On Microcontinuum Theories of Polycrystals at Small Strain

摘要

Microcontinuum theories for inelastic analysis of rate-independent polycrystals at small strain are investigated. For a macroscopically homogeneous solid, the infinite aggregate model of T. H. Lin is extended to include more general crystal hardening theories and an ordered elastic anisotropy. Corresponding integrodifferential equations for incremental response under uniform averaged stress are derived. The macroscopic (apparent) plastic strain rate is newly defined in terms of a microcontinum velocity field due to continuous crystalline slip and aggregate self-stressing, and several general theoretical results of R. Hill are shown to apply to the extended infinite model. The question of an appropriate definition of latent strain energy in the unloaded aggregate also is considered. (Author)