The local geometrical randomness of metal foams brings complexities to the
performance prediction of porous structures. Although the relative density is
commonly deemed as the key factor, the stochasticity of internal cell sizes and
shapes has an apparent effect on the porous structural behaviour but the
corresponding measurement is challenging. To address this issue, we are aimed
to develop an assessment strategy for efficiently examining the foam properties
by combining multiscale modelling and deep learning. The multiscale modelling
is based on the finite element (FE) simulation employing representative volume
elements (RVEs) with random cellular morphologies, mimicking the typical
features of closed-cell Aluminium foams. A deep learning database is
constructed for training the designed convolutional neural networks (CNNs) to
establish a direct link between the mesoscopic porosity characteristics and the
effective Youngs modulus of foams. The error range of CNN models leads to an
uncertain mechanical performance, which is further evaluated in a structural
uncertainty analysis on the FG porous three-layer beam consisting of two thin
high-density layers and a thick low-density one, where the imprecise CNN
predicted moduli are represented as triangular fuzzy numbers in double
parametric form. The uncertain beam bending deflections under a mid-span point
load are calculated with the aid of Timoshenko beam theory and the Ritz method.
Our findings suggest the success in training CNN models to estimate RVE modulus
using images with an average error of 5.92%. The evaluation of FG porous
structures can be significantly simplified with the proposed method and
connects to the mesoscopic cellular morphologies without establishing the
mechanics model for local foams.

本文旨在通过多尺度建模和深度学习相结合的方法，建立中等孔隙度密闭铝泡沫的细胞形态与泡沫有效杨氏模量之间的直接联系，并通过模糊等价模型来评估模型预测模量的不确定性，进而简化 FG 多层泡沫结构的评估。