Abstract
On the basis of the one-dimensional Schapery representation for non-linear viscoelasticity, a three-dimensional constitutive model incorporating the effects of temperature and physical ageing is developed for isotropic non-linear viscoelastic materials. Adopting the assumption that the hydrostatic and deviatoric responses are uncoupled, the contitutive equation is expressed in incremental form for both compressible and incompressible materials, with the hereditary integral updated at the end of each time increment by recursive computation. The proposed model is implemented in the finite element package MARC. Numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms.
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References
Buckley, C. P.; McCrum, N. G. 1974: The relation between linear and non-linear viscoelasticity of polypropylene. J. Mater. Sci. 9: 2064–2066
Flory, R. J. 1961: Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57: 829–838
Henriksen, M. 1984: Non-linear viscoelastic stress analysis — a finite element approach, Computers and Structures 18: 133–139
Heidweiller, A. J. 1994: Proc. 10th Biennial European Conference on Fracture, Berlin, Germany, September 1994, 741–746
Lai, J. 1995: Non-linear deformation behaviour of high-density polyethylene, Ph.D. thesis, Delft University Press
Lubliner, J. 1985: A model for rubber viscoelasticity, Mech. Res. Comm. 12, 233–245
MARK k5.2 1993: User's Manuals
Mindel, M. J.; Brown, N. 1993: Creep and recovery of polycarbonate, J. Mater. Sci. 8: 863–870
Ogden, R. W. 1984: Non-linear elastic deformation, Chichester, UK., Ellis, Horwood
Pao, Y. H.; Marin, J. 1953: J. Appl. Mech. 19: 478–484
Rooijackers, H. F. L. 1988: A numerical implementation of the Schapery model for nonlinear viscoelasticity, PhD thesis, Eindhoven University of Technology, The Netherlands
Schapery, R. A. 1969: On the characterisation of non-linear viscoelastic materials. J. Polym. Eng. Sci. 9, 295–310
Simo, J. C.; Taylor, R. L.; Pister, K. S. 1985: Variational and projection methods for the volume constraint in finite deformation, Comput. Meths. Appl. Mech. Eng. 51, 177–208
Simo, J. C. 1987: On a fully three-dimensional finite strain viscoelastic damage model: formulation and computational aspects, Comput. Meths. Appl. Mech. Eng. 60: 153–173
Struik, L. C. E. 1978: Physical ageing in amorphous polymers and other materials, Amsterdam, Elsevier
Williams, M. L.; Landel, R. F.; Ferry, J. D. 1955: J. Amer. Chem. Soc. 77: 3701–3707
Zhang, L.; Ernst, L. J. 1993: A three dimensional model for non-linear viscoelasticity. In: Dijksman, J. F.; Nieuwstradt, F. T. M. (ed): Topics in applied mechanics, pp. 253–260, Kluwer Academic Publisher
Van der Zwet, M. J. M. 1992: Proc. 9th Biennial European Conference on Fracture, Varna, Bulgaria, September 1992, 196–201
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Communicated by S. N. Atluri, 9 February 1996
Laboratory for Engineering Mechanics, Delft University of Technology, P. O. Box 5033, 2600 GA Delft, The Netherlands
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Lai, J., Bakker, A. 3-D schapery representation for non-linear viscoelasticity and finite element implementation. Computational Mechanics 18, 182–191 (1996). https://doi.org/10.1007/BF00369936
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DOI: https://doi.org/10.1007/BF00369936