Abstract
Nonequilibrium thermodynamics, rate-process theory, viscoelastic fracture mechanics and various experimentally-motivated simplifications are used to develop constitutive equations that account for effects of viscoelasticity, viscoplasticity, growing damage and aging. Their form is more general than previously developed by the author, and allows for relatively general tensorial effects of damage. Some important special cases are then covered, with emphasis on viscoelasticity. Evolution equations for the damage expressed in terms of internal state variables (ISVs) are discussed, comparing formulations using scalar ISVs and tensor ISVs. Finally, some experimental support for the theory is described. An Appendix illustrates the theory for an aging, linear viscoelastic material with growing cracks.
Similar content being viewed by others
References
Abdel-Tawab, Kh., Smith, L.V. and Weitsman, Y. (1997). The inelastic/damage response of swirl-mat polymeric composites: experiments and theory. The Lazar M. Kachanov Symposium on Inelasticity and Damage in Solids Subject to Microstructural Change. (Edited by I.J. Jordaan, R. Seshadri and I.L. Meglis). Memorial Univ. of Newfoundland, St. Johns, 291–300.
Allen, D.H. and Yoon, C. (1998). Homogenization techniques for thermoviscoelastic solids containing cracks. International Journal of Solids and Structures 35. (In press).
Biot, M.A. (1954). Theory of stress-strain relations in anisotropic viscoelaslicity and relaxation phenomena. Journal of Applied Physics 25, 1385–1391.
Fung, Y.C. (1965). Fundamentals of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
Graham, G.A.C. (1968). The correspondence principle of linear viscoelasticity theory for mixed boundary value problems involving time-dependent boundary regions. Quarterly of Applied Mathematics 26, 167–174.
Ha, K. and Schapery, R.A. (1998). A three-dimensional viscoelastic constitutive model for particulate composites with growing damage and its experimental validation. International Journal of Solids and Structures 35, 3497–3517.
Henriksen, M. (1984). Nonlinear viscoelastic stress analysis — a finite element approach. Computers & Structures 18, 133–139.
Hult, J.A.H. (1966). Creep in Engineering Structures. Blaisdell. Waltham Ma.
Kachanov, L.M. (1958). Rupture time under creep conditions. Izv. Akad Nauk, SSSR, Otd. Tekhn. Nauk, 8, 26–31 (in Russian).
Kachanov, M. (1998). Solids with cracks and non-spherical pores: proper parameters of defect density and effective elastic properties. International Journal of Fracture 97, 1–31.
Krajcinovic, D. (1996). Damage Mechanics. North-Holland, Amsterdam.
Lai, J. and Bakker, A. (1995). An integral constitutive equation for nonlinear plasto-viscoelastic behavior of highdensity polyethylene. Polymer Engineering and Science 35, 1339–1347.
Lee, H.J. and Kim, Y.R. (1998). A viscoelastic continuum damage model of asphalt concrete with healing. Journal of Engineering Mechanics. ASCE, 124. (in press).
Lemaitre, J. (1992). A Course on Damage Mechanics, Springer-Verlag, Berlin.
Lifshitz, J.M. and Rotem, A. (1970). Time-dependent longitudinal strength of unidirectional fibrous composites. Fiber Science and Technology 3, 1–20.
Lou, Y.C. and Schapery, R.A. (1971). Viscoelastic characterization of a non-linear fiber-reinforced plastic. Journal of Composite Materials 5, 208–234.
Lubliner, J. (1972). International Journal of Non-Linear Mechanics 7, 237–254.
McClintock, F.A. and Argon, A.S. (1966). Mechanical Behavior of Materials, Addison-Wesley, Reading, MA.
Moore, R.H. and Dillard, D.A. (1990). Time-dependent matrix cracking in cross-ply laminates. Composites Science and Technology 39, 1–12.
Park, S.W., Kim, Y.R. and Schapery, R.A. (1996). A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete. Mechanics of Materials 24, 241–255.
Park, S.W. and Schapery, R.A. (1997). A viscoelastic constitutive model for particulate composites with growing damage. International Journal of Solids and Structures 34, 931–947.
Raghaven, J. and Meshii, M. (1996). Time-dependent damage in carbon fibre-reinforced polymer composites. Composites Part A 27A, 1223–1227.
Rice, J.R. (1971). Inelastic contitutive relations for solids: An internal variable theory and its application to metal plasticity. Journal of the Mechanics and Physics of Solids 19, 433–455.
Schapery, R.A. (1969a). Further Development of a Thermodynamic Constitutive Theory: Stress Formulation. Purdue University Report No. AA & ES 69–2.
Schapery, R.A. (1969b). On the characterization of non-linear viscoelastic materials. Polymer Engineering and Science 9, 295–310.
Schapery, R.A. (1974). Viscoelastic behavior and analysis of composite materials. In: Mechanics of Composite Materials, (Edited by G.P. Sendeckyj), Academic Press, New York, 85–168.
Schapery, R.A. (1981). On viscoelastic deformation and failure behavior of composite materials with distributed flaws. 1981 Advances in Aerospace Structures and Materials. ASME, AD-01. (Edited by S.S. Wang and W.J. Renton), pp. 5–20.
Schapery, R.A. (1982). Models for damage growth and fracture in nonlinear viscoelastic particulate composites. Proc. Ninth U.S. National Congress of Applied Mechanics, ASME book no. H0028, 237–245.
Schapery, R.A. (1984). Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media. International Journal of Fracture 25, 195–223.
Schapery, R.A. (1991a). Models for the deformation behavior of viscoelastic media with distributed damage and their applicability to ice. IUTAM-IAHR Symposium on Ice-Structure Interaction. (Edited by S. Jones, R.F. McKenna, J. Tillotson, and I. Jordaan). Springer-Verlag, Berlin, 191–230.
Schapery, R.A. (1991b). Analysis of damage growth in particulate composites using a work potential. Composites Engineering 1, 167–182.
Schapery, R.A. (1991c). Simplifications in the behavior of viscoelastic composites with growing damage. In IUTAM Symposium on Inelastic Deformation of Composite Materials. (Edited by G.J. Dvorak), Springer-Verlag, New York, 193–214.
Schapery, R.A. (1997a). Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics. Mechanics of Time Dependent Materials 1, 209–240.
Schapery, R.A. (1997b). Non-linear viscoelastic constitutive equations for polymers and polymeric composites with distributed damage. The Lazar M. Kachanov Symposium on Inelasticity and Damage in Solids Subject to Microstructural Change. (Edited by I.J. Jordaan, R. Seshadri, and I.L. Meglis). Memorial Univ. of Newfoundland, St. Johns, 35–45.
Schapery, R.A. (1997c). Thermoviscoelastic constitutive equations for polycrystalline ice. Journal of Cold Regions Engineering, ASCE 11, 146–157.
Schapery, R.A. and Sicking, D.L. (1995). On nonlinear constitutive equations for elastic and viscoelastic composites with growing damage. In: Mechanical Behavior of Materials (Edited by A. Bakker), Delft University Press, Delft, 45–76.
Sinha, N.K. (1988). Crack-enhanced creep in polycrystalline material: strain-rate sensitive strength and deformation of ice. Philosophical Magazine A43, 4415–4428.
Uzan, J. (1996). Asphalt concrete characterization for pavement performance prediction. Journal of the Association of Asphalt Paving Technologists 65, 573–607.
Uzan, J., Perl, M. and Sides, A. (1986). Numerical simulation of fatigue creep crack growth in a visco-elastoplastic material.-II: Experimental validation and application. Engineering Fracture Mechanics 23, 333–344.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schapery, R. Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage. International Journal of Fracture 97, 33–66 (1999). https://doi.org/10.1023/A:1018695329398
Issue Date:
DOI: https://doi.org/10.1023/A:1018695329398