Base Force Element Method for Finite Strain Problems Based on Artificial Neural Network

The combination of artificial intelligence and finite element method (FEM) is a hot topic in the field of computational mechanics. This study proposes a novel base force element method (BFEM) for finite strain problems based on the complementary energy principle. Using the back-propagation (BP) neural network in the field of artificial intelligence to construct the constitutive relationship of the BFEM for finite strain problems. First, a BFEM model for finite strain problems was derived. Second, using the BP neural network model and learning from test samples, a constitutive relationship for incompressible finite strain problems has been efficiently established. Third, the program has been upgraded using parallel computing and sparse matrices, which greatly improves the computational efficiency of this study. Finally, several finite strain examples were used to verify the correctness of the BFEM based on the BP neural network proposed in this study, as well as the efficiency of the parallel computing method. This study combines BP neural network with a new type of FEM — BFEM, which fills the gap in using complementary energy FEM to calculate the finite strain problem of incompressible hyperelastic materials.