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

Martin Lévesque1, Katell Derrien2, D. Baptiste2, Michael D. Gilchrist3
1Ecole Polytechnique De Montréal
2Laboratoire d’Ingénierie des Matériaux, UMR8006 CNRS, Ecole. Nat. Sup. Arts et Métiers, Paris, France
3School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Ireland

Tóm tắt

Từ khóa


Tài liệu tham khảo

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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)

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)

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

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)

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

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)

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)

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

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)

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)

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

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

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)

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

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)

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)

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)

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

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

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)

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

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)

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

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

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

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

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

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)

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)

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)

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)

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)