Physics-Informed Neural Networks for Koiter's Shell Theory

Abstract

Magneto-active elastomers (MAEs) is one of the smart materials which have rapid response and wireless actuation by application of a magnetic field. These materials consist of magnetic particles, such as iron or NdFeB powder, dispersed in an elastomer, such as rubber. In the designing of applications using MAEs, the accurate prediction of MAEs’ behavior under given magnetic fields is required. In this regard, many studies have theoretically and experimentally analyzed the behavior of MAEs under magnetic fields. However, depending on the shape of the surface and boundary conditions, analytical solutions can be found for special cases. To obtain solutions, numerical methods, e.g., the finite element method (FEM) is widely used, but the implementation of shell models into the FEM is technically tricky. Recently, methods of machine learning have gained interest in applications of engineering. These methods typically use data-driven models which require a large dataset gathered from experiments or simulations. In contrast to such methods, Physics-Informed Neural Networks (PINNs) require the governing equations which are incorporated into the loss function. Also, in the field of shell theory, PINNs have the advantage of applying to complex shapes. Here, we use PINNs to obtain the solution and verify the solution with experiments. In the PINNs part, we develop a theoretical model for magneto-active elastic shells using Koiter’s shell theory and implement the theoretical model into PINNs. In experiments, we fabricate magneto-active shells in various complex shapes. This work can simplify the prediction of MAEs’ behavior and contribute to the study of magneto-active soft grippers and soft robotics.