Integration of material composition, microstructure, and mechanical properties with geometry information enables many product development activities, including design, analysis, and manufacturing. To address such needs, models of material composition have been integrated into CAD systems, creating systems called heterogeneous CAD modeling. In order to support the heterogeneous CAD system, extensive process-structure-property relationships have to be captured and integrated into current CAD system. A new method for reverse engineering of materials will be presented such that microstructure models can be constructed and used in the heterogeneous CAD system. Reverse engineering of material consists of three parts: image analysis, structure-property-process relationship, and repository. In this research, an image processing method, which comprises the Radon transform and the wavelet transform, will be used in order to recognize geometric features from a microstructure image. Recognizing geometric features can be obtained by combinations of three techniques, masking, clustering, and high frequency component on wavelet transform, that are integrated with the Radon transform. Then, recognized geometric features can be used to construct an explicit geometric model of microstructure. The proposed work will provide an explicit mathematical method to recognize and to quantify microstructure features from an image. In addition, explicit geometric models of microstructure can be automatically constructed and utilized to get effective mechanical properties, establishing structure-property relationship of the material. In order to demonstrate this, polymer nano-composite sample and metal alloy sample will be used.

The application of heterogeneous materials has become common in modern product design such as composites and porous media. Computational design tools for such materials, with higher complexity than the traditional homogeneous ones, will be a critical component in the realization of the heterogeneity systematically. It is foreseen that computer-aided design (CAD) systems will include computer-aided materials design modules in future so that the design of functional materials and structures can be integrated for optimal product design. The traditional CAD systems model three-dimensional (3D) geometry at macro-scales with boundary representation (B-Rep), whereas computer-aided materials design is concerned with the specification of material composition at scales ranging from nano-, meso-, to micro-. Thus, multi-scale CAD systems are desirable for the integration of product and materials information. The existing B-Rep based modeling scheme needs to be extended to incorporate heterogeneous material compositions. The new modeling scheme should also support seamless zoom-in and zoom-out operations in multi-scale CAD systems. Recently, a multi-scale model, dual-Rep, was proposed to represent geometry and material property distribution implicitly. The core part of dual-Rep is a new basis function called surfacelet. Surfacelet is able to represent boundary information more efficiently than the traditional wavelets, while keeping a unified form with wavelets so that the role exchange of boundary and internal structures during zooming operations is enabled. A surfacelet transform is able to represent microstructure distributions in 3D images with surfacelet coefficients. In this dissertation, three enabling techniques for surfacelet-based heterogeneous materials modeling are developed. First, a method of inverse surfacelet transform is developed such that the original images can be reconstructed from the surfacelet coefficients. The surface integrals of voxel (i.e., volumetric pixel) values are obtained from the surfacelet coefficients using the one-dimensional inverse wavelet transform. The images are then reconstructed by solving linear equations from discretized surface integrals. The prior knowledge of material properties and distributions is applied to solve the under-constrained problems. Second, composite surfacelets with the combinations of different types of primitive surfacelets are created to increase the flexibility of the surfacelet transform with potentially fewer surfacelets and improved reconstruction accuracy. Third, a multi-scale materials modeling method is proposed to support interactive design and visualization of material microstructures at multiple levels of details. It has the capability to support seamless zoom-in and zoom-out. This method provides a feature-based design approach based on the surfacelet basis.