Evaluating the Stress-Strain Relationship of the Additively Manufactured Lattice Structures

Long Zhang; Farzana Bibi; Imtiyaz Hussain; Muhammad Sultan; Adeel Arshad; Saqib Hasnain; Ibrahim M Alarifi; Mohammed A Alamir; Uzair Sajjad

doi:10.3390/mi14010075

Evaluating the Stress-Strain Relationship of the Additively Manufactured Lattice Structures

Micromachines (Basel). 2022 Dec 27;14(1):75. doi: 10.3390/mi14010075.

Authors

Long Zhang¹, Farzana Bibi², Imtiyaz Hussain², Muhammad Sultan³, Adeel Arshad⁴, Saqib Hasnain⁵, Ibrahim M Alarifi⁶, Mohammed A Alamir⁷, Uzair Sajjad²

Affiliations

¹ School of Metallurgy, Lanzhou Resources & Environment Voc-Tech University, Lanzhou 730123, China.
² Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan.
³ Department of Agriculture Engineering, Faculty of Agriculture Sciences & Technology, Bahauddin Zakariya University, Multan 60800, Pakistan.
⁴ Department of Mechanical and Construction Engineering, Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK.
⁵ School of Chemical Engineering, University of New South Wales, Sydney, NSW 2052, Australia.
⁶ Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah, Riyadh 11952, Saudi Arabia.
⁷ Department of Mechanical Engineering, College of Engineering, Jazan University, Jazan 45142, Saudi Arabia.

Abstract

Extensive amount of research on additively manufactured (AM) lattice structures has been made to develop a generalized model that can interpret how strongly operational variables affect mechanical properties. However, the currently used techniques such as physics models and multi-physics simulations provide a specific interpretation of those qualities, and are not general enough to assess the mechanical properties of AM lattice structures of different topologies produced on different materials via several fabrication methods. To tackle this problem, this study develops an optimal deep learning (DL) model based on more than 4000 data points, which has been optimized by analyzing three different hyper-parameters optimization schemes including gradient boost regression trees (GBRT), gaussian process (GP), and random forest (RF) with different data distribution schemes such as normal distribution, nth root transformation, and robust scaler. With the robust scaler and nth root transformation, the accuracy of the model increases from R² = 0.85 (for simple distribution) to R² = 0.94 and R² = 0.88, respectively. After feature engineering and data correlation, the stress, unit cell size, total height, width, and relative density are chosen to be the input parameters to model the strain. The optimal DL model is able to predict the strain of different topologies of lattices (such as circular, octagonal, Gyroid, truncated cube, Truncated cuboctahedron, Rhombic do-decahedron, and many others) with decent accuracy (R² = 0.936, MAE = 0.05, and MSE = 0.025). The parametric sensitivity analysis and explainable artificial intelligence (by using DeepSHAP library) based insights confirm that stress is the most sensitive input to the strain followed by the relative density from the modeling perspective of the AM lattices. The findings of this study would be helpful for the industry and the researchers to design AM lattice structures of different topologies for various engineering applications.

Keywords: Bayesian optimization; additive manufacturing; deep learning; explainable artificial intelligence; lattice structure; mechanical properties; stress-strain relationship.

Grants and funding

L.Z. has received the funds from the Gansu Provincial University Innovation Fund Project(2020A-218). U.S. has received financial support from the National Science and Technology Council Taiwan under the Contract No. NSTC 111-2222-E-027-009.