Skip to main content
SpringerLink
Log in

A predictive multiphase model of silica aerogels for building envelope insulations

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

This work develops a systematic uncertainty quantification framework to assess the reliability of prediction delivered by physics-based material models in the presence of incomplete measurement data and modeling error. The framework consists of global sensitivity analysis, Bayesian inference, and forward propagation of uncertainty through the computational model. The implementation of this framework on a new multiphase model of novel porous silica aerogel materials is demonstrated to predict the thermomechanical performances of a building envelope insulation component. The uncertainty analyses rely on sampling methods, including Markov-chain Monte Carlo and a mixed finite element solution of the multiphase model. Notable features of this work are investigating a new noise model within the Bayesian inversion to prevent biased estimations and characterizing various sources of uncertainty, such as measurements variabilities, model inadequacy in capturing microstructural randomness, and modeling errors incurred by the theoretical model and numerical solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. Throughout this section we use the abbreviated notation \(\sum _{\alpha }=\sum _{\alpha =1}^{M}\).

References

  1. Alhawari A, Mukhopadhyaya P (2018) Thermal bridges in building envelopes—an overview of impacts and solutions. Int Rev Appl Sci Eng 9(1):31–40

    Google Scholar 

  2. Alnæs MS, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes ME, Wells GN (2015) The FEniCS project version 1.5. Arch Numer Softw 3(100):9–23

    Google Scholar 

  3. An L, Liang B, Guo Z, Wang J, Li C, Huang Y, Hu Y, Li Z, Armstrong JN, Zhou C et al (2021) Wearable aramid-ceramic aerogel composite for harsh environment. Adv Eng Mater 23(3):2001169

    Article  Google Scholar 

  4. An L, Petit D, Di Luigi M, Sheng A, Huang Y, Hu Y, Li Z, Ren S (2021) Reflective paint consisting of mesoporous silica aerogel and Titania nanoparticles for thermal management. ACS Appl Nano Mater 4:6357–6363

    Article  Google Scholar 

  5. An L, Wang J, Petit D, Armstrong JN, Hanson K, Hamilton J, Souza M, Zhao D, Li C, Liu Y et al (2020) An all-ceramic, anisotropic, and flexible aerogel insulation material. Nano Lett 20(5):3828–3835

    Article  Google Scholar 

  6. Berardi U (2017) The benefits of using aerogel-enhanced systems in building retrofits. Energy Procedia 134:626–635

    Article  Google Scholar 

  7. Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26(2):182–185

    Article  MathSciNet  MATH  Google Scholar 

  8. Bowen RM (1980) Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci 18(9):1129–1148

    Article  MATH  Google Scholar 

  9. Bruggi M, Cinquini C (2011) Topology optimization for thermal insulation: an application to building engineering. Eng Optim 43(11):1223–1242

    Article  MathSciNet  Google Scholar 

  10. Chen Z, Wang X, Atkinson A, Brandon N (2016) Spherical indentation of porous ceramics: elasticity and hardness. J Eur Ceram Soc 36(6):1435–1445

    Article  Google Scholar 

  11. Cuce E, Cuce PM, Wood CJ, Riffat SB (2014) Toward aerogel based thermal superinsulation in buildings: a comprehensive review. Renew Sustain Energy Rev 34:273–299

    Article  Google Scholar 

  12. Dalbey K, Eldred MS, Geraci G, Jakeman JD, Maupin KA, Monschke JA, Seidl DT, Swiler LP, Tran A, Menhorn F et al (2020) Dakota, a multilevel parallel object-oriented framework for design optimization parameter estimation uncertainty quantification and sensitivity analysis: Version 6.12 theory manual. Technical report, Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)

  13. De Boer R (2012) Theory of porous media: highlights in historical development and current state. Springer, Berlin

    Google Scholar 

  14. Dehghannasiri R, Xue D, Balachandran PV, Yousefi MR, Dalton LA, Lookman T, Dougherty ER (2017) Optimal experimental design for materials discovery. Comput Mater Sci 129:311–322

    Article  Google Scholar 

  15. Ding C, Tamma KK, Lian H, Ding Y, Dodwell TJ, Bordas SP (2021) Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method. Comput Mech 67(5):1255–1271

    Article  MathSciNet  MATH  Google Scholar 

  16. Eringen AC, Ingram JD (1965) A continuum theory of chemically reacting media-I. Int J Eng Sci 3(2):197–212

    Article  Google Scholar 

  17. Faghihi D, Feng X, Lima EA, Oden JT, Yankeelov TE (2020) A coupled mass transport and deformation theory of multi-constituent tumor growth. J Mech Phys Solids 139:103936

    Article  MathSciNet  MATH  Google Scholar 

  18. Faghihi D, Sarkar S, Naderi M, Rankin JE, Hackel L, Iyyer N (2018) A probabilistic design method for fatigue life of metallic component. ASCE-ASME J Risk Uncertain Eng Syst Part B Mech Eng 4(3):031005

    Article  Google Scholar 

  19. Faghihi D, Voyiadjis GZ (2012) Determination of nanoindentation size effects and variable material intrinsic length scale for body-centered cubic metals. Mech Mater 44:189–211

    Article  Google Scholar 

  20. Faghihi D, Voyiadjis GZ (2012) Thermal and mechanical responses of BCC metals to the fast-transient process in small volumes. J Nanomech Micromech 2(3):29–41

    Article  Google Scholar 

  21. Faghihi D, Voyiadjis GZ (2014) A thermodynamic consistent model for coupled strain-gradient plasticity with temperature. J Eng Mater Technol 136(1):011002

    Article  Google Scholar 

  22. Farrell K, Oden JT, Faghihi D (2015) A Bayesian framework for adaptive selection, calibration, and validation of coarse-grained models of atomistic systems. J Comput Phys 295:189–208

    Article  MathSciNet  MATH  Google Scholar 

  23. Feng Q, Chen K, Ma D, Lin H, Liu Z, Qin S, Luo Y (2018) Synthesis of high specific surface area silica aerogel from rice husk ash via ambient pressure drying. Colloids Surf A 539:399–406

    Article  Google Scholar 

  24. Ferronato M, Castelletto N, Gambolati G (2010) A fully coupled 3-D mixed finite element model of Biot consolidation. J Comput Phys 229(12):4813–4830

    Article  MATH  Google Scholar 

  25. Frey S, Martins-Costa M, da Gama SR (1996) On the numerical heat transfer based upon mixture theory. Rev Bras Cienc Mec/J Braz Soc Mech Sci 18(3):282

    Google Scholar 

  26. Gandomkar A, Gray K (2018) Local thermal non-equilibrium in porous media with heat conduction. Int J Heat Mass Transf 124:1212–1216

    Article  Google Scholar 

  27. Gao T, Jelle BP, Gustavsen A, He J (2014) Lightweight and thermally insulating aerogel glass materials. Appl Phys A 117(2):799–808

    Article  Google Scholar 

  28. Gao T, Jelle BP, Gustavsen A, Jacobsen S (2014) Aerogel-incorporated concrete: an experimental study. Constr Build Mater 52:130–136

    Article  Google Scholar 

  29. Gelman A, Rubin DB et al (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472

    Article  MATH  Google Scholar 

  30. Goulouti K, De Castro J, Keller T (2016) Aramid/glass fiber-reinforced thermal break-thermal and structural performance. Compos Struct 136:113–123

    Article  Google Scholar 

  31. Guo Z, Yang R, Wang T, An L, Ren S, Zhou C (2021) Cost-effective additive manufacturing of ambient pressure-dried silica aerogel. J Manuf Sci Eng 143(1):011011

    Article  Google Scholar 

  32. Haagenson R, Rajaram H, Allen J (2020) A generalized poroelastic model using FEnics with insights into the Noordbergum effect. Comput Geosci 135:104399

    Article  Google Scholar 

  33. Haga JB, Osnes H, Langtangen HP (2012) Biot’s consolidation, pressure oscillations, elastic locking, low-permeable media, finite elements. Int J Numer Anal Methods Geomech 36(12):1507–1522

    Article  Google Scholar 

  34. Hamel S, Peterman K (2019) Thermal breaks in building envelopes. Struct Sustain

  35. Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1):97–109

    Article  MathSciNet  MATH  Google Scholar 

  36. He Y-L, Xie T (2015) Advances of thermal conductivity models of nanoscale silica aerogel insulation material. Appl Therm Eng 81:28–50

    Article  Google Scholar 

  37. Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52(1):1–17

    Article  Google Scholar 

  38. Honarmandi P, Arroyave R (2017) Using Bayesian framework to calibrate a physically based model describing strain-stress behavior of trip steels. Comput Mater Sci 129:66–81

    Article  Google Scholar 

  39. Honarmandi P, Johnson L, Arroyave R (2020) Bayesian probabilistic prediction of precipitation behavior in Ni-Ti shape memory alloys. Comput Mater Sci 172:109334

    Article  Google Scholar 

  40. Jaynes ET (1982) On the rationale of maximum-entropy methods. Proc IEEE 70(9):939–952

    Article  Google Scholar 

  41. Jaynes ET (2003) Probability theory: the logic of science. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  42. Jelle BP, Baetens R, Gustavsen A (2015) Aerogel insulation for building applications. The sol–gel handbook. In: Levy D, Zayat M (eds.) pp 1385–1412

  43. Jha PK, Cao L, Oden JT (2020) Bayesian-based predictions of covid-19 evolution in Texas using multispecies mixture-theoretic continuum models. Comput Mech 66(5):1055–1068

  44. Kaipio J, Kolehmainen V (2013) Approximate marginalization over modeling errors and uncertainties in inverse problems. In: Bayesian theory and applications, pp 644–672

  45. Kaipio J, Somersalo E (2006) Statistical and computational inverse problems, vol 160. Springer, Berlin

    MATH  Google Scholar 

  46. Karamikamkar S, Naguib HE, Park CB (2020) Advances in precursor system for silica-based aerogel production toward improved mechanical properties, customized morphology, and multifunctionality: a review. Adv Coll Interface Sci 276:102101

    Article  Google Scholar 

  47. Kennedy MC, O’Hagan A (2001) Bayesian calibration of computer models. J R Stat Soc Ser B (Stat Methodol) 63(3):425–464

    Article  MathSciNet  MATH  Google Scholar 

  48. Kim H, Inoue J, Kasuya T, Okada M, Nagata K (2020) Bayesian inference of ferrite transformation kinetics from dilatometric measurement. Comput Mater Sci 184:109837

    Article  Google Scholar 

  49. Maleki H, Durães L, Portugal A (2014) An overview on silica aerogels synthesis and different mechanical reinforcing strategies. J Non-Cryst Solids 385:55–74

    Article  Google Scholar 

  50. Matouš K, Geers MG, Kouznetsova VG, Gillman A (2017) A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J Comput Phys 330:192–220

    Article  MathSciNet  Google Scholar 

  51. Merxhani A (2016) An introduction to linear poroelasticity. arXiv:1607.04274

  52. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092

    Article  MATH  Google Scholar 

  53. Niskanen M, Dazel O, Groby J-P, Duclos A, Lähivaara T (2019) Characterising poroelastic materials in the ultrasonic range—a Bayesian approach. J Sound Vib 456:30–48

    Article  Google Scholar 

  54. Oden JT, Babuška I, Faghihi D (2017) Predictive computational science: computer predictions in the presence of uncertainty. In: Encyclopedia of computational mechanics, 2nd edn, pp 1–26

  55. Oden JT, Farrell K, Faghihi D (2015) Estimation of error in observables of coarse-grained models of atomic systems. Adv Model Simul Eng Sci 2(1):1–20

    Article  Google Scholar 

  56. Oden JT, Hawkins A, Prudhomme S (2010) General diffuse-interface theories and an approach to predictive tumor growth modeling. Math Models Methods Appl Sci 20(03):477–517

    Article  MathSciNet  MATH  Google Scholar 

  57. Oden JT, Moser R, Ghattas O (2010) Computer predictions with quantified uncertainty, part II. SIAM News 43(10):1–4

    Google Scholar 

  58. Oliver TA, Terejanu G, Simmons CS, Moser RD (2015) Validating predictions of unobserved quantities. Comput Methods Appl Mech Eng 283:1310–1335

    Article  Google Scholar 

  59. Oskay C, Su Z, Kapusuzoglu B (2020) Discrete eigenseparation-based reduced order homogenization method for failure modeling of composite materials. Comput Methods Appl Mech Eng 359:112656

    Article  MathSciNet  MATH  Google Scholar 

  60. Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–25

    Article  Google Scholar 

  61. Patki P, Costanzo F (2020) A mixture theory-based finite element formulation for the study of biodegradation of poroelastic scaffolds. Comput Mech 66:351–371

    Article  MathSciNet  MATH  Google Scholar 

  62. Phillips PJ (2005) Finite element methods in linear poroelasticity: theoretical and computational results. Ph.D. Thesis, The University of Texas at Austin

  63. Phillips PJ, Wheeler MF (2009) Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach. Comput Geosci 13(1):5–12

    Article  MATH  Google Scholar 

  64. Prevost JH (1985) Wave propagation in fluid-saturated porous media: an efficient finite element procedure. Int J Soil Dyn Earthq Eng 4(4):183–202

  65. Prudencio E, Bauman P, Faghihi D, Ravi-Chandar K, Oden J (2015) A computational framework for dynamic data-driven material damage control, based on Bayesian inference and model selection. Int J Numer Methods Eng 102(3–4):379–403

    Article  MathSciNet  MATH  Google Scholar 

  66. Prudencio E, Bauman P, Williams S, Faghihi D, Ravi-Chandar K, Oden J (2014) Real-time inference of stochastic damage in composite materials. Compos B Eng 67:209–219

    Article  Google Scholar 

  67. Rajagopal KR, Tao L (1995) Mechanics of mixtures, vol 35. World Scientific, Singapore

    Book  MATH  Google Scholar 

  68. Roberts GO, Rosenthal JS et al (2004) General state space Markov chains and MCMC algorithms. Probab Surv 1:20–71

    Article  MathSciNet  MATH  Google Scholar 

  69. Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comput Phys Commun 145(2):280–297

    Article  MathSciNet  MATH  Google Scholar 

  70. Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index. Comput Phys Commun 181(2):259–270

    Article  MathSciNet  MATH  Google Scholar 

  71. Saltelli A, Chan K, Scott E (2009) Sensitivity analysis. Number no. 2008 in Wiley paperback series. Wiley, New York

    Google Scholar 

  72. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New York

    MATH  Google Scholar 

  73. Saltelli A, Sobol’ IM (1995) About the use of rank transformation in sensitivity analysis of model output. Reliab Eng Syst Saf 50(3):225–239

    Article  Google Scholar 

  74. Saltelli A, Tarantola S (2002) On the relative importance of input factors in mathematical models. J Am Stat Assoc 97(459):702–709

    Article  MATH  Google Scholar 

  75. Singer B, Hyatt S, Drekic S (2013) A Bayesian approach to 2d triple junction modeling. Comput Mater Sci 71:97–100

    Article  Google Scholar 

  76. Sobol’ IM (1990) Sensitivity estimates for nonlinear mathematical models. Mat Model 2:112–118

    MathSciNet  MATH  Google Scholar 

  77. Sobol’ IM (1993) Sensitivity analysis for non-linear mathematical models. Math Model Comput Exp 1:407–414

    MATH  Google Scholar 

  78. Sobol’ IM (2007) Global sensitivity analysis indices for the investigation of nonlinear mathematical models. Mat Model 19:23–24

    MathSciNet  MATH  Google Scholar 

  79. Song P, Mignolet MP (2019) Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems. Comput Mech 64(6):1557–1566

    Article  MathSciNet  MATH  Google Scholar 

  80. Tan J, Villa U, Shamsaei N, Shao S, Zbib HM, Faghihi D (2021) A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty. Int J Plast 138:102935

    Article  Google Scholar 

  81. Topuzi D (2020) Structural thermal breaks. Struct Des

  82. Torquato S, Haslach H Jr (2002) Random heterogeneous materials: microstructure and macroscopic properties. Appl Mech Rev 55(4):B62–B63

    Article  Google Scholar 

  83. Truesdell C (1962) Mechanical basis of diffusion. J Chem Phys 37(10):2336–2344

    Article  Google Scholar 

  84. U.S. Energy Information Administration. https://www.eia.gov/

  85. Van Bommel M, De Haan A (1995) Drying of silica aerogel with supercritical carbon dioxide. J Non-Cryst Solids 186:78–82

    Article  Google Scholar 

  86. Wang C, Mobedi M, Kuwahara F (2019) Simulation of heat transfer in a closed-cell porous media under local thermal non-equilibrium condition. Int J Numer Methods Heat Fluid Flow 30:2478–2500

    Article  Google Scholar 

  87. Wang Y, McDowell DL (2020) Uncertainty quantification in multiscale materials modeling. Woodhead Publishing Limited, Sawston

    Google Scholar 

  88. Wei T-Y, Chang T-F, Lu S-Y, Chang Y-C (2007) Preparation of monolithic silica aerogel of low thermal conductivity by ambient pressure drying. J Am Ceram Soc 90(7):2003–2007

    Article  Google Scholar 

  89. Yang R, Hu F, An L, Armstrong J, Hu Y, Li C, Huang Y, Ren S (2019) A hierarchical mesoporous insulation ceramic. Nano Lett 20(2):1110–1116

  90. Yang Z, Wang Z, Yang Z, Sun Y (2018) Multiscale analysis and computation for coupled conduction, convection and radiation heat transfer problem in porous materials. Appl Math Comput 326:56–74

  91. Zhang W, Bostanabad R, Liang B, Su X, Zeng D, Bessa MA, Wang Y, Chen W, Cao J (2019) A numerical Bayesian-calibrated characterization method for multiscale prepreg preforming simulations with tension-shear coupling. Compos Sci Technol 170:15–24

Download references

Acknowledgements

DF and JT gratefully acknowledge the support by the U.S. National Science Foundation (NSF) CAREER Award CMMI-2143662. SR gratefully acknowledges support from the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE) under the Building Technology Office (BTO) Award Number DE-EE0008675. CZ acknowledges the support by the NSF under Award CMMI-1846863. DF and JT also thank the Center for Computational Research (http://www.buffalo.edu/ccr.html) at University at Buffalo for providing HPC resources that have contributed to the research results reported here. The authors are grateful to the referees for their constructive inputs.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, USA

    Jingye Tan, Lu An, Massimigliano Di Luigi, Shenqiang Ren & Danial Faghihi

  2. Department of Materials Science, Sharif University of Technology, Tehran, Iran

    Pedram Maleki

  3. Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, USA

    Umberto Villa

  4. Department of Industrial and Systems Engineering, University at Buffalo, Buffalo, USA

    Chi Zhou

Authors
  1. Jingye Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pedram Maleki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lu An
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Massimigliano Di Luigi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Umberto Villa
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Chi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shenqiang Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Danial Faghihi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Danial Faghihi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Jingye Tan and Pedram Maleki have contributed equally to this work.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tan, J., Maleki, P., An, L. et al. A predictive multiphase model of silica aerogels for building envelope insulations. Comput Mech 69, 1457–1479 (2022). https://doi.org/10.1007/s00466-022-02150-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-022-02150-5

Keywords

Search

Navigation