Machine Learning Algorithms for Predicting Mechanical Stiffness of Lattice Structure-Based Polymer Foam

Abstract

Polymer foams are extensively utilized because of their superior mechanical and energy-absorbing capabilities; however, foam materials of consistent geometry are difficult to produce because of their random microstructure and stochastic nature. Alternatively, lattice structures provide greater design freedom to achieve desired material properties by replicating mesoscale unit cells. Such complex lattice structures can only be manufactured effectively by additive manufacturing or 3D printing. The mechanical properties of lattice parts are greatly influenced by the lattice parameters that define the lattice geometries. To study the effect of lattice parameters on the mechanical stiffness of lattice parts, 360 lattice parts were designed by varying five lattice parameters, namely, lattice type, cell length along the X, Y, and Z axes, and cell wall thickness. Computational analyses were performed by applying the same loading condition on these lattice parts and recording corresponding strain deformations. To effectively capture the correlation between these lattice parameters and parts' stiffness, five machine learning (ML) algorithms were compared. These are Linear Regression (LR), Polynomial Regression (PR), Decision Tree (DT), Random Forest (RF), and Artificial Neural Network (ANN). Using evaluation metrics such as mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE), all ML algorithms exhibited significantly low prediction errors during the training and testing phases; however, the Taylor diagram demonstrated that ANN surpassed other algorithms, with a correlation coefficient of 0.93. That finding was further supported by the relative error box plot and by comparing actual vs. predicted values plots. This study revealed the accurate prediction of the mechanical stiffness of lattice parts for the desired set of lattice parameters.

Keywords: additive manufacturing; lattice structures; machine learning; mechanical stiffness; polymer foams.

Figure 1

Flow chart of the design process.

Figure 2

(a) Solid body after applying the boundary conditions; (b) Solid model after the simulation showing strain distribution; (c) Scale bar.

Figure 3

Schematic of best model of ANN for this study.

Figure 4

Taylor Diagram.

Figure 5

Relative error box plot.

Figure 6

Comparison between predicted vs. actual values of training and test models.

Figure 7

The importance of each feature using SHAP with (a) beeswarm plot and (b) plot bar of absolute SHAP values.