Simultaneous Hierarchical and Multi-Level Optimization for Material Characterization and Design of Experiments

A hierarchical algorithmic and computational scheme based on a staggered design optimization approach is presented. This scheme is structured for unique characterization of many continuum systems and their associated datasets of experimental measurements related to their response characteristics. This methodology achieves both online (real-time) and offline design of optimum experiments required for characterization of the material system under consideration, while also achieving a constitutive characterization of the system. The approach assumes that mechatronic systems are available for exposing specimens to multidimensional loading paths and for the acquisition of data associated with stimulus and response behavior. Material characterization is achieved by minimizing the difference between system responses that are measured experimentally and predicted based on model representation. The performance metrics of the material characterization process are used to construct objective functions for the design of experiments at a higher-level optimization. The distinguishability and uniqueness of solutions that characterize the system are used as two of many possible measures adopted for construction of objective functions required for design of experiments. Finally, a demonstration of the methodology is presented that considers the best loading path of a two degree-of-freedom loading machine for characterization of the linear elastic constitutive response of anisotropic materials.