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Computational Mechanics

, Volume 42, Issue 4, pp 485–510 | Cite as

Materials integrity in microsystems: a framework for a petascale predictive-science-based multiscale modeling and simulation system

  • Albert C. To
  • Wing Kam Liu
  • Gregory B. Olson
  • Ted Belytschko
  • Wei Chen
  • Mark S. Shephard
  • Yip-Wah Chung
  • Roger Ghanem
  • Peter W. Voorhees
  • David N. Seidman
  • Chris Wolverton
  • J. S. Chen
  • Brian Moran
  • Arthur J. Freeman
  • Rong Tian
  • Xiaojuan Luo
  • Eric Lautenschlager
  • A. Dorian Challoner
Original Paper

Abstract

Microsystems have become an integral part of our lives and can be found in homeland security, medical science, aerospace applications and beyond. Many critical microsystem applications are in harsh environments, in which long-term reliability needs to be guaranteed and repair is not feasible. For example, gyroscope microsystems on satellites need to function for over 20 years under severe radiation, thermal cycling, and shock loading. Hence a predictive-science-based, verified and validated computational models and algorithms to predict the performance and materials integrity of microsystems in these situations is needed. Confidence in these predictions is improved by quantifying uncertainties and approximation errors. With no full system testing and limited sub-system testings, petascale computing is certainly necessary to span both time and space scales and to reduce the uncertainty in the prediction of long-term reliability. This paper presents the necessary steps to develop predictive-science-based multiscale modeling and simulation system. The development of this system will be focused on the prediction of the long-term performance of a gyroscope microsystem. The environmental effects to be considered include radiation, thermo-mechanical cycling and shock. Since there will be many material performance issues, attention is restricted to creep resulting from thermal aging and radiation-enhanced mass diffusion, material instability due to radiation and thermo-mechanical cycling and damage and fracture due to shock. To meet these challenges, we aim to develop an integrated multiscale software analysis system that spans the length scales from the atomistic scale to the scale of the device. The proposed software system will include molecular mechanics, phase field evolution, micromechanics and continuum mechanics software, and the state-of-the-art model identification strategies where atomistic properties are calibrated by quantum calculations. We aim to predict the long-term (in excess of 20 years) integrity of the resonator, electrode base, multilayer metallic bonding pads, and vacuum seals in a prescribed mission. Although multiscale simulations are efficient in the sense that they focus the most computationally intensive models and methods on only the portions of the space–time domain needed, the execution of the multiscale simulations associated with evaluating materials and device integrity for aerospace microsystems will require the application of petascale computing. A component-based software strategy will be used in the development of our massively parallel multiscale simulation system. This approach will allow us to take full advantage of existing single scale modeling components. An extensive, pervasive thrust in the software system development is verification, validation, and uncertainty quantification (UQ). Each component and the integrated software system need to be carefully verified. An UQ methodology that determines the quality of predictive information available from experimental measurements and packages the information in a form suitable for UQ at various scales needs to be developed. Experiments to validate the model at the nanoscale, microscale, and macroscale are proposed. The development of a petascale predictive-science-based multiscale modeling and simulation system will advance the field of predictive multiscale science so that it can be used to reliably analyze problems of unprecedented complexity, where limited testing resources can be adequately replaced by petascale computational power, advanced verification, validation, and UQ methodologies.

Keywords

Multiscale modeling Petascale computing Microsystems MEMS 

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References

  1. 1.
    RF MEMS market 2004–2009 by Wicht Techonologie Consulting, October 2005Google Scholar
  2. 2.
    Micro power sources: opportunities from fuel cells and batteries for mobile applications by NanoMarkets. http://www.nanomarkets.net, September 2005
  3. 3.
    MEMS microphones and micro-speakers market. Workshop by Wicht Technologie Consulting (2006)Google Scholar
  4. 4.
    Microelectromechanical Systems Technology: Current and Future Markets by Andrew McWilliams, February 2006Google Scholar
  5. 5.
    Chicago Tribune on July 6, 2006Google Scholar
  6. 6.
    abcnews.com on September 6, 2006Google Scholar
  7. 7.
    Mechanical Engineering, April 2006Google Scholar
  8. 8.
    Liu WK, Karpov EG, Park HS (2005) Nano-mechanics and materials: theory, multiscale methods and applications. Wiley, New YorkGoogle Scholar
  9. 9.
    Mao Z, Sudbrack CK, Yoon KE, Martin G, Seidman DN (2007) The mechanism of morphogenesis in a phase separating concentrated multi-component alloy. Nat Mater 6: 210–216CrossRefGoogle Scholar
  10. 10.
    Vaithynanathan V, Wolverton C, Chen LQ (2002) Multiscale modeling of precipitate microstructure evolution. Phys Rev Lett 88: 125503CrossRefGoogle Scholar
  11. 11.
    Wolverton C, Zunger A (1995) Ising-like description of structurally relaxed ordered and disordered alloys. Phys Rev Lett 75: 3162CrossRefGoogle Scholar
  12. 12.
    Sizmann R (1978) The effect of radiation upon diffusion in metals. J Nucl Mater 69–70: 386–412CrossRefGoogle Scholar
  13. 13.
    Wimmer E, Krakauer H, Weinert M, Freeman AJ (1981) Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic-structure of molecules and surfaces—O2 molecule. Phys Rev B 24: 864–875CrossRefGoogle Scholar
  14. 14.
    Rittner JD, Seidman DN (1996) Limitations of the structural unit model. In: Materials Science Forum, pp 207–209Google Scholar
  15. 15.
    Mantina M, Wang Y, Arroyave R, Wolverton C, Chen L-Q, Liu Z-K (2007) First-principles calculation of self-diffusion coefficients. Phys Rev Lett (submitted)Google Scholar
  16. 16.
    Wilson JR, Kobsiriphat W, Mendoza R, Chen HY, Hiller JM, Miller DJ, Thornton K, Voorhees PW, Adler SB, Barnett SA (2006) Three-dimensional reconstruction of a solid-oxide fuel-cell anode. Nat Mater 5: 541–544CrossRefGoogle Scholar
  17. 17.
    Eggleston J, Voorhees PW (2002) Ordered growth of nanocrystals via a morphological instability. Appl Phys Lett 80: 306–308CrossRefGoogle Scholar
  18. 18.
    Seidman DN, Averback RS, Benedek R (1987) Displacement cascades: dynamics and atomic structure. Phys Stat Sol (b) 144: 85CrossRefGoogle Scholar
  19. 19.
    Bammann DJ, Chiesa ML, Horstemeyer MF, Weingarten LI (1993) Failure in ductile materials using finite element methods. In: Jones N, Weirzbicki T (eds) Structural crashworthness and failure. Elsevier, Amsterdam, p 1Google Scholar
  20. 20.
    Bammann DJ, Chiesa ML, Johnson GC (1996) Modeling large deformation and failure in manufacturing processes. In: Tatsumi, Wannabe, Kambe (eds) Theor. app. mech. Elsevier, Amsterdam, p 259Google Scholar
  21. 21.
    Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11: 357–372zbMATHCrossRefGoogle Scholar
  22. 22.
    Bazant ZP, Belytschko T (1987) Strain-softening continuum damage: localization and size effect. In: Constitutive laws of engineering materials: theory and applications, pp 11–33Google Scholar
  23. 23.
    Fleck NA, Hutchinson JW (1993) A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids 41(12):1825–1857zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    In Newscientist.com news, May 19, 2005Google Scholar
  25. 25.
    Liu WK, Karpov EG, Park HS (2005) Nano-mechanics and materials: theory, multiscale methods and applications. Wiley, New YorkGoogle Scholar
  26. 26.
    Hao S, Liu WK, Moran B, Vernerey F, Olson GB (2004) Multi-scale constitutive model and computational framework for the design of ultra-high strength, high-toughness steels. Comput Methods Appl Mech Eng 193: 1865zbMATHCrossRefGoogle Scholar
  27. 27.
    McVeigh C, Vernerey F, Liu WK, Brinson LC (2006) Multiresolution analysis for material design. Comput Methods Appl Mech Eng 195(37–40): 5053–5076zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Vernerey F, Liu WK, Moran B (2007) A micromorphic model for the multiple scale failure of heterogeneous materials. J Mech Phys Solids (under revision)Google Scholar
  29. 29.
    Zhang X, Mehraeen S, Chen JS, Ghoniem N (2006) Multiscale total Lagrangian formulation for modeling dislocation-induced plastic deformation in polycrystalline materials. Int J Multisc Comput Eng 4: 29–46CrossRefGoogle Scholar
  30. 30.
    Chen JS, Mehraeen S (2005) Multi-scale modeling of heterogeneous materials with fixed and evolving microstructures. Model Simul Mater Sci Eng 13: 95–121CrossRefGoogle Scholar
  31. 31.
    Chen JS, Mehraeen S (2004) Variationally consistent multi-scale modeling and homogenization of stressed grain growth. Comput Methods Appl Mech Eng 193: 1825–1848zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Chen JS, Kotta V, Lu H, Wang D, Moldovan D, Wolf D (2004) A variational formulation and a double-grid method for meso-scale modeling of stressed grain growth in polycrystalline materials. Comput Methods Appl Mech Eng 193: 1277–1303zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Lee TY, Chen JS (2006) Modeling of grain growth using Voronoi discretization and natural neighbour interpolants. Int J Comput Methods Eng Sci Mech 7: 475–484CrossRefGoogle Scholar
  34. 34.
    Shi J, Ghanem R (2006) A stochastic nonlocal model for materials with multiscale behavior. Int J Multisc Comput Eng 4(4): 501–519CrossRefGoogle Scholar
  35. 35.
    Gel’fand IM, Vilenkin NYa (1964) Generalized function, vol 4. Academic Press, New YorkGoogle Scholar
  36. 36.
    Shi J (2003) Stochastic modeling of materials with complex microstructure. PhD thesis, Johns Hopkins UniversityGoogle Scholar
  37. 37.
    Seidman DN (1973) The direct observation of point defects in irradiated or quenched metals by quantitative field-ion microscopy. J Phys F Metal Phys 3: 393–421CrossRefGoogle Scholar
  38. 38.
    Seidman DN (2007) Three-dimensional atom-probe tomography: advances and applications. Annu Rev Mater Res 37: 127CrossRefGoogle Scholar
  39. 39.
    Richards SA (1997) Completed Richardson extrapolation in space and time. Commun Numer Methods Eng 13: 558–73CrossRefMathSciNetGoogle Scholar
  40. 40.
    Roache PJ (1998) Verification and validation in computational science and engineering. Hermosa Publishers, AlbuquerqueGoogle Scholar
  41. 41.
    Ainsworth M, Oden JT (1997) A posteriori error estimation in finite element analysis. Comput Methods Appl Mech Engrg 142:1–88zbMATHCrossRefMathSciNetGoogle Scholar
  42. 42.
    Babuska I, Strouboulis T (2001) The reliability of the FE method. Oxford Press, New YorkGoogle Scholar
  43. 43.
    Oden JT, Babuska I, Nobile F, Feng Y, Tempone T (2005) Theory and methology for estimation and control of errors due to modeling, approximation and uncertainty. Comput Methods Appl Mech Eng 194: 195–204zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Nuggehally MA, Picu CR, Shephard MS, Fish J (2007) Adaptive model selection procedure for concurrent multiscale problems. J Multisc Comput Eng (to appear)Google Scholar
  45. 45.
    Ghanem R, Doostan A (2006) On the construction and analysis of stochastic predictive models: Characterization and propagation of the errors associated with limited data. J Comput Phys 217(1): 63–81zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Oberkampf W, Barone M (2004) Measures of agreement between computation and experiment: validation metrics. In: 34th AIAA fluid dynamics conference and exhibit, AIAA-2004-2626, Portland, Oregon, June 28–1Google Scholar
  47. 47.
    Romero V (2007) Validated model? Not so fast—the need for model “Conditioning” as an essential addendum to model validation. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, Hawaii, April 23–26Google Scholar
  48. 48.
    Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer experiments. J R Stat Soc B 63: 425–464zbMATHCrossRefMathSciNetGoogle Scholar
  49. 49.
    Chen W, Xiong Y, Tsui K-L, Wang S (2006) Some metrics and a Bayesian procedure for validating predictive models in engineering design. In: ASME design technical conference, design automation conference, Philadelphia, PA, September 10–13 (accepted by J Mech Des)Google Scholar
  50. 50.
    Mahadevan S, Rebba R (2005) Model predictive capability assessment under uncertainty. In: 46th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Austin, Texas, April 18–21Google Scholar
  51. 51.
    Ghanem RG, Spanos PD (1991) Stochastic finite elements: a spectral approach. Springer, New YorkzbMATHGoogle Scholar
  52. 52.
    Descelliers C, Soize C, Ghanem R (2006) Maximum likelihood estimation of stochastic chaos representation from experimental data. Int J Numer Methods Eng 66(6): 978–1001CrossRefGoogle Scholar
  53. 53.
    Descelliers C, Soize C, Ghanem R (2007) Identification of chaos representations of elastic properties of random media using experimental vibration tests. Comput Mech 39(6): 831–838CrossRefGoogle Scholar
  54. 54.
    Doostan A, Ghanem R, Red-Horse J (2007) Stochastic model reduction for chaos representations. Comput Methods Appl Mech Eng 196: 3951–3966CrossRefMathSciNetGoogle Scholar
  55. 55.
    Ghanem R, Saad G, Doostan A (2007) Efficient solution of stochastic systems: application to the embankment dam problem. Struct Saf 29(3): 238–251CrossRefGoogle Scholar
  56. 56.
    Zou Y, Ghanem R (2004) Multiscale data assimilation with the ensemble kalman filter. SIAM J Multisc Model 3(1): 131–150zbMATHCrossRefMathSciNetGoogle Scholar
  57. 57.
    Liu H, Chen W, Sudjianto A (2006) Relative entropy based method for global and regional sensitivity analysis in probabilistic design. ASME J Mech Des 128(2): 1–11Google Scholar
  58. 58.
    Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. ASME J Mech Des 127(5): 875–886CrossRefGoogle Scholar
  59. 59.
    Yin X, Chen W (2007) A hierarchical statistical sensitivity analysis nethod for complex engineering systems, DETC2007-35528. In: 2007 ASME design technical conference, design automation conference, September 4–7, Las Vegas, NVGoogle Scholar
  60. 60.
    Giunta AA, Swiler LP, Brown SL, Eldred MS, Richards MD, Cyr EC (2006) The surfpack software library for surrogate modeling of sparse irregularly spaced multidimensional data, paper AIAA-2006-7049. In: Proceedings of the 11th AIAA/ISSMO multidisciplinary analysis and optimization conference, Portsmouth, VA, September 6–8Google Scholar
  61. 61.
    http://www.scidac.gov/viz/SDM.html, The Scientific Data Management Center for Enabling Technologies SciDAC Center
  62. 62.
  63. 63.
    Chand KK, Diachin LF, Li X, Ollivier-Gooch C, Seol ES, Shephard MS, Tautges R, Trease H (2006) Toward interoperable mesh, geometry and field components for PDE simulation development. Eng Comput (to appear)Google Scholar
  64. 64.
    Beall MW, Walsh J, Shephard MS (2004) A comparison of techniques for geometry access related to mesh generation. Eng Comput 20(3): 210–221CrossRefGoogle Scholar
  65. 65.
  66. 66.
    Shephard MS, Jansen KE, Sahni O, Luo X-J, Diachin L (2007) Toward massively parallel adaptive simulations on unstructured meshes. In: Proceedings of SciDAC 2006, DOE. J Phys Conf Ser (to appear)Google Scholar
  67. 67.
    Shephard MS, Seol ES, FrantzDale B (2007) Toward a multi-model hierarchy to support multiscale simulations. In: Fishwick PA (ed) Handbook of dynamic system modeling, vol 12. Chapman & Hall, Boca Raton, pp 1–18Google Scholar
  68. 68.
    Luo X, Stylianopoulos T, Barocas VH, Shephard MS (2007) Multiscale computation for soft tissues with complex geometries. Eng Comput (to appear)Google Scholar
  69. 69.
    Nuggehally MA, Picu CR, Shephard MS, Fish J (2007) Adaptive model selection procedure for concurrent multiscale problems. J Multisc Comput Eng (to appear)Google Scholar
  70. 70.
  71. 71.
  72. 72.
  73. 73.
  74. 74.
  75. 75.
    Devine K, Boman E, Heaphy R, Hendrickson B, Vaughan C (2002) Zoltan data management services for parallel dynamic applications. Comput Sci Eng 4(2): 90–97CrossRefGoogle Scholar
  76. 76.
  77. 77.
    Seol ES, Shephard MS (2006) Efficient distributed mesh data structure for parallel automated adaptive analysis. Eng Comput 22(3–4): 197–213CrossRefGoogle Scholar
  78. 78.
    Shephard MS, Flaherty JE, Bottasso CL, de Cougny HL, Ozturan C, Simone ML (1997) Parallel automated adaptive analysis. Parallel Comput 23: 1327–1347zbMATHCrossRefMathSciNetGoogle Scholar
  79. 79.
    Yazdi N, Ayazi F, Najafi K (1998) Micromachined inertial sensors. Proc IEEE 86(8): 1640–1659CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Albert C. To
    • 1
  • Wing Kam Liu
    • 1
  • Gregory B. Olson
    • 2
  • Ted Belytschko
    • 1
  • Wei Chen
    • 1
  • Mark S. Shephard
    • 3
  • Yip-Wah Chung
    • 2
  • Roger Ghanem
    • 4
  • Peter W. Voorhees
    • 2
  • David N. Seidman
    • 2
  • Chris Wolverton
    • 2
  • J. S. Chen
    • 5
  • Brian Moran
    • 1
  • Arthur J. Freeman
    • 2
    • 6
  • Rong Tian
    • 1
  • Xiaojuan Luo
    • 3
  • Eric Lautenschlager
    • 7
  • A. Dorian Challoner
    • 8
  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Materials Science and EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Scientific Computation and Research CenterRensselaer Polytechnic InstituteTroyUSA
  4. 4.Department of Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  5. 5.Department of Civil and Environmental EngineeringUniversity of California at Los AngelesWestwoodUSA
  6. 6.Department of PhysicsNorthwestern UniversityEvanstonUSA
  7. 7.Honeywell AerospacePlymouthUSA
  8. 8.Boeing Satellite Design CenterLos AngelesUSA

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