The random nature of the micro-structural attributes in materials in general and composite material systems in particular requires expansion of material modeling in a way that will incorporate their inherent uncertainty and predict its impact on material properties and mechanical response in multiple scales. Despite the importance of capturing and modeling material randomness, there are numerous challenges in structural characterization that are yet to be addressed. The work presented in this essay takes a few steps towards an improved material modeling approach which encompasses structural randomness in order to produce a more realistic representation of material systems. For this end a computational framework was developed to generate a realistic representative volume element which reflects the inherent structural randomness. First stochastic structural elements were identified and registered from imaging data and parameters were assigned to represent those elements. Statistical characterization of the random attributes was followed by the construction of a representative volume element which shared the same structural statistical characteristics with the original material system.

The resultant statistical equivalent representative volume element (SERVE) was then used in finite element simulations which provided homogenized properties and mechanical response predictions. The suggested framework was developed and then implemented on 3 different material systems. Image processing and analysis in one of the material systems extended the original scope of this work to solving a machine vision and learning problem. Object segmentation for the purpose object and pattern recognition has been a long standing subject of interest in the field of machine vision. Despite the significant attention given to the development of segmentation and recognition methods, the critical challenge of separating merged objects did not share the spotlight. A simple yet original approach to overcome this hurdle was developed using unsupervised classification and separation of objects in 3D. Lower dimensionality classifiers were joined to provide a powerful higher dimensionality classification tool.

The robustness of this approach is illustrated through its implementation on two case studies of merged objects. Applications of this methodology can further extend from structural classification to general problems of clustering and classification in various fields.