Abstract
We present a new strategy for calibration and validation of hierarchical multiscale models based on computational homogenization. The proposed strategy hinges on the concept of the experimental simulator repository (SIMEX) which provides the basis for a generic algorithmic framework in calibration and validation of multiscale models. Gradient-based and genetic algorithms are incorporated into SIMEX framework to investigate the validity of these algorithms in multiscale model calibration. The strategy is implemented using the eigendeformation-based reduced order homogenization (EHM) model and integrated into a commercial finite element package (Abaqus). Ceramic- and polymer- matrix composite problems are analyzed to study the capabilities of the proposed calibration and validation framework.
Similar content being viewed by others
References
Oskay C and Fish J (2007). Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comp Meth Appl Mech Eng 196: 1216–1243
Fish J, Shek KL, Pandheeradi M and Shephard MS (1997). Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Comput Meth Appl Mech Eng 148: 53–73
Fish J and Shek KL (1999). Finite deformation plasticity of composite structures: computational models and adaptive strategies. Comput Meth Appl Mech Eng 172: 145–174
Fish J, Yu Q and Shek KL (1999). Computational damage mechanics for composite materials based on mathematical homogenization. Int J Numer Methods Eng 45: 1657–1679
Dvorak GJ (1992). Transformation field analysis of inelastic composite materials. Proc R Soc Lond A 437: 311–327
Michel JC and Suquet P (2003). Nonuniform transformation field analysis. Int J Solids Struct 40: 6937–6955
Michel JC and Suquet P (2004). Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput Meth Appl Mech Eng 193: 5477–5502
Babuska I and Oden JT (2004). Verification and validation in computational engineering and science: basic concepts. Comp Meth Appl Mech Eng 193: 4057–4066
Lahellec N, Mazerolle F and Michel JC (2004). Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation. J Mech Phys Solids 52: 27–49
Jeryan R, Warren CD, Carpenter J, Sklad PS (2004) Composite crash energy management. In: Automotive lightweighting materials, FY2004 progress report. Department of Energy, 2004
Goldberg DE (1989). Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading
Michalewicz Z (1992). Genetic algorithms + data structures = evolution programs. Springer, Berlin
Suquet PM (1987). Elements of homogenization for inelastic solid mechanics. In: Sanchez-Palencia, E and Zaoui, A (eds) Homogenization techniques for composite media, pp. Springer, Heidelberg
Terada K, Kikuchi N (1995) Nonlinear homogenization method for practical applications. In: Ghosh S, Ostoja-Starzewski M (eds) Computational methods in micromechanics, vol AMD-212/MD-62. pp 1–16. ASME
Feyel F and Chaboche J-L (2000). Fe2 multiscale approach for modelling the elastoviscoplastic behavior of long fiber sic/ti composite materials. Comput Methods Appl Mech Eng 183: 309–330
Simo JC and Ju JW (1987). Strain- and stress-based continuum damage models—i. formulation. Int J Solids Struct 23(7): 821–840
Dube J-F, Pijaudier-Cabot G and La Borderie C (1996). Rate dependent damage model for concrete in dynamics. J Eng Mech 122(10): 939–947
Lipetzky P, Dvorak GJ and Stoloff NS (1996). Tensile properties of a sic/sic composite. Mater Sci Eng A 216: 11–19
Ianucci L (2006). Progressive failure modelling of woven carbon composite under impact. Int J Impact Eng 32: 1013–1043
Kim K and Voyiadjis GZ (1999). Non-linear finite element analysis of composite panels. Composites: Part B, 30: 365–381
Perzyna P (1966). Fundamental problems in viscoplasticity. Adv Appl Mech 9: 244–368
Griswold C, Cross WM, Kjerengtroen L and Kellar JJ (2005). Interphase variation in silane-treated glass-fiber-reinforced epoxy composites. J Adhesion Sci Technol 19(3–5): 279–290
Fish J (2006). Bridging the scales in nano engineering and science. J Nanoparticle Res 8: 577–594
Dennis JE Jr and Schnabel RB (1996). Numerical methods for unconstrained optimization and nonlinear equations. Classics in applied mathematics, vol 16. SIAM, Philadelphia
More JJ (1977) The Levenberg–Marquardt algorithm: implementation and theory. In: Watson GA (ed) Numerical analysis, lecture notes in Mathamatics, vol 630. Springer, Heidelberg, pp 105–116
IMSL Math/Library Volumes 1 and 2 user’s manual. Visual numerics, 1997
Gill PE, Murray W (1976) Minimization subject to bounds on the variables. Technical report NAC72, National Physical Laboratory, England
Charbonneau P, Knapp B (1996) A user’s guide to PIKAIA 1.0. NCAR technical note, National Center for Atmospheric Research
Ibrahimbegovic A., Knopf-Lenoir C, Kucerova A and Villon P (2004). Optimal design and optimal control of structures undergoing finite rotations and elastic deformations. Int J Numer Methods Eng 61: 2428–2460
Hrstka O and Kucerova A (2004). Improvements of real coded genetic algorithms based on differential operators preventing premature convergence. Adv Eng Softw 35: 237–246
Brewer D (1999). HSR/EPM combustor materials development program. Mater Sci Eng A 261: 284–291
Verilli M, Robinson RC, Calomino AM, Thomas DJ (2004) Ceramic matrix composite vane subelement testing in a gas turbine environment. In: Proceedings of ASME Turbo Expo 2004, number GT2004-53970, Vienna, Austria, June 14–17
Morscher GN, Pujar VV (2004) Melt-infiltrated sic composites for gas turbine engine applications. In: Proceedings of 49th ASME IGTI Power for land, sea and air, number GT2004-53196, Vienna, Austria, June 14–17 2004
Zinkle SJ, Snead LL (1998) Thermophysical and mechanical properties of sic/sic composites in fusion materials. Progress Report for Period Ending June 30 1998 DOE/ER-0313/24, Oak Ridge National Laboratory
Thiruppukuzhi SV and Sun CT (2001). Models for the strain-rate-dependent behavior of polymer composites. Compos Sci Technol 61: 1–12
Assessment of Research Needs for Wind Turbine Rotor Materials Technology. National Academies Press, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Oskay, C., Fish, J. On calibration and validation of eigendeformation-based multiscale models for failure analysis of heterogeneous systems. Comput Mech 42, 181–195 (2008). https://doi.org/10.1007/s00466-007-0197-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-007-0197-3