Skip to main content
SpringerLink
Log in

Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

For arbitrary linear Kelvin model viscoelastic constitutive relations, generalized analyses based on collocation, least squares, Lagrangean multipliers, calculus of variation and inverse formulations are presented for determining viscoelastic designer material properties tailored and engineered to be best suited for specific boundary and loading conditions and their time histories. Optimum 3-D anisotropic designer materials, including auxetic viscoelastic functionally graded ones, are studied to minimize thermal stresses, creep buckling, creep rates, deflections, aero- and hydro- dynamic noise and static and dynamic aero-viscoelastic effects while concurrently lowering failure probabilities and extending structural survival times and maximizing or minimizing energy dissipation and its rate. The analyses are formulated for single structural elements as well as the entire structure. Extensions to the entire vehicle that incorporate aerodynamics, stability and control are discussed and the dimensions of computational requirements are estimated.

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

Similar content being viewed by others

References

  • Anonymous. (2008). http://www.ncsa.uiuc.edu/BlueWaters/

  • Abanto-Bueno, J.L.: Fracture of a model functionally graded material manufactured from a photo-sensitive polyethylene. Ph.D. Thesis in Aerospace Engineering, University of Illinois at Urbana-Champaign (2004)

  • Abanto-Bueno, J.L., Lambros, J.: Investigation of a crack growth in functionally graded materials using digital image correlation. Eng. Fract. Mech. 69, 1695–1711 (2002)

    Article  Google Scholar 

  • Abanto-Bueno, J.L., Lambros, J.: Mechanical and fracture behavior of an artificially ultraviolet-irradiated ploy(ethylene carbon monoxide copolymer. J. Appl. Polym. Sci. 92, 139–148 (2004)

    Article  Google Scholar 

  • Aik, K.K.: Plasma sprayed functionally graded ZrO2/NiCoCrAlY thermal barrier coating (2003). http://www.ntu.edu.sg/mae/research/programmes/adv_materials/FGM.htm

  • Beldica, C.E., Hilton, H.H.: Analytical simulations of optimum anisotropic linear viscoelastic damping properties. J. Reinf. Plast. Compos. 18, 1658–1676 (1999)

    Google Scholar 

  • Bisplinhoff, R.L., Ashley, H.: Principles of Aeroelasticity. Wiley, New York (1962)

    Google Scholar 

  • Bisplinhoff, R.L., Ashley, H., Halfman, R.L.: Aeroelasticity. Addison-Wesley, Cambridge (1955)

    Google Scholar 

  • Cagle, C.M., Schlecht, R.W.: Composite elastic skins for shape changing structures. NASA Tech Briefs LAR-16599-1 (2007). http://www.techbriefs.com/content/view/1113/34/

  • Chen, C.P., Lakes, R.S.: Viscoelastic behaviour of composite materials with conventional- or negative-Poisson’s ratio foam as one phase. J. Mater. Sci. 28, 4288–4299 (1993)

    Article  ADS  Google Scholar 

  • Christensen, R.M.: Theory of Viscoelasticity – An Introduction, 2nd edn. Academic Press, New York (1982)

    Google Scholar 

  • Dave, E.V., Buttlar, W.G., Paulino, G.H., Hilton, H.H.: Graded viscoelastic approach for modeling of asphalt concrete pavements. In: Proceedings Multiscale and Functionally Graded Materials Conference (FGM-2006). Honolulu, HI (2006)

  • de Coulomb, C.-A.: Théorie des machines simples, en ayant égard au frottement de leurs parties et à la roideur des cordages. Bachelier, Paris (1821)

    Google Scholar 

  • Dillard, D.A., Brinson, H.F.: A numerical procedure for predicting creep and delayed failures in laminated composites. In: O’Brien, T.K. (ed.) Long-Term Behavior of Composites, ASTM STP 813, pp. 23–37. ASTM, Philadelphia (1983)

    Google Scholar 

  • Dowell, E.H.: Aeroelasticity of Plates and Shells. Noordhoff International Publishers, Leiden (1975)

    MATH  Google Scholar 

  • Dowell, E., Ilgamov, M.: Studies in Nonlinear Aeroelasticity. Springer, New York (1988)

    MATH  Google Scholar 

  • Dowell, E.H., Crawley, E.F., Curtis Jr., H.C., Peters, D.A., Scanlan, R.H., Sisto, F.: A Modern Course in Aeroelasticity, 3rd edn. Kluwer, Boston (2004)

    MATH  Google Scholar 

  • Friis, E.A., Lakes, R.S., Parks, J.B.: Negative Poisson’s ratio polymeric and metallic foams. J. Mater. Sci. 23, 4406–4414 (1988)

    Article  ADS  Google Scholar 

  • Gerard, G.: Introduction to Structural Stability Theory. McGraw-Hill, New York (1962)

    Google Scholar 

  • Goldstein, M.E.: Aeroacoustics. McGraw-Hill, New York (1976)

    MATH  Google Scholar 

  • Gunasekaran, S., Mehmet Ak, M.: Cheese Rheology and Texture. CRC Press, Boca Raton (2003)

    Google Scholar 

  • Hiel, C., Sumich, M., Chappell, D.P.: A curved beam test specimen for determining the interlaminar tensile strength of a laminated composite. J. Compos. Mater. 25, 854–868 (1991)

    Google Scholar 

  • Hilton, H.H.: Creep collapse of viscoelastic columns with initial curvatures. J. Aeronaut. Sci. 19, 844–846 (1952)

    Google Scholar 

  • Hilton, H.H.: On the nonexistence of finite critical times for generalized linear viscoelastic columns with arbitrary initial curvatures. J. Aero/Space Sci. 28, 655–656 (1961)

    MATH  Google Scholar 

  • Hilton, H.H.: An introduction to viscoelastic analysis. In: Baer, E. (ed.) Engineering Design for Plastics, pp. 199–276. Reinhold Publishing Corp., New York (1964)

    Google Scholar 

  • Hilton, H.H.: On the inadmissibility of separation of variable solutions in linear anisotropic viscoelasticity. Int. J. Mech. Compos. Mater. Struct. 3, 97–100 (1996)

    Article  Google Scholar 

  • Hilton, H.H.: Implications and constraints of time independent Poisson ratios in linear isotropic and anisotropic viscoelasticity. J. Elast. 63, 221–251 (2001)

    Article  MATH  Google Scholar 

  • Hilton, H.H.: Dynamic creep buckling of linear viscoelastic columns including failure probabilities and survival times. University of Illinois UIUC, Technical Report UILU ENG 02-0503. J. Elast. (2002a, submitted)

  • Hilton, H.H.: Viscoelastic column dynamic creep buckling – failure probabilities and survival times. In: Proceedings International Conference on Nonlinear Problems in Aviation and Aerospace, p. 18. Melbourne, FL (2002b)

  • Hilton, H.H.: Comments regarding ‘viscoelastic properties of an epoxy resin during cure’ by D.J. O’Brien, P.T. Mather and S.R. White. J. Compos. Mater. 37, 89–94 (2003a)

    Article  Google Scholar 

  • Hilton, H.H.: Optimum viscoelastic designer materials for minimizing failure probabilities during composite cure. J. Therm. Stress. 26, 547–557 (2003b)

    Article  Google Scholar 

  • Hilton, H.H.: Designer light weight viscoelastic composite structures – embedded electrical wiring, tailored mechanical properties and failure probabilities. The 2004 Gordon Conference on Composites, p. 12. Ventura, CA (2004a)

  • Hilton, H.H.: Viscoelastic thermal control of probabilistic failures and survival times of panels subjected to aerodynamic noise. In: Proceedings of EUROMECH Colloquium 455 on Semi-Active Vibration Suppression, p. 16. Prague, Czech Republic (2004b)

  • Hilton, H.H.: Designer mechanical properties and failure probabilities for tailored light weight viscoelastic structures under thermal and piezoelectric control. In: Proceedings Conference on Engineered Adaptive Structures IV, pp. 11–18. The Center for Acoustics and Vibration, The Pennsylvania State University, State College (2004c)

    Google Scholar 

  • Hilton, H.H.: Designer linear viscoelastic materials tailored to maximize aero-dynamic noise control. In: Proceedings of the Second International Workshop on High Speed Transport Noise and Environmental Acoustics (HSTNEA 2005), p. 11. Computer Center of the Russian Academy of Sciences, Moscow (2005a)

    Google Scholar 

  • Hilton, H.H.: Designer linear viscoelastic material properties tailored to minimize probabilistic failures for dynamic composite plate creep buckling. In: Proceedings American Society of Composites 20th Annual Technical Conference. CD-ROM: Paper No. 146, Drexel University, Philadelphia, PA (2005b)

  • Hilton, H.H.: Optimum linear and nonlinear viscoelastic designer functionally graded materials—characterization and analysis. Composites Part A: Appl. Sci. Manuf. 36, 1329–1334 (2005c)

    Article  Google Scholar 

  • Hilton, H.H.: Designer viscoelastic materials tailored to minimize probabilistic failures for thermal stress induced dynamic column creep buckling. J. Therm. Stress. 29, 403–421 (2006a)

    Article  Google Scholar 

  • Hilton, H.H.: Designer viscoelastic materials tailored to minimize probabilistic failures in composite columns with lateral buckling. In: Proceedings American Society for Composites 21st Annual Technical Conference. Dearborn, MI (2006b)

  • Hilton, H.H.: Functionally graded designer viscoelastic materials tailored to perform prescribed tasks with failure probabilities and survival times. In: Proceedings Multiscale and Functionally Graded Materials Conference (FGM-2006), CD-ROM. Honolulu, HI (2006c)

  • Hilton, H.H.: Designer linear viscoelastic material properties tailored to minimize probabilistic failures or thermal stress induced dynamic column creep buckling. J. Therm. Stress. 29, 403–421 (2006d)

    Article  Google Scholar 

  • Hilton, H.H., Ariaratnam, S.T.: Invariant anisotropic large deformation deterministic and stochastic combined load failure criteria. Int. J. Solids Struct. 31, 3285–3293 (1994)

    Article  MATH  Google Scholar 

  • Hilton, H.H., Dong, S.B.: An Analogy for Anisotropic, Nonhomogeneous, Linear Viscoelasticity Including Thermal Stresses. Development in Mechanics, pp. 58–73. Pergamon, New York (1964)

    Google Scholar 

  • Hilton, H.H., El Fouly, A.R.A.: Designer auxetic viscoelastic sandwich columns tailored to minimize creep buckling failure probabilities and prolong survival times. In: Proceedings 48th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference. AIAA Paper AIAA-2007-2400. Honolulu, HI (2007)

  • Hilton, H.H., Feigen, M.: Minimum weight analysis based on structural reliability. J. Aero/Space Sci. 27, 641–652 (1960)

    MathSciNet  MATH  Google Scholar 

  • Hilton, H.H., Lee, D.H.: Designer functionally graded viscoelastic materials performance tailored to minimize probabilistic failures of panels subjected to aerodynamic noise. In: Proceedings Ninth International Conference on Recent Advances in Structural Dynamics, CD-ROM: 1–16, University of Southampton, UK (2006)

  • Hilton, H.H., Yi, S.: Analytical formulation of optimum material properties for viscoelastic damping. J. Smart Mater. Struct. 1, 113–122 (1992)

    Article  ADS  Google Scholar 

  • Hilton, H.H., Yi, S.: Stochastic viscoelastic delamination onset failure analysis of composites. J. Compos. Mater. 27, 1097–1113 (1993)

    Article  Google Scholar 

  • Hilton, H.H., Yi, S.: The significance of anisotropic viscoelastic Poisson ratio stress and time dependencies. Int. J. Solids Struct. 35, 3081–3095 (1998)

    Article  MATH  Google Scholar 

  • Hoff, N.J.: The Analysis of Structures. Wiley, New York (1956)

    MATH  Google Scholar 

  • Hoff, N.J., Boley, B.A., Coan, J.A.: The development of a technique for testing stiff panels in edgewise compression. Proc. Soc. Exp. Stress Analysis 5(2), 14–24 (1948)

    Google Scholar 

  • Jaglinski, T.M., Lakes, R.S.: Negative stiffness and negative Poisson’s ratio in materials which undergo a phase transformation. In: Wagg, D., Bond, I. (eds.) Adaptive Structures – Engineering Applications, pp. 231–246. Wiley, New York (2007)

    Google Scholar 

  • Jones, D.I.G.: Handbook of Viscoelastic Vibration Damping. Wiley, New York (2001)

    Google Scholar 

  • Kanai, H.: Noninvasive measurement of myocardial viscoelasticity. In: Proceeding of 8th Sendai Symposium on Ultrasonic Tissue Characterization, pp. 17–21. Institute of Development, Aging and Cancer, Tohoku University (2005)

    Google Scholar 

  • Kempner, J., Pohle, F.V.: On the non-existence of a finite critical time for linear viscoelastic columns. J. Aeronaut. Sci. 20, 572–573 (1953)

    MathSciNet  Google Scholar 

  • Lakes, R.S.: Foam structures with a negative Poisson’s ratio. Science 235, 1038–1040 (1987)

    Article  ADS  Google Scholar 

  • Lakes, R.S.: The time-dependent Poisson’s ratio of viscoelastic materials can increase or decrease. Cell. Compos. 11, 466–469 (1992)

    Google Scholar 

  • Lakes, R.S.: (2005). http://silver.neep.wisc.edu/~lakes/Poisson.html

  • Lakes, R.S., Wineman, A.: On Poisson’s ratio in linearly viscoelastic solids. J. Elast. 85, 45–63 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Lambros, J., Narayanaswamy, A., Santare, M.H., Anlas, G.: Manufacture and testing of a functionally graded material. ASME J. Eng. Mater. Technol. 121, 488–493 (1999a)

    Article  Google Scholar 

  • Lambros, J., Santare, M.H., Li, H., Sapna, G.H.: A novel technique for the fabrication of laboratory scale model functionally graded materials. Exp. Mech. 39, 184–190 (1999b)

    Article  Google Scholar 

  • Lanzos, C.: The Variational Principles of Mechanics, pp. 43–48. The University of Toronto Press, Toronto (1949)

    Google Scholar 

  • Lazan, B.J.: Damping of Materials and Members in Structural Mechanics. Pergamon Press, Oxford (1968)

    Google Scholar 

  • Leaderman, H.: Elastic and Creep Properties of Filamentous Materials. The Textile Foundation, Washington (1943)

    Google Scholar 

  • Libove, C.: Creep buckling of columns. J. Aeronaut. Sci. 19, 459–467 (1952)

    Google Scholar 

  • Lifshitz, J.M., Rotem, A.: Time-dependent longitudinal strength of unidirectional fibrous composites. Fibre Sci. Technol. 3, 1–20 (1970)

    Article  Google Scholar 

  • Lighthill, M.J.: On sound generated aerodynamically. I. General theory. Proc. R. Soc. (Lond.) A 222, 564–587 (1952)

    Article  ADS  MathSciNet  Google Scholar 

  • Lighthill, M.J.: On sound generated aerodynamically. II. Turbulence as a source of sound. Proc. R. Soc. (Lond.) A 231, 1–32 (1954)

    ADS  Google Scholar 

  • Lindquist, E.S.: Strength of materials and the Weibull distribution. J. Probab. Eng. Mech. 9, 191–194 (1994)

    Article  Google Scholar 

  • Merrett, C.G., Hilton, H.H.: Generalized linear aero-servo-viscoelasticity: theory and applications. In: Proceedings 49th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, AIAA Paper AIAA-2008-1997 (2008)

  • Murthy, D., Prabhakar, N., Xie, M., Jiang, R.: Weibull Models. Wiley, Hoboken (2004)

    MATH  Google Scholar 

  • Nashif, A.D., Jones, D.I.G., Henderson, J.P.: Vibration Damping. Wiley, New York (1985)

    Google Scholar 

  • Phoenix, S.L.: Statistical aspects of failure of fibrous materials. In: Tsai, S.W. (ed.) Composite Materials: Testing and Design. ASTM STP 674, pp. 455–483 (1979)

  • Phoenix, S.L., Tierney, L.-J.: A statistical model for the time dependent failure of unidirectional composite materials under local elastic load-sharing among fibers. Eng. Fract. Mech. 18, 193–215 (1982)

    Article  Google Scholar 

  • Poisson, S.-D.: Mémoire sur l’équilibre et le mouvement des corps élastiques. Mémoires de l’Académie Royal des Sciences de l’Institut de France 8, 357–570 (1829), 623–627

    Google Scholar 

  • Prony, G.C., Baron de, F.M.R.: Essai experimental et analytique. J. l’École Polytechnique de Paris 1, 24–76 (1795)

    Google Scholar 

  • Ricker, K.: The shape of things to come (2006). http://www.trecc.org/features/USSAshville/

  • Schapery, R.A.: Approximate methods of transform inversion for viscoelastic stress analysis. In: Proceedings Fourth US National Congress of Applied Mechanics, vol. 2, pp. 1075–1085. ASME, New York (1962)

    Google Scholar 

  • Sears, W.R.: Some aspects of non-stationary airfoil theory and its practical applications. J. Aeronaut. Sci. 8, 104–108 (1941)

    MathSciNet  MATH  Google Scholar 

  • Shanley, F.R., Ryder, E.I.: Stress Ratios: The Answer to the Combined Loading Problem. Aviation 36, 28–70 (1937)

    Google Scholar 

  • Shtark, A., Grozbeyn, H., Sameach, G., Hilton, H.H.: An alternate protocol for determining viscoelastic material properties based on tensile tests without use of Poisson ratios. In: Proceedings of the 2007 International Mechanical Engineering Congress and Exposition. ASME Paper IMECE2007-41068. Seattle, WA (2007)

  • Steinbacker, F.R., Gerard, G.: Aircraft Structural Mechanics. Pitman Publishing Co., New York (1952)

    Google Scholar 

  • Tschoegl, N.W.: Time dependence in material properties: an overview. Mech. Time-Depend. Mater. 1, 3–31 (1997)

    Article  Google Scholar 

  • Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity – a critical review. Mech. Time-Depend. Mater. 6, 3–51 (2002)

    Article  Google Scholar 

  • Van Krevelen, D.W.: Properties of Polymers – Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions, 3rd edn. Elsevier, Amsterdam (1990)

    Google Scholar 

  • Watson, A.S., Smith, R.L.: An examination of statistical theories for fibrous materials in the light of experimental data. J. Mater. Sci. 20, 3260–3270 (1985)

    Article  ADS  Google Scholar 

  • Weaver, P.M., Ashby, M.F.: The optimal selection of material and section shape. J. Eng. Des. 7, 129–150 (1996)

    Article  Google Scholar 

  • Weibull, W.: A statistical distribution function of wide applicability. ASME J. Appl. Mech. 18, 293–297 (1951)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace Engineering (AE), Technology Research, Education and Commercialization Center (TRECC), National Center for Supercomputing Applications (NCSA), University of Illinois at Urbana-Champaign (UIUC), 104 South Wright Street, MC-236, Urbana, IL, 61801-2935, USA

    Harry H. Hilton, Daniel H. Lee & Abdul Rahman A. El Fouly

Authors
  1. Harry H. Hilton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdul Rahman A. El Fouly
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harry H. Hilton.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hilton, H.H., Lee, D.H. & El Fouly, A.R.A. Generalized viscoelastic designer functionally graded auxetic materials engineered/tailored for specific task performances. Mech Time-Depend Mater 12, 151–178 (2008). https://doi.org/10.1007/s11043-008-9054-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-008-9054-9

Keywords

Search

Navigation