Journal Article

Modeling a Typical Non-Uniform Deformation of Materials Using Physics-Informed Deep Learning: Applications to Forward and Inverse Problems

Wang, Qingxin, Deng, Yawen, Chen, Changchang, Li, Yunzi, Li, Xiaohe, Fan, Zide

2023

Overview

Numerical methods, such as finite element or finite difference, have been widely used in the past decades for modeling solid mechanics problems by solving partial differential equations (PDEs). Differently from the traditional computational paradigm employed in numerical methods, physics-informed deep learning approximates the physics domains using a neural network and embeds physics laws to regularize the network. In this work, a physics-informed neural network (PINN) is extended for application to linear elasticity problems that arise in modeling non-uniform deformation for a typical open-holed plate specimen. The main focus will be on investigating the performance of a conventional PINN approach to modeling non-uniform deformation with high stress concentration in relation to solid mechanics involving forward and inverse problems. Compared to the conventional finite element method, our results show the promise of using PINN in modeling the non-uniform deformation of materials with the occurrence of both forward and inverse problems.

• Publisher: MDPI AG
• Subject: Accuracy / Boundary conditions / Computational linguistics / Deep learning / Deformation / Differential equations / Digital twins / Fluid dynamics / forward and inverse mechanics problems / Geophysics / Inverse problems / Language processing / Laws, regulations and rules / Measurement techniques / Mechanical properties / Mechanics / Natural language interfaces / Neural networks / non-uniform deformation / Numerical analysis / Partial differential equations / Physics / physics-informed neural network / Simulation / solid mechanics / Stress analysis / Stress concentration