Scale-dependent bounds on effective elastoplastic response of random composites

We consider the mechanical response of random, heterogeneous materials, whe re each phase is elastic-plastic with an associated flow rule, and the micr ostructure's statistics is homogeneous and ergodic. Under proportional mono tonic loading, the effective tin the macroscopic sense, or overall) elastop lastic response is shown to be bounded from above and below by those obtain ed, respectively, from displacement and traction boundary conditions applie d to finite size domains (square shaped windows). A scale dependent hierarc hy of these bounds is obtained by extending the methods used earlier for th e elastic moduli estimation: the larger the scale relative to the heterogen eity, the closer are the bounds. A fiber reinforced metal matrix composite is employed to illustrate the theoretical results. Its constitutive respons e and plastic strain field are investigated by computational micromechanics for different window sizes under both types of boundary conditions; it is found here that the displacement conditions result in denser and more unifo rmly distributed slip band patterns, while the traction conditions lead to more localized fields. We also investigate a mixed boundary condition, unde r which the mechanical response of composite is found to fall between those under displacement and traction controlled boundary conditions. (C) 2001 E lsevier Science Ltd. All rights reserved.