Abstract
In this paper, a new methodology for reconstructing spatially varying random material properties is presented by combining stochastic finite element (SFE) models with Self-Optimizing Inverse Method (Self-OPTIM). The Self-OPTIM can identify model parameters based on partial boundary force and displacement data from experimental tests. Statistical information (i.e. spatial mean, variance, correlation length and Gaussian normal random variables) of spatially varying random fields (RFs) are parameterized by Karhunen-Loève (KL) expansion method and integrated into SFE models. In addition, a new software framework is also presented that can simultaneously utilize any number of remote computers in a network domain for the Self-OPTIM simulation. This can result in a significant decrease of computational times required for the optimization task. Two important issues in the inverse reconstruction problem are addressed in this paper: (1) effects of the number of internal measurements and (2) non-uniform reaction forces along the boundary on the reconstruction accuracy. The proposed method is partially proven to offer new capabilities of reconstructing spatially inhomogeneous material properties and estimating their statistical parameters from incomplete experimental measurements.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R. Mahnken, A comprehensive study of a multiplicative elastoplasticity model coupled to damage including parameter identification. Comput. Struct. 74(2), 179–200 (2000)
R. Mahnken, An inverse finite-element algorithm for parameter identification of thermoelastic damage models. Int. J. Numer. Methods Eng. 48(7), 1015–1036 (2000)
R. Mahnken, Identification of material parameters for constitutive equations. Encyclopedia Comput. Mech. 2, 637–655 (2004)
R. Mahnken, M. Johansson, K. Runesson, Parameter estimation for a viscoplastic damage model using a gradient-based optimization algorithm. Eng. Comput. 15(6–7), 925 (1998)
R. Mahnken, E. Stein, A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Comput. Methods Appl. Mech. Eng. 136(3-4), 225–258 (1996)
A.F. Saleeb, A.S. Gendy, T.E. Wilt, Parameter-estimation algorithms for characterizing a class of isotropic and anisotropic viscoplastic material models. Mech. Time-Depend. Mater. 6(4), 323–362 (2002)
A.F. Saleeb et al., Interactive software for material parameter characterization of advanced engineering constitutive models. Adv. Eng. Softw. 35(6), 383–398 (2004)
A.F. Saleeb et al., Effective strategy for automated characterization in complex viscoelastoplastic and damage modeling for isotropic/anisotropic aerospace materials (vol 15, pg 84, 2002). J. Aerosp. Eng. 15(4), 166–166 (2002)
A.F. Saleeb et al., An anisotropic viscoelastoplastic model for composites—sensitivity analysis and parameter estimation. Composites Part B Engineering 34(1), 21–39 (2003)
S. Gerlach, A. Matzenmiller, On parameter identification for material and microstructural properties. GAMM-Mitteilungen 30(2), 481–505 (2007)
A. Matzenmiller, S. Gerlach, Parameter identification of elastic interphase properties in fiber composites. Composites Part B Engineering 37(2-3), 117–126 (2006)
P. Akerstrom, B. Wikman, M. Oldenburg, Material parameter estimation for boron steel from simultaneous cooling and compression experiments. Model. Simul. Mater. Sci. Eng. 13(8), 1291–1308 (2005)
D.A. Castello et al., Constitutive parameter estimation of a viscoelastic model with internal variables. Mech. Syst. Signal Process 22(8), 1840–1857 (2008)
E. Pagnacco, et al. Inverse strategy from displacement field measurement and distributed forces using FEA. SEM Annual Conference and Exposition on Experimental and Applied Mechanics, Poland, 2005
A. Constantinescu, On the identification of elastic moduli from displacement-force boundary measurements. Inverse Prob. Eng. 1(4), 293–313 (1995)
G. Geymonat, S. Pagano, Identification of mechanical properties by displacement field measurement: a variational approach. Meccanica 38(5), 535–545 (2003)
M. Grediac, F. Pierron, Applying the virtual fields method to the identification of elasto-plastic constitutive parameters. Int. J. Plast. 22(4), 602–627 (2006)
M. Grediac et al., The virtual fields method for extracting constitutive parameters from full-field measurements: a review. Strain 42(4), 233–253 (2006)
D. Claire, F. Hild, S. Roux, A finite element formulation to identify damage fields: the equilibrium gap method. Int. J. Numer. Methods Eng. 61(2), 189–208 (2004)
A. Ben Abda, H. Ben Ameur, M. Jaoua, Identification of 2D cracks by elastic boundary measurements. Inverse Prob. 15(1), 67–77 (1999)
G.J. Yun, S. Shang, A self-optimizing inverse analysis method for estimation of cyclic elasto-plasticity model parameters. Int. J Plast. 27, 576–595 (2011)
S. Shang, G.J. Yun, Identification of elasto-plastic constitutive parameters by self-optimizing inverse method: experimental verifications. Comput. Mater. Continua 635(1), 1–18 (2012)
M.R. Rahimi, G.J. Yun, S. Shen, Inverse estimation of dynamic stiffness of highway bridge embankment from earthquake records. J. Bridge Eng. 19(SPECIAL ISSUE: Recent Advances in Seismic Design, Analysis, and Protection of Highway Bridges): p. A4014005 (2014)
M. Wolff, M. Böhm, Zu einem neuen Ansatz zur Parameterbestimmung in der Mechanik der Festkörper, (University of Bremen, Bremen, 2013)
F. Latourte et al., Elastoplastic behavior identification for heterogeneous loadings and materials. Exp. Mech. 48(4), 435–449 (2008)
A. Teughels, J. Maeck, G. De Roeck, Damage assessment by FE model updating using damage functions. Comput. Struct. 80(25), 1869–1879 (2002)
A. Teughels, G. De Roeck, Structural damage identification of the highway bridge Z24 by FE model updating. J. Sound Vib. 278(3), 589–610 (2004)
M.M.A. Wahab, G. De Roeck, B. Peeters, Parameterization of damage in reinforced concrete structures using model updating. J. Sound Vib. 228(4), 717–730 (1999)
S. Adhikari, M.I. Friswell, Distributed parameter model updating using the karhunen-loeve expansion. Mech. Syst. Signal Process 24(2), 326–339 (2010)
S. Shang, Stochastic material characterization of heterogeneous media with randomly distributed material properties. Department of Civil Engineering 2012, The University of Akron: Doctoral Dissertation
G.J. Yun, L. Zhao, E. Iarve, Probabilistic mesh-independent discrete damage analyses of laminate composites. Comp. Sci. Tech. (2015)
S. Shang, G.J. Yun, Stochastic material characterization for spatially varying random macroscopic material properties by stochastic self-optimizng inverse method. Probab. Eng. Mech. (2014)
S. Shang, G.J. Yun, Stochastic finite element with material uncertainties: implementation in a general-purpose simulation program. Finite Elem. Anal. Des. 64, 65–78 (2013)
X.S. Yang, Firefly algorithms for multimodal optimization. Stochastic Algorithms Foundations Appl. Proc. 5792, 169–178 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Weaver, J.M., Yun, G.J. (2016). Reconstruction of Spatially Varying Random Material Properties by Self-Optimizing Inverse Method. In: Bossuyt, S., Schajer, G., Carpinteri, A. (eds) Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-21765-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-21765-9_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21764-2
Online ISBN: 978-3-319-21765-9
eBook Packages: EngineeringEngineering (R0)