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On the development and parameter identification of Schapery-type constitutive theories

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An Erratum to this article was published on 10 June 2008

Abstract

Schapery-type constitutive theories for nonlinearly viscoelastic materials have been used extensively within the literature. Most of the applications are 1D but some 3D applications can be found. Most of the 3D applications are thermodynamically inconsistent extensions of the 1D constitutive theory. This paper shows and illustrates how thermodynamically admissible Schapery-type constitutive theories can be generated. In addition, a new 3D constitutive theory is introduced. A new data reduction procedure for obtaining the material parameters, which does not rely on creep–recovery tests, is introduced. The procedure leads to material parameters that are thermodynamically admissible and considers the whole mechanical response rather than particular values, as in most data reduction procedures. This procedure is tested on a thermoplastic material and the constitutive theory thus obtained is compared with data from other load histories.

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References

  • Aboudi, J.: Micromechanical characterization of the non-linear viscoelastic behavior of resin matrix composites. Compos. Sci. Technol. 38, 371–386 (1990)

    Article  Google Scholar 

  • Augl, J.M., Land, D.J.: A numerical method approach for obtaining nonlinear viscoelastic parameters of polymeric materials and composites. J. Appl. Polym. Sci. 30, 4203–4233 (1985)

    Article  Google Scholar 

  • Beijer, J.G.J., Spoormaker, J.L.: Solution strategies for FEM analysis with nonlinear viscoleastic polymers. Comp. Struct. 80, 1213–1229 (2002)

    Article  Google Scholar 

  • Biot, M.A.: Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena. J. Appl. Phys. 25(1), 1385–1391 (1954)

    Article  ADS  MATH  Google Scholar 

  • Bouleau, N.: Interprétation probabiliste de la viscoélasticité linéaire. Mech. Res. Commun. 19, 15–20 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  • Bouleau, N.: Viscoélasticité et processus de lévy. J. Potential Analysis 11(3), 289–302 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Brueller, O.S.: On the nonlinear characterization of the long term behavior of polymeric materials. Polym. Eng. Sci. 27(2), 144–148 (1987)

    Article  Google Scholar 

  • Chailleux, E., Davies, P.: Modelling the non-linear viscoelastic and viscoplastic behaviour of aramid fibre yarns. Mech. Time-Depend. Mater. 7, 291–303 (2003)

    Article  ADS  Google Scholar 

  • Chailleux, E., Davies, P.: A non-linear viscoelastic viscoplastic model for the behaviour of polyester fibres. Mech. Time-Depend. Mater. 9, 147–160 (2005)

    Article  ADS  Google Scholar 

  • Chazal, C., Arfaoui, M.: Further development in thermodynamic approach for thermoviscoelastic materials. Mech. Time-Depend. Mater. 5, 177–198 (2001)

    Article  Google Scholar 

  • Cunat, C.: The DNLR approach and relaxation phenomena. Part I – Historical account and DNLR formalism. Mech. Time-Depend. Mater. 5(1), 39–65 (2001)

    Article  Google Scholar 

  • Drozdov, A.D.: A constitutive model for nonlinear viscoelastic media. Int. J. Solids Struct. 34(21), 2685–2707 (1997)

    Article  MATH  Google Scholar 

  • Eringen, A.C.: Mechanics of Continua. Wiley, New York (1967)

    MATH  Google Scholar 

  • Fung, Y.C.: Fundations of Solids Mechanics. Prentice-Hall Inc., New York (1965)

    Google Scholar 

  • Gamby, D., Blugeon, L.: On the characterization by Schapery’s model of non-linear viscoelastic materials. Polym. Test. 7, 137–147 (1987)

    Article  Google Scholar 

  • Green, A.E., Rivlin, R.S.: The mechanics of nonlinear materials with memory. Arch. Ration. Mech. Analysis 1, 1–21 (1957)

    ADS  MathSciNet  MATH  Google Scholar 

  • Green, A.E., Rivlin, R.S.: The mechanics of nonlinear materials with memory – Part III. Arch. Ration. Mech. Analysis 4, 387–404 (1960)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Green, A.E., Rivlin, R.S., Spencer, A.J.S.: The mechanics of nonlinear materials with memory – Part II. Arch. Ration. Mech. Analysis 3, 82–90 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Haj-Ali, R.M., Muliana, A.H.: Numerical finite element formulation of the Schapery non-linear viscoelastic material model. Int. J. Numer. Methods Eng. 59, 25–45 (2004)

    Article  MATH  Google Scholar 

  • Henriksen, M.: Nonlinear viscoelastic stress analysis – A finite element approach. Comp. Struct. 18(1), 133–139 (1984)

    Article  MATH  Google Scholar 

  • Howard, C.M., Hollaway, L.: The characterization of the non-linear viscoelastic properties of a randomly orientated fibre/matrix composites. Composites 18(4), 317–323 (1987)

    Article  Google Scholar 

  • Hu, Y., Ellyin, F., Xia, Z.: An experimental investigation of normal and shear stress interaction of an epoxy resin and model predictions. Polym. Eng. Sci. 41(11), 2047–2060 (2001)

    Article  Google Scholar 

  • Knauss, W.G., Emri, I.: Volume change and the nonlinearly thermo-viscoelastic constitution of polymers. Polym. Eng. Sci. 27(1), 86–100 (1987)

    Article  Google Scholar 

  • Lai, J., Bakker, A.: An integral constitutive equation for nonlinear plasto-viscoelastic behavior of High-Density polyethylene. Polym. Eng. Sci. 35(17), 1339–1347 (1995)

    Article  Google Scholar 

  • Lai, J., Bakker, A.: 3-D Schapery representation for non-linear viscoelasticity and finite element implementation. Comput. Mech. 18, 182–191 (1996)

    Article  MATH  Google Scholar 

  • Lee, S., Knauss, W.G.: A note of the determination of relaxation and creep data from ramp tests. Mech. Time-Depend. Mater. 4, 1–7 (2000)

    Article  Google Scholar 

  • Lin, W.S., Pramanick, A.K., Sain, M.: Determination of material constants for nonlinear viscoelastic predictive model. J. Compos. Mater. 38(1), 19–29 (2004)

    Article  Google Scholar 

  • Lou, Y.C., Schapery, R.A.: Viscoelastic characterisation of a nonlinear fibre-reinforced plastic. J. Compos. Mater. 5, 208–234 (1971)

    Article  Google Scholar 

  • Lu, H., Knauss, W.G.: The role of dilatation in the nonlinearly viscoelastic behavior of pmma under multiaxial stress states. Mech. Time-Depend. Mater. 2, 307–334 (1998)

    Article  Google Scholar 

  • Lévesque, M., Derrien, K., Mishnaevsky, L. Jr., Baptiste, D., Gilchrist, M.D.: A micromechanical model for nonlinear viscoelastic particle reinforced polymeric composite materials-undamaged state. Compos. Part A: Appl. Sci. Manuf. 35(7–8), 905–913 (2004)

    Article  Google Scholar 

  • Megnis, M., Varna, J.: Nonlinear viscoelastic, viscoplastic characterization of unidirectional GF/EP composite. Mech. Time-Depend. Mater. 7, 269–290 (2003)

    Article  ADS  Google Scholar 

  • Mohan, R., Adams, D.F.: Nonlinear creep–recovery response of a polymer matrix and its composites. Exp. Mech. 25(4), 262–271 (1985)

    Article  Google Scholar 

  • Nordin, L.O., Varna, J.: Nonlinear viscoplastic and nonlinear viscoelastic material model for paper fiber composites in compression. Composites: Part A 37, 344–355 (2006a)

    Article  Google Scholar 

  • Nordin, L.O., Varna, J.: Methodology for parameter identification in nonlinear viscoelastic material model. Mech. Time-Depend. Mater. 9, 259–280 (2006b)

    Article  Google Scholar 

  • Papanicolaou, G.C., Zaoutsos, S.P., Cardon, A.H.: Further development of a data reduction method for the nonlinear viscoelastic characterization of FRP. Composites Part A: Appl. Sci. Manuf. 30, 839–848 (1999)

    Article  Google Scholar 

  • Papanicolaou, G.C., Zaoutsos, S.P., Kontou, E.A.: Fiber orientation dependence of continuous carbon/epoxy composites nonlinear viscoelastic behavior. Compos. Sci. Technol. 64, 2535–2545 (2004)

    Article  Google Scholar 

  • Poon, H., Ahmad, F.: A finite element constitutive update scheme for anisotropic viscoelastic solids exhibiting non-linearity of the Schapery type. Int. J. Numer. Methods Eng. 46, 2027–2041 (1999)

    Article  MATH  Google Scholar 

  • Pramanick, A., Sain, M.: Nonlinear viscoelastic creep prediction of HDPE – agro-fiber composites. J. Compos. Mater. 40(5), 417–431 (2006)

    Article  Google Scholar 

  • Schapery, R.A.: Application of thermodynamics to thermomechanical, fracture, and berefringent phenomena in viscoelastic media. J. Appl. Phys. 35(5), 1451–1465 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  • Schapery, R.A.: A theory of nonlinear thermoviscoelasticity based on irreversible thermodynamics. In: Proceedings of the 5th U.S. National Congress on Applied Mechanics, ASME 511 (1966a)

  • Schapery, R.A.: An engineering theory of nonlinear viscoelasticity with applications. Int. J. Solids Struct. 2, 407–425 (1966b)

    Article  Google Scholar 

  • Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9(4), 295–310 (1969a)

    Article  Google Scholar 

  • Schapery, R.A.: Further Development of a Thermodynamic Constitutive Theory: Stress Formulation. Purdue University (1969b)

  • Schapery, R.A.: Viscoelastic behavior and analysis of composite materials. In: Sendeckyj, G.P. (ed.) Mechanics of Composite Materials, pp. 85–168. Academic Press, New York (1974)

    Google Scholar 

  • Schapery, R.A.: Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics. Mech. Time-Depend. Mater. 1, 209–240 (1997a)

    Article  Google Scholar 

  • Schapery, R.A.: Thermoviscoelastic constitutive equations for polycrystalline ice. J. Cold Regions Eng. 11(2), 146–157 (1997b)

    Article  Google Scholar 

  • Schapery, R.A.: Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage. Int. J. Fract. 97, 33–66 (1999)

    Article  Google Scholar 

  • Sridharan, S.: Nonlinear viscoelastic analysis of composites using competing micromechanical models. J. Compos. Mater. 40(3), 257–282 (2006)

    Article  MathSciNet  Google Scholar 

  • Touati, D., Cederbaum, G.: Postbuckling of non-linear viscoleastic imperfect laminated plates. Part I: material considerations. Compos. Struct. 42, 33–41 (1998)

    Article  Google Scholar 

  • Wu, P.D., van der Giessen, E.: On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers. J. Mech. Phys. Solids 41(3), 427–456 (1993)

    Article  ADS  MATH  Google Scholar 

  • Zaoutsos, S.P., Papanicolaou, G.C., Cardon, A.H.: On the nonlinear viscoelastic characterization of polymer matrix composites. Compos. Sci. Technol. 58(6), 883–889 (1998)

    Article  Google Scholar 

  • Zapas, L.J., Crissman, J.M.: Creep and recovery behaviour of ultra-high molecular weight polyethylene in the region of small uniaxial deformations. Polymer 25, 57–62 (1983)

    Article  Google Scholar 

  • Zhang, L., Ernst, L.J., Brouwer, H.R.: A study of nonlinear viscoelasticity of an unsaturated polyester resin. Part 2. 3D Model. Mech. Mater. 26, 167–195 (1997a)

    Article  Google Scholar 

  • Zhang, L., Ernst, L.J., Brouwer, H.R.: A study of nonlinear viscoelasticity of an unsaturated polyester resin. Part 1. Uniaxial model. Mech. Mater. 26, 141–166 (1997b)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. CREPEC, Département de Génie Mécanique, École Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montréal, Québec, H3C 3A7, Canada

    Martin Lévesque

  2. Laboratoire d’Ingénierie des Matériaux, UMR8006 CNRS, Ecole. Nat. Sup. Arts et Métiers, 151 bd. de l’Hopital, 75 013, Paris, France

    Katell Derrien & Didier Baptiste

  3. School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Dublin, 4, Ireland

    Michael D. Gilchrist

Authors
  1. Martin Lévesque
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  2. Katell Derrien
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  3. Didier Baptiste
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  4. Michael D. Gilchrist
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Correspondence to Martin Lévesque.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s11043-008-9057-6

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Lévesque, M., Derrien, K., Baptiste, D. et al. On the development and parameter identification of Schapery-type constitutive theories. Mech Time-Depend Mater 12, 95–127 (2008). https://doi.org/10.1007/s11043-008-9052-y

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  • DOI: https://doi.org/10.1007/s11043-008-9052-y

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