Abstract
New predictions for the effective behavior of nonlinear polycrystals are obtained from the nonlinear variational procedure of deBotton and Ponte Castaneda (1995), using the classical self-consistent estimates for a suitable choice of the “linear comparison polycrystal”. A distinctive feature of the new self-consistent estimates is that not only do they satisfy the Taylor and Hashin-Shtrikman bounds, but also a recent bound of Kohn & Little (1997) for two-dimensional polycrystals, which is significantly more restrictive than the Taylor bound at large grain anisotropy. This result suggests that the new self-consistent estimates may also be more accurate than other self-consistent estimates, such as those arising from the incremental model of Hill (1965), for three-dimensional nonlinear polycrystals.
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