Comparative study of artificial neural network and physics-informed neural network application in sheet metal forming

Accurate prediction of the resultant geometry in sheet metal forming simulation is necessary to achieve zero-defect production. To quantify the effect of process parameters on the final geometry, numerical methods are used to simulate the process outputs for a given set of process variables. Finite element methods are employed in process optimization and design exploration. However, these computationally expensive models are unhelpful for process control applications. Surrogate models allowing fast prediction of resultant geometry or stress distribution can be plausible solutions. In the current study, we propose a sequential surrogate model to fit the stress field as a function of the process variable and the initial spatial coordinates. The framework is composed of two surrogate models. First, an artificial neural network (ANN) evaluates the displacement and the strain. Then, a second surrogate is employed to fit the stress using input strain and displacement. Here, ANN and physics-informed neural networks (PINN) are compared concerning prediction accuracy for the second surrogate model. The PINN is enhanced with the equilibrium equations. The developed method is demonstrated using a v-bending process. The results show that both surrogate models return good approximations, with ANN showing slightly better results.