Physics-informed neural networks for solving thermo-mechanics problems of functionally graded material

TL;DR

This paper demonstrates the application of physics-informed neural networks (PINNs) to solve complex coupled thermo-mechanics problems in functionally graded materials, achieving high accuracy and pioneering this approach in composite materials.

Contribution

It introduces the first implementation of PINNs for coupled thermo-mechanics in functionally graded composite materials, expanding the scope of PINN applications.

Findings

R2 score > 99% for primary variables

PINNs outperform traditional methods in meshless solutions

Challenges remain in accurately predicting secondary variables

Abstract

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of being meshless, scalable, and can potentially be intelligent in terms of transferring the knowledge learned from solving one differential equation to the other. The exploration in this field has majorly been limited to solving linear-elasticity problems, crack propagation problems. This study uses PINNs to solve coupled thermo-mechanics problems of materials with functionally graded properties. An in-depth analysis of the PINN framework has been carried out by understanding the training datasets, model architecture, and loss functions. The efficacy of the PINN models in solving thermo-mechanics differential equations has been measured by comparing the obtained solutions either with analytical solutions or finite element method-based solutions. While R2 score of more than 99% has been achieved in predicting primary variables such as displacement and temperature fields, achieving the same for secondary variables such as stress turns out to be more challenging. This study is the first to implement the PINN framework for solving coupled thermo-mechanics problems on composite materials. This study is expected to enhance the understanding of the novel PINN framework and will be seminal for further research on PINNs.