A thermodynamic framework for a gradient theory of continuum damage
In this paper, we present a formulation of state variable based gradient theory to model damage evolution and alleviate numerical instability associated within the post-bifurcation regime. This proposed theory is developed using basic microforce balance laws and appropriate state variables within a consistent thermodynamic framework. The proposed theory provides a strong coupling and consistent framework to prescribe energy storage and dissipation associated with internal damage. Moreover, the temporal evolution equation derived here naturally shows the effect of damage—nucleation, growth and coalescence. In addition, the theoretical framework presented here is easily extendable to the addition of other defects (not shown here), and can be generalized to the development of consistent coupled transport equations for species, such as hydrogen (Bammann et al. in JMPS, 2009, submitted), as well as providing a consistent structure for modeling events at diverse length scales.
Unable to display preview. Download preview PDF.
- 1.Bammann, D.J., Novak, P., Sofronis, P., Somerday, B.: A coupled dislocation-hydrogen based model of inelastic deformation of metals and alloys. JMPS (2009, submitted)Google Scholar
- 2.Cosserat E., Cosserat F.: Theorie des corps deformables. Hermann et Fils, Paris (1909)Google Scholar
- 3.Dillon O.W., Kratochvil J.: A strain gradient theory of plasticity. Int. J. Solids Struct. 6, 1533–1566 (1970)Google Scholar
- 5.Bammann, D.J., Aifantis, E.C.: On the perfect lattice-dislocated state interaction. In: Selvadurai, A.P.S. (ed.) Mechanics of Structured Media. In: Proceedings of the International Symposium on the Mechanical Behaviour of Structured Media, Ottawa, pp. 79–91 (1981)Google Scholar
- 7.Aifantis E.C.: On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 95, 215–229 (1984)Google Scholar
- 21.Bammann, D.J., Solanki, K.N.: On kinematic, thermodynamic and coupling of a damage theory for polycrystalline material. IJP (2009, submitted)Google Scholar
- 24.Kachanov M.: Time of the rupture process under creep conditions. Izv. Akad. Nauk. USSR Otdelenie Tech. Nauk 8, 26–31 (1958)Google Scholar