A computational multi-scale approach for the stochastic mechanical response of foam-filled honeycomb cores

This paper investigates the uncertainty in the mechanical response of foam-filled honeycomb cores by means of a computational multi-scale approach. A finite element procedure is adopted within a purely kinematical multi-scale constitutive modelling framework to determine the response of a periodic arrangement of aluminium honeycomb core filled with PVC foam. By considering uncertainty in the geometric properties of the microstructure, a significant computational cost is added to the solution of a large set of microscopic equilibrium problems. In order to tackle this high cost, we combine two strategies. Firstly, we make use of symmetry conditions present in a representative volume element of material. Secondly, we build a statistical approximation to the output of the computer model, known as a Gaussian process emulator. Following this double approach, we are able to reduce the cost of performing uncertainty analysis of the mechanical response. In particular, we are able to estimate the 5th, 50th, and 95th percentile of the mechanical response without resorting to more computationally expensive methods such as Monte Carlo simulation. We validate our results by applying a statistical adequacy test to the emulator.