Machine learning-enabled inverse design of bimaterial thermoelastic lattice metamaterials

TL;DR

Six different models, each defined by different combinations of target effective properties and structural design variables, can be applied to efficiently solving specific inverse design tasks involved in the practical application of the thermoelastic metamaterial in novel engineering systems.

Abstract

The thermoelastic metamaterial based on a bimaterial hybrid-honeycomb structure, exhibiting simultaneously negative Poisson's ratios and negative thermal expansion coefficients is very promising for various application. This work is dedicated to the machine learning (ML)-enabled inverse design of such structure, on the basis of high-throughput simulation and neural network models. A large dataset is generated through computational homogenization of structures with varying geometrical features and base material properties. A forward ML model is first trained to efficiently and accurately predict the effective thermoelastic properties for a given structure design. Subsequently, inverse ML models are developed to suggest geometrical features and base materials for desired target properties. To address various inverse design scenarios, six different models are proposed, each defined by different combinations of target effective properties and structural design variables. The trained forward model is integrated into the loss functions of the inverse models and is also employed to generate additional datasets for cases with fixed base materials. The good predictive performance of the forward and inverse ML models is demonstrated by representative design examples. These ML models can be applied to efficiently solving specific inverse design tasks involved in the practical application of the thermoelastic metamaterial in novel engineering systems.

Figures (4)

• Figure 1: ML-enabled forward and inverse design of hybrid-honeycomb structure. (a) Geometry of the hybrid-honeycomb structure. (b) Illustration of ANN models for forward prediction and inverse design. During the training of the inverse ML models, the already trained forward ML model is used to evaluate the loss function. More details are found in Section \ref{['surrogate_method']}.
• Figure 2: Effective thermoelastic properties of structures in the dataset: (a) $E^{\star}_{x}/E_\text{N}$ versus $E^{\star}_{y}/E_\text{N}$, (b) $E^{\star}_{x}/E_\text{N}$ versus $\nu^{\star}_{xy}$, (c) $E^{\star}_{x}/E_\text{N}$ versus $\alpha^{\star}_{x}/\alpha_\text{N}$, and (d) $\nu^{\star}_{xy}$ versus $\alpha^{\star}_{x}/\alpha_\text{N}$. The effective properties vary broadly in the property space. The dataset is representative.
• Figure 3: Comparison between forward ML model prediction and the ground truth from FE simulations: (a) $E^{\star}_{x}/E_\text{N}$, (b) $E^{\star}_{y}/E_\text{N}$, (c) $\nu^{\star}_{xy}$, (d) $G^{\star}_{xy}/E_\text{N}$, (e) $\alpha^{\star}_{x}/\alpha_\text{N}$, and (f) $\alpha^{\star}_{y}/\alpha_\text{N}$. The ML model prediction shows good agreement with the ground truth with a coefficient of determination (i.e., $\text{R}^2$) higher than 0.994 for all six properties.
• Figure 4: Effective properties varying with the strut angle $\theta_1=\theta_2=\theta$ and the relative density $\rho$: (a) $E^{\star}_{x}/E_\text{N}$, (b) $G^{\star}_{xy}/E_\text{N}$, (c) $\nu^{\star}_{xy}$, and (d) $\alpha^{\star}_{x}/\alpha_\text{N}$. The ML model prediction aligns well with those from FE simulations.