An Approach for Robust Micro-Scale Materials Design under Unparameterizable Variability

In this paper, we propose a method for the robust design of materials involving processes that are computationally intensive and selectively random. The material system considered is a Reactive Powder Metal Mixture (RPMM) composed of Al and Fe2O3. Shock simulations of discrete energetic particle mixtures are performed to predict the system's mechanical and thermal behavior that will be used by a designer of the mixture to achieve robust reaction initiation. The method proposed in this paper is the Robust Concept Exploration Method with Error Margin Indices (RCEM-EMI), which employs error margin indices as metrics to determine satisfying design specifications for given performance requirement ranges. An error margin index is a mathematical construct indicating the location of mean system performance and the spread of the performance considering both variability in design variables and models of the system. Variability in responses of a model may be due to system variation that cannot be easily parameterized as noise factors. Furthermore, lack of data, due to the cost of simulations and experiments, leads to uncertain parameters in empirical models. System response variability and parameter uncertainty in a response surface model are estimated in a computationally efficient manner to formulate the error margin indices, which are then leveraged to search for ranged sets of design specifications. Finally, the use of the proposed robust design method is illustrated by the design of a RPMM.