Modeling Aperiodic Dimensionally Reducible Structures Using Mechanics of Structure Genome

Abstract

This work systematically constructs multiscale constitutive models for aperiodic dimensionally reducible structures (beams/plates) using Mechanics of Structure Genome (MSG). MSG simplifies the original complex analysis into a dimensionally reduced structural analysis and a constitutive modeling over the Structure Genome (SG). The approach starts with expressing the kinematics including both displacements and strains of the original heterogeneous structures in terms of those of the dimensionally reduced structures and fluctuating functions. To ensure the kinematic equivalency of the original heterogeneous structures and the dimensionally reduced structures, integral constraints on the fluctuating functions are developed. Then based on the principle of minimum information loss, the variational statement governing the SG can be formulated and solved. As this theory does not require boundary conditions, one is free to choose the analysis domain of arbitrary shape and they need not to be volumes with periodic boundaries. This theory can also handle periodic microstructures by enforcing the periodicity of the fluctuating functions. As a partial validation of this new theory, the results using the current approach are shown to converge to those of periodic heterogeneous beam/plate structures obtained using periodic boundary conditions.