COMPUTATIONAL PLASTICITY FOR COMPOSITE STRUCTURES BASED ON MATHEMATICAL HOMOGENIZATION - THEORY AND PRACTICE

This paper generalizes the classical mathematical homogenization theor y for heterogeneous medium to account for eigenstrains. Starting from the double scale asymptotic expansion for the displacement and eigenst rain fields we derive a close form expression relating arbitrary eigen strains to the mechanical fields in the phases. The overall structural response is computed using an averaging scheme by which phase concent ration factors are computed in the average sense for each micro-consti tuent, and history data is updated at two points (reinforcement and ma trix) in the microstructure, one for each phase. Macroscopic history d ata is stored in the database and then subjected in the post-processin g stage onto the unit cell in the critical locations. For numerical ex amples considered, the CPU time obtained by means of the two-point ave raging scheme with variational micro-history recovery with 30 seconds on SPARC 10/51 as opposed to 7 hours using classical mathematical homo genization theory. At the same time the maximum error in the microstre ss field in the critical unit cell was only 3.5% in comparison with th e classical mathematical homogenization theory.