Second-order estimates for the effective behaviour of viscoplastic polycrystalline materials

摘要

This paper is concerned with the application of the "second-order" nonlinear homogenisation procedure (Ponte Castaneda, J. Mech. Phys. Solids 44(6) (1996) 827) to generate estimates of the self-consistent type for the effective behaviour of fcc and hcp viscoplastic polycrystals. The method has the distinctive property that it leads to estimates that are exact to second-order In the heterogeneity contrast, and which are expected to be more accurate, particularly when Compared to rigorous bounds, than those resulting form earlier homogenisation schemes such As the Hill "incremental" method or its "total" formulation(Hutchinson) for pure power-law Viscous materials.