### Achievement

Computational simulation provides an efficient means to predict the behavior of customized hybrid material configurations using validated, physics-based models. One limitation to this approach is the quality and quantity of available data to characterize the many constituent input properties. Therefore, a systematic approach to identify the most influential parameters on the hybrid behavior and quantify the corresponding uncertainty in predictive capabilities is required.

In this work, an approach using Bayesian multimodel inference and imprecise global sensitivity analysis is presented to investigate the effects of sparse constituent data on the prediction of composite material properties. The methodology allows the identification, using quantified uncertainties, of the most influential constituent material parameters for specified homogenized properties. This sensitivity analysis further enables a dimension reduction when assessing the influence of uncertainties on material properties and can be used to inform testing programs of the constituent properties that require additional testing/data collection in order to minimize uncertainty in macro-scale composite properties. The methodology is specifically demonstrated on the prediction and sensitivity analysis of out-of-plane mechanical properties of a unidirectional lamina.

**Publications**:

Jiaxin Zhang, Michael Shields, and Stephanie TerMaath. "Probabilistic modeling and prediction of out-of-plane unidirectional composite lamina properties." ** Mechanics of Advanced Materials and Structures** (2020): 1-17.

### Significance and Impact

Within this probabilistic analysis framework, an effective method is presented to estimate the imprecise sensitivity indices and further reduce the model dimensionality. Based on the variance-based sampling method for Sobol index estimation, a novel importance sampling-based formulation is proposed to efficiently quantify imprecision in the Sobol indices. The developed algorithm therefore achieves simultaneous estimates of the first-order and total-order Sobol indices given an ensemble of candidate target distributions at a low computational cost, when compared to the traditional Monte Carlo method which requires multiple loops. Through the efficient IGSA approach, we can first identify the interaction among all random variables and second rank the input variables according to their relative importance. As a result, the model dimension reduction is achieved by varying only the most important variables instead of all of the model parameters.

Last Updated: November 11, 2020 - 4:37 pm