Forward and Inverse Approaches for Uncertainty Quantification of the In-Plane Elastic Properties of Cellular Structures

Abstract

Uncertainty quantification is essential to exploiting the complete potential of cellular structures. Forward methods allow quantifying the uncertainties in the mechanical properties of cellular structures by propagating the uncertainties of the input parameters, while inverse methods allow using experimental data to indirectly infer the uncertainty of the input parameters. In this paper, a closed-loop forward and inverse quantification of the in-plane elastic properties of cellular structures was proposed. A polynomial chaos expansion model was used in the forward model for uncertainty propagation and quantification of the in-plane elastic properties using the results from the Fast Fourier Transform simulations. The random input parameters field in the Fast Fourier Transform simulations, including geometry and material parameters of cellular structures, was involved by Karhunen–Loève expansion. Furthermore, the inverse uncertainty quantification was conducted in the framework of Markov Chain Monte Carlo sampling-based Bayesian inference using the constructed polynomial chaos surrogate model. The approach introduced was applied to analyze the uncertainty quantification in two types of cellular structures. The results showed that the thickness of the cell wall dramatically influences the effective in-plane elastic modulus of the cellular structures. The PCE could significantly reduce the iterations compared to the Monte Carlo simulation while ensuring the accuracy of uncertainty quantification of the in-plane elastic modulus. In addition, effective evaluation and calibration of the geometry and material parameters of the cellular structures based on the obtained posterior probability distribution have been achieved. This addresses the problem of uncertainty quantification of the in-plane elastic properties and the difficulty in measuring the geometry and material parameters of cellular structures.