PSI - Issue 80

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ScienceDirect

Procedia Structural Integrity 80 (2026) 23–30 Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000

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© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi Abstract Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving solid mechanics problems. In this work, we propose a novel PINN architecture designed for homogenisation problems of metamaterials under large deformation. The architecture incorporates periodic functions to ensure exactly imposed boundary con ditions and employs an energy-based loss for e ffi cient training. Three representative metamaterial structures—octet truss, gyroid, and spindoid—are selected as case studies. The results demonstrate that the proposed PINN achieves accuracy comparable to finite element analysis (FEA), while o ff ering improved computational e ffi ciency for high-volume-fraction structures. Beyond accuracy and speed, the meshfree nature and flexibility of PINNs provide clear advantages, highlighting their potential as a scalable tool for modelling complex materials. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Physics informed neural network; Homogenisation; Metamaterials; Multiscale Analysis Fracture, Damage and Structural Health Monitoring Physics-Informed Neural Networks for Multiscale Large Deformation Analysis of Metamaterials HaolinLi a, , Zahra Sharif Khodaei a , Michal Kotoul b , M.H. Aliabadi a a Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK b Institute of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czech Republic Abstract Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving solid mechanics problems. In this work, we propose a novel PINN architecture designed for homogenisation problems of metamaterials under large deformation. The architecture incorporates periodic functions to ensure exactly imposed boundary con ditions and employs an energy-based loss for e ffi cient training. Three representative metamaterial structures—octet truss, gyroid, and spindoid—are selected as case studies. The results demonstrate that the proposed PINN achieves accuracy comparable to finite element analysis (FEA), while o ff ering improved computational e ffi ciency for high-volume-fraction structures. Beyond accuracy and speed, the meshfree nature and flexibility of PINNs provide clear advantages, highlighting their potential as a scalable tool for modelling complex materials. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Physics informed neural network; Homogenisation; Metamaterials; Multiscale Analysis Fracture, Damage and Structural Health Monitoring Physics-Informed Neural Networks for Multiscale Large Deformation Analysis of Metamaterials HaolinLi a, , Zahra Sharif Khodaei a , Michal Kotoul b , M.H. Aliabadi a a Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK b Institute of Solid Mechanics, Mechatronics and Biomechanics, Brno University of Technology, Faculty of Mechanical Engineering, Brno, Czech Republic

1. Introduction 1. Introduction

Physics-informed neural networks (PINNs) have seen rapid development in recent years Raissi et al. [2019], Karni adakis et al. [2021]. Their application in solid mechanics has also begun to emerge. As a new meshfree method, PINNs di ff er not only from mesh-based approaches such as the finite element method (FEM), but also from other meshfree approaches like radial basis function (RBF) methods Li and Liu [2002] or the boundary element method Aliabadi [2002], owing to their global implementation and approximation nature. Compared with these methods, PINNs as PDE solvers for solid mechanics o ff er several advantages: a) they do not require prescribed meshes, which are often expensive and sensitive to generate in FEM; b) they provide inherently smooth and di ff erentiable approximations of the solution field, unlike most traditional numerical methods that allow only limited derivative orders, restricting their Physics-informed neural networks (PINNs) have seen rapid development in recent years Raissi et al. [2019], Karni adakis et al. [2021]. Their application in solid mechanics has also begun to emerge. As a new meshfree method, PINNs di ff er not only from mesh-based approaches such as the finite element method (FEM), but also from other meshfree approaches like radial basis function (RBF) methods Li and Liu [2002] or the boundary element method Aliabadi [2002], owing to their global implementation and approximation nature. Compared with these methods, PINNs as PDE solvers for solid mechanics o ff er several advantages: a) they do not require prescribed meshes, which are often expensive and sensitive to generate in FEM; b) they provide inherently smooth and di ff erentiable approximations of the solution field, unlike most traditional numerical methods that allow only limited derivative orders, restricting their

∗ Corresponding author. Tel.: + 44 07742631644. E-mail address: haolin.li20@imperial.ac.uk ∗ Corresponding author. Tel.: + 44 07742631644. E-mail address: haolin.li20@imperial.ac.uk

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi 10.1016/j.prostr.2026.02.003 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi.