| The thesis is concerned with development of practical multiscale asymptotic methods that can be successfully applied in various industrial settings. The thesis addresses three major barriers: (i) developing multiscale technologies compatible with conventional finite element code architecture, (ii) reducing computational cost of existing multiscale technologies, and (iii) extending the range of applicability to problems where the classical homogenization assumptions do not hold.;To overcome the first barrier, a computational homogenization approach fully compatible with conventional finite element code architecture is derived. A seamless implementation in ABAQUS is achieved including Python script, user-defined subroutines and specific input files. For linear problems, ABAQUS existing facilities are utilized to develop analysis attributes required for solving a unit cell problem. For nonlinear problems, a Python script is invoked by a coarse scale stress update procedure to carry out the scale bridging.;To meet the second challenge, a new model reduction approach is developed. The method combines the multiple scale asymptotic expansion method with the transformation field analysis to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy. The inelastic constitutive relations in micro phases and interfaces are modeled using eigenstrains and eigendisplacements, respectively. The original approach is extended to arbitrary number of scales and is reformulated to account for arbitrary inelastic eigendeformation of microconstituents. A Multiscale Design System for two-scale analysis has been developed and integrated in ABAQUS. The system has been verified and validated. Finally, a Multiscale Enrichment method based on the Partition of Unity (MEPU) method is developed. It is a synthesis of mathematical homogenization theory and the Partition of Unity method. Its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible. The method is generalized to account for boundary layers, nonperiodic fields and nonlinear systems. Performance studies for both continuum and coarse grained discrete systems are conducted to validate the formulation. |
