On finite linear viscoelasticity of incompressible isotropic materials

Acta Mechanica

Volumn 159, Issue 1-4, 2002, Pages 87-124

  Haupt, P ^a   Lion, A ^a  

^a UNIVERSITY OF KASSEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONSTRAINT THEORY; DECOMPOSITION; DEFORMATION; STRAIN;

ISOTROPIC MATERIALS;

VISCOELASTICITY;

EID: 0036960890     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01171450     Document Type: Article

References (45)

1. Besdo, D., Ihlemann, J.: Zur Modellierung des Stoffverhaltens von Elastomeren. Kautsch. Gummi Kunstst. 49, 495-503 (1996).
2. Beris, A. N., Edwards, B. J.: On the admissibility criteria for viscoelastic kernels. Rheol. Acta 32, 505-510 (1993).
3. Bronstein, I. N., Semendjajew, K. A.: Taschenbuch der Mathematik. Harri Deutsch 1997.
4. Caputo, M., Mainardi, F.: Linear models in anelastic solids, riv. Il nuovo cimento (Sere. II) 1, 161-198 (1971).
5. Coleman, B. D.: Thermodynamics of materials with memory. Arch. Rat. Mech. Anal. 17, 1-46 (1964).
6. Coleman, B. D., Gurtin, M. E.: Thermodynamics with internal state variables. J. Chem. Phys. 47, 597-613 (1967).
7. Coleman, B. D., Mizel, V. J.: Norms and semi-groups in the theory of fading memory. Arch. Rat. Mech. Anal. 23, 87-274 (1966).
8. Coleman, B. D., Noll, W.: An approximation theorem for functionals with application in continuum mechanics. Arch. Rat. Mech. Anal. 6, 355-370 (1960).
9. Coleman, B. D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 33, 239-249 (1961).
10. Coleman, B. D., Owen, D. R.: On the thermodynamics of materials with memory. Arch. Rat. Mech. Anal. 36, 245-269 (1970).
11. Drozdov, A. D.: Fractional differential models in finite viscoelasticity. Acta Mech. 124, 155-180 (1997).
12. Drozdov, A. D.: Viscoelastic structures. Boston: Academic Press 1998.
13. Erdelyi, M., Oberhettinger, T.: Higher transcendental functions, vol. 3. New York: McGraw Hill 1954.
14. Ferry, J. D.: Viscoelastic properties of polymers. New York: Wiley 1980.
15. Findley, W. N., Lai, J. S., Onaran, K.: Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Amsterdam New York Oxford: North Holland 1976.
16. Gross, B.: Mathematical structure of the theories of linear viscoelasticity. Paris: Hermann 1968.
17. Hartmann, S.: Computation in finite strain viscoelasticity: Finite elements based on the interpretation as differential-algebraic equations (submitted for publication) Comp. Meth. Appl. Mech. Engng 2000.
18. Hartmann, S.: Finite-element computation of large strain viscoelastic structures using diagonally implicit Runge-Kutta methods. Proc. European Conference on Computational Mechanics 2001, 26. 6.-29.6. 2001, Krakow, Poland on CD-ROM 2001.
19. Haupt, P., Tsakmakis, C.: On the application of dual variables in continuum mechanics. Continuum Mech. Thermodyn. 1, 165-196 (1989).
20. Haupt, P., Lion, A., Backhaus, E.: On the dynamic behavior of polymers under finite strains: constitutive modelling and identification of parameters. Int. J. Solids Struct. 37, 3633-3646 (2000).
21. Haupt, P.: Continuum mechanics and theory of materials. Berlin: 2th Edition, Springer 2002.
22. Haupt, P., Sedlan, K.: Viscoplasticity of elastomeric materials. Experimental facts and constitutive modelling. Arch. Appl. Mech. 71, 89-109 (2001).
23. Huber, H., Tsakmakis, C.: Finite deformation viscoelasticity laws. Mech. Mat. 32, 1-18 (2000).
24. Lion, A.: On the thermodynamics of fractional damping elements. Continuum Mech. Thermodyn. 9, 83-96 (1997).
25. Lion, A.: A physically based method to represent the thermomechanical behavior of elastomers. Acta Mech. 123, 1-25 (1997).
26. Lion, A.: On the large deformation behavior of reinforced rubber at different temperatures. J. Mech. Phys. Solids 45, 1805-1834(1997).
27. Lion, A.: Thixotropic behavior of rubber under dynamic loading histories: Experiments and theory. J. Mech. Phys. Solids. 46, 895-930 (1998).
28. Lion, A.: Strain-dependent dynamic properties of filled rubber: A nonlinear viscoelastic approach based on structural variables. Rubber Chem. Technol. 72, 410-429 (1999).
29. Lion, A.: Constitutive modelling in finite thermoviscoplasticity: A physical approach based on non-linear rheological models. Int. J. Plast. 16, 469-494 (2000).
30. Lion, A.: Thermomechanically consistent formulations of the standard linear solid using fractional derivatives. Arch. Mech. 53, 253-273 (2001).
31. Lu, S. C. H., Pister K. D.: Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids. Int. J. Solids Struct. 11, 927-934 (1975).
32. Lubliner, J.: On fading memory in materials of evolutionary type. Acta Mech. 8, 75-81 (1969).
33. Lubliner, J.: A Model for rubber viscoelasticity. Mech. Res. Comp. 12, 93-99 (1985).
34. Miehe, C., Keck, J.: Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation. J. Mech. Phys. Solids 48, 323-365 (2000).
35. Oldham, K. B., Spanier, J.: The fractional calculus: Theory and applications of differentiation and integration to arbitrary order. London: Academic Press 1974.
36. Rabotnov, J. N., Iljushin, A. A.: Methoden der Viskoelastizitätstheorie. München: Carl Hanser Verlag 1970.
37. Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solids Struct. 35, 3455-3482 (1998).
38. Reese, S., Govindjee, S.: Theoretical and numerical aspects in the thermo-viscoelastic material behavior of rubber-like polymers. Mech. Time-dependent Mat. 1, 357-396 (1998).
39. Schwarzl, F. R.: Polymermechanik: Struktur und mechanisches Verhalten von Polymeren. Berlin Heidelberg: Springer 1990.
40. Sedlan, K.: Viskoelastisches Materialverhalten von Elastomerwerkstoffen: Experimentelle Untersuchung und Modellbildung. Dr.-Ing. Thesis, University of Kassel, Department of Mechanical Engineering, Germany 2001.
41. Sullivan, J. L., Demery, V. C.: The nonlinear viscoelastic behaviour of a carbon black-filled elastomer. J. Polym. Sci. 20, 2083-2101 (1982).
42. Truesdell, C., Noll, W.: The nonlinear field theories of mechanics. Encyclopedia of Physics III/3, (Flügge, S., ed.). Berlin: Springer 1965.
43. Tschoegl, N. W.: The phenomenological theory of linear viscoelastic behavior. Berlin: Springer 1989.
44. Valanis, K.: A theory of viscoplasticity without a yield surface. Arch. Mech. 23, 517-533 (1971).
45. Slonimsky, G. L.: Laws of mechanical relaxation processes in polymers. J. Polymer Sci., Part C 16, 1667-1672 (1967).