix, U., Görke, U.J., Kreißig, R., Kretzschmar, S.: Local and global analysis of inhomogeneous displacement fields for the identification of material parameters. In: Hoa, S.V., De Wilde, W.P., Blain, W.R. (eds) Computer Methods in Composite Materials VI (CADCOMP 98), pp 159–168 (1998)
7.
Beveridge, G.S.G., Schechter, R.S.: Optimization: Theory and Practice, 1st edn. McGraw-Hill Book Company, New York (1970)MATH
8.
Bier, W., Dariel, M.P., Frage, N., Hartmann, S., Michailov, O.: Die compaction of copper powder designed for material parameter identification. Int. J. Mech. Sci. 49, 766–777 (2007)CrossRef
9.
Björck, A.: Numerical Methods for Least Squares Problems. SIAM (Society for Industrial and Applied Mathematics), Philadelphia (1996)CrossRefMATH
10.
Bourgoyne, A.: Applied Drilling Engineering. Society of Petroleum Engineers, Dallas (1986). SPE textbook series
11.
Calloch, S., Marquis, D.: Triaxial tension-compression tests for multiaxial cyclic plasticity. Int. J. Plast 15, 521–549 (1999)CrossRefMATH
12.
Carnavas, P.C., Page, N.W.: Elastic properties of compacted metal powders. J. Mater. Sci. 33, 4647–4655 (1998)CrossRef
13.
Chen, Z., Diebels, S.: Nanoindentation of soft polymers: modeling, experiments and parameter identification. Tech. Mech. 34, 166–189 (2014)
14.
Clifton, R.J., Simonson, E.R., Jones, A.H., Green, S.J.: Determination of the critical-stress-intensity factor kic from internally pressurized thick-walled vessels. Exp. Mech. 16(6), 233–238 (1976)CrossRef
15.
Coleman, B.D., Gurtin, M.E.: Thermodynamics with internal state variables. J. Chem. Phys. 47, 597–613 (1967)CrossRef
16.
Consigny, P.M., Tulenko, T.N., Nicosia, R.F.: Immediate and long-term effects of angioplasty-balloon dilation on normal rabbit iliac artery. Arterioscler. Thromb. Vasc. Biol. 6(3), 265–276 (1986)CrossRef
17.
Cox, R.H.: Comparison of mechanical and chemical properties of extra- and intralobar canine pulmonary arterie. Am. J. Physiol. Heart Circ. Physiol. 242, H245–H253 (1982)CrossRef
18.
Cox, R.H.: Comparison of arterial wall mechanics using ring and cylindrical segments. Am. J. Physiol. Heart Circ. Physiol. 244, H298–H303 (1983)CrossRef
19.
Davis, J.R.: Tensile Testing, 2nd edn. ASM International, Materials Park (2004)
20.
Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Classics in Applied Mathematics, vol. 16. SIAM Society for Industrial and Applied Mathematics, Philadelphia (1996)CrossRefMATH
21.
Diebels, S., Chen, Z., Scheffer, T., Seibert, H.: Macroindentation of a soft polymer: identification of hyperelasticity and validation by uni/biaxial tensile tests. Mech. Mater. 64, 111–127 (2013)CrossRef
22.
Draper, N.R., Smith, H.: Applied Regression Analysis, 3rd edn. Wiley, New York (1998)MATH
23.
24.
Forsberg, F., Sjödahl, M., Mooser, R., Hack, E., Wyss, P.: Full three-dimensional strain measurements on wood exposed to three-point bending: analysis by use of digital volume correlation applied to synchrotron radiation micro-computed tomography image data. Strain 46, 47–60 (2010)CrossRef
25.
Gasser, T.C., Ogden, R.W., Holzapfel, G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6), 15–35 (2006)CrossRef
26.
Gilbert, R.R., Hartmann, S., Kudela, L., Rank, E., Sahar, G., Yosibash, Z., Yossef, O.: Parameter identification of the passive response in arteries. Technical Report Series Fac3-16-01, Faculty of Mathematics/Computer Science and Mechanical Engineering, Clausthal University of Technology (Germany) (2016)
27.
Hannon, A., Tiernan, P.: A review of planar biaxial tensile test systems for sheet metal. J. Mater. Process. Technol. 198(1–3), 1–13 (2008)CrossRef
28.
Hartmann, S.: Numerical studies on the identification of the material parameters of Rivlin’s hyperelasticity using tension–torsion tests. Acta Mech. 148, 129–155 (2001a)CrossRefMATH
29.
Hartmann, S.: Parameter estimation of hyperelasticity relations of generalized polynomial-type with constraint conditions. Int. J. Solids Struct. 38(44–45), 7999–8018 (2001b)CrossRefMATH
30.
Hartmann, S., Tschöpe, T., Schreiber, L., Haupt, P.: Large deformations of a carbon black-filled rubber. Experiment, optical measurement and parameter identification using finite elements. Eur. J. Mech. Ser. A Solids 22, 309–324 (2003)CrossRefMATH
31.
Hartmann, S., Gibmeier, J., Scholtes, B.: Experiments and material parameter identification using finite elements. Uniaxial tests and validation using instrumented indentation tests. Exp. Mech. 46(1), 5–18 (2006)CrossRef
32.
Hartmann, S., Neff, P.: Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility. Int. J. Solids Struct. 40(11), 2767–2791 (2003)MathSciNetCrossRefMATH
33.
34.
Haupt, P., Lion, A.: Experimental identification and mathematical modelling of viscoplastic material behavior. J. Contin. Mech. Thermodyn. 7, 73–96 (1995)CrossRef
35.
Haupt, P., Sedlan, K.: Viscoplasticity of elastomeric materials: experimental facts and constitutive modelling. Arch. Appl. Mech. 71, 89–109 (2001)CrossRefMATH
36.
Huber, N., Tsakmakis, C.: Determination of constitutive properties from spherical indentation data using neural networks, Part I: plasticity with nonlinear and kinematic hardening. J. Mech. Phys. Solids 47, 1589–1607 (1999a)CrossRefMATH
37.
Huber, N., Tsakmakis, C.: Determination of constitutive properties from spherical indentation data using neural networks, Part II: the case of pure kinematic hardening in plasticity laws. J. Mech. Phys. Solids 47, 1569–1588 (1999b)CrossRefMATH
38.
Johlitz, M., Diebels, S., Jan, B., Steeb, H., Wulff, P.: Size effects in polyurethane bonds: experiments, modelling and parameter identification. J. Mater. Sci. 43, 4768–4779 (2008)CrossRef
39.
Kadlowec, J., Wineman, A., Hulbert, G.: Elastomer bushing response: experiments and finite element modeling. Acta Mech. 163, 25–38 (2003)MATH
40.
Krämer, S., Rothe, S., Hartmann, S.: Homogeneous stress-strain states computed by 3D-stress algorithms of FE-codes: application to material parameter identification. Eng. Comput. 31, 141–159 (2015)CrossRef
41.
Kreißig, R.: Auswertung inhomogener Verschiebungsfelder zur Identifikation der Parameter elastisch-plastischer Deformationsgesetze. Forsch. Ingenieurwes. 64, 99–109 (1998)CrossRef
42.
Kreissig, R., Benedix, U., Goerke, U.J.: Statistical aspects of the identification of material parameters for elasto-plastic models. Arch. Appl. Mech. 71, 123–134 (2001)CrossRefMATH
43.
Lamkanfi, E., Paepegem, W.V., Degrieck, J.: Shape optimization of a cruciform geometry for biaxial testing of polymers. Polym. Testing 41, 7–16 (2015)CrossRef
44.
Lawson, C.L., Hanson, R.J.: Solving least squares problems. Siam Society for Industrial and Applied Mathematics, Philadelphia (1995)CrossRefMATH
45.
Lee, H., Lee, J.H., Pharr, G.M.: A numerical approach to spherical indentation techniques for material property evaluation. J. Mech. Phys. Solids 53, 2037–2069 (2005)CrossRefMATH
46.
Lefebvre, D., Chebl, C., Thibodeau, L., Khazzari, E.: A high-strain biaxial-testing rig for thin-walled tubes under axial load and pressure. Exp. Mech. 23, 384–392 (1983)CrossRef
47.
48.
Lemaitre, J., Chaboche, J.L.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1990)CrossRefMATH
49.
Liu, M.C.M., Krempl, E.: A uniaxial viscoplastic model based on total strain and overstress. J. Mech. Phys. Solids 27, 377–391 (1979)CrossRefMATH
50.
Lubliner, J.: Plasticity Theory. Macmillan Publishing Company, New York (1990)MATH
51.
Luenberger, D.G.: Linear and Nonlinear Programming. Addison-Wesley, Reading (1989)MATH
52.
Mahnken, R., Stein, E.: A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput. Methods Appl. Mech. Eng. 136, 225–258 (1996)CrossRefMATH
53.
Mahnken, R., Stein, E.: Parameter identification for finite deformation elasto-plasticity in principal directions. Comput. Methods Appl. Mech. Eng. 147, 17–39 (1997)CrossRefMATH
54.
Malvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs (1969)MATH
55.
Nedjar, B.: On a concept of directional damage gradient in transversely isotropic materials. Int. J. Solids Struct. 88–89, 56–67 (2016)CrossRef
56.
57.
Ogden, R.W.: Non-linear Elastic Deformations. Ellis Horwood, Chichester (1984)MATH
58.
Ognedal, A.S., Clausen, A.H., Polanco-Loria, M., Benallal, A., Raka, B., Hopperstad, O.S.: Experimental and numerical study on the behaviour of PVC and HDPE in biaxial tension. Mech. Mater. 54, 18–31 (2012)CrossRef
59.
Press, W.H., Teukolsky, S.A., Vetterling, WTa: Numerical Recipes in Fortran, 2nd edn. Cambridge University Press, Cambridge (1992)MATH
60.
Rachev, A., Shazly, T.: A preliminary analysis of the data from an in vitro inflation-extension test can validate the assumption of arterial tissue elasticity. ASME J. Biomech. Eng. 135(8), 084502 (2013)CrossRef
61.
Rauchs, G., Bardon, J., Georges, D.: Identification of the material parameters of a viscous hyperelastic constitutive law from spherical indentation tests of rubber and validation by tensile tests. Mech. Mater. 42, 961–973 (2010)CrossRef
62.
Rothe, S.: Electro-thermo-mechanical modeling of field assisted sintering technology: Experiments, constitutive modeling and finite element analysis. Ph.D.-thesis, report no. 1/2015, Institute of Applied Mechanics, Clausthal University of Technology, Clausthal-Zellerfeld (2015)
63.
Scheday, G.: Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden. Ph.D.-thesis, Report No. I–11 (2003), University of Stuttgart (Germany), Institute of Mechanics (2003)
64.
Schittkowski, K.: Numerical Data Fitting in Dynamical Systems. Kluwer Academic Publication, Dordrecht (2002)CrossRefMATH
65.
Schmaltz, S., Willner, K.: Comparison of different biaxial tests for the identification of sheet steel material parameters. Strain 40, 389–403 (2014)
66.
Schmaltz, S., Willner, K.: Material parameter identification utilizing optical full-field strain measurement and digital image correlation. J. Jpn. Soc. Exp. Mech. 13, s120–s125 (2013)
67.
Schmidt, U., Mergheim, J., Steinmann, P.: Identification of elastoplastic microscopic material parameters within a homogenization scheme. Int. J. Numer. Methods Eng. 104, 391–407 (2015)MathSciNetCrossRefMATH
68.
Schmidt, U., Steinmann, P., Mergheim, J.: Two-scale elastic parameter identification from noisy macroscopic data. Arch. Appl. Mech. 86, 303–320 (2016)CrossRef
69.
Serban, R., Freeman, J.S.: Identification and identifiability of unknown parameters in multibody dynamic systems. Multibody Syst. Dyn. 5, 335–350 (2001)CrossRefMATH
70.
Shafiq, M., Ayyagari, R.S., Ehaab, M., Vural, M.: Multiaxial yield surface of transversely isotropic foams: Part II—experimental. J. Mech. Phys. Solids 76, 224–236 (2015)CrossRef
71.
Shildip, D.U., Bhope, D.V., Khamankar, S.D.: Stress analysis of multilayer pressure vessel. J. Appl. Mech. Eng. 4(2), 1–6 (2015)
72.
Sutton, M.A., Orteu, J.J., Schreier, H.W.: Image Correlation for Shape, Motion and Deformation Measurements. Springer, New York (2009)
73.
Sutton, M., Badel, P., Avril, S., Lessner, S.: Mechanical identification of hyperelastic anisotropic properties of mouse carotid arteries. In: Proulx, T. (ed.) Mechanics of Biological Systems and Materials, Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics, vol. 2, pp. 11–17. Springer, New York (2011)
74.
Thielecke, F.: Parameteridentifizierung von Simulationsmodellen für das viskoplastische Verhalten von Metallen—Theorie, Numerik, Anwendung. No. 34-1998, Technische Universität Braunschweig (1997)
75.
Tikhonov, A.N., Goncharsky, A.V., Stepanov, V.V., Yagola, A.G.: Numerical Methods for the Solution of Ill-posed Problems. Kluwer Academic Publishers, Dordrecht (1995)CrossRefMATH
76.
Timoschenko, S.P., Goodier, J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill Book Company, Singapore (1985)
77.
Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics, Encyclopedia of Physics. Springer, Berlin (1965)MATH
78.
Twizell, E.H., Ogden, R.W.: Non-linear optimization of the material constants in Ogden’s stress-deformation function for incompressible isotropic elastic materials. J. Aust. Math. Soc. Ser. B 24, 424–434 (1983)CrossRefMATH
79.
Yeh, M., Kyriakides, S.: On the collapse of inelastic thick-walled tubes under external pressure. ASME J. Energy Resour. Technol. 108(1), 35–47 (1986)CrossRef
80.
Young, W., Budynas, R.: Roark’s Formulas for Stress and Strain. McGraw-Hill Professional, New York (2001)
Metadata
Title
Identifiability of material parameters in solid mechanics
Authors
Stefan Hartmann
Rose Rogin Gilbert
Publication date
08-05-2017
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 1-2/2018
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-017-1259-4

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