| Composite materials are the well-known substitutes for traditional metals in various industries because of their micro-structural character. Micro-structures provide a high strength-to-weight ratio, which makes them suitable for manufacturing large variety of applications ranging from simple toys to complicated space/aircraft structures. Since, these materials are widely used in high performance structures, their stress/thermal analysis issues are of major concern. Due to the high degree of material heterogeneity, it is extremely difficult to analyze such structures.;Homogenization (rigorous averaging) is a process that overcomes the difficulty of modeling each micro-structure. It replaces an individual micro-structure by an equivalent material model representation (unit cell). Periodic micro-structures appear in regular intervals throughout the domain, in contrast aperiodic micro-structures follows an irregular pattern. Further, this method bridges the analysis gap between micro and macro domain of the structures. In this thesis, Homogenization procedure based on anti-periodic displacement fields for aperiodic micro-structures and aperiodic boundary conditions are considered to model the constitutive material matrix. This work could be easily implemented with the traditional finite element packages. In addition, it eventually increases the convergence accuracy and reduces the high computational expenses. Different problems are analyzed by the implementation of digital image processing schemes for the extraction of a unit cell around the Gauss quadrature points and the mesh-generation. In the future, this research defines a new path for the analysis of any random heterogeneous materials by its ease of implementation and the state-of-the-art micro-structure material modeling capabilities and digital image based micro-meshing. |
