A physics-informed neural network for simulation of finite deformation in hyperelastic-magnetic coupling problems

Recently, numerous studies have demonstrated that the physics-informed neural network (PINN) can effectively and accurately resolve hyperelastic finite deformation problems. In this paper, a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed. Since the solution space consists of two-phase domains, two separate networks are constructed to independently predict the solution for each phase region. In addition, a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients. With the developed framework, the magnetic fields and deformation fields of magnetorheological elastomers (MREs) are solved under the control of hyperelastic-magnetic coupling equations. Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework. Moreover, the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated, particularly in handling small data sets, as well as its ability in swiftly and precisely forecasting magnetostrictive motion.