Thoughts on Hierarchical Modeling Methods for Complex Structures

Hierarchical modeling refers to the modeling of parts with solid geometry, material composition, and possibly distributions of properties at multiple scales. Typical solid and heterogeneous models represent geometry at one scale but do not contain geometric information about features at scales that are orders of magnitude smaller. In this paper, the related topics of heterogeneous and hybrid modeling, subdivision methods, and level of detail approaches are surveyed. The capabilities of these technologies are compared against the requirements for modeling cellular materials and other structures with complex geometric and material constructions. A specific hierarchical modeling method is proposed. Three 2D examples are used to illustrate the application of the proposed modeling method.