A Novel Research on the Base Force Element Method of Complementary Energy Principle for Finite Strain and Finite Rotation Problems

The finite element method based on the complementary energy principle and its combination with artificial neural networks is a worthwhile research topic. A new Base Force Element Method (BFEM) model is proposed in this study, which can solve the problems of large elastic deformation and finite strain in incompressible hyperelastic materials. The complementary energy function of nonlinear elasticity has not yet been proposed. The complementary energy function is replaced by a pre-trained Back-Propagation (BP) neural network to establish the constitutive relationship. This makes it easy for finite strain problems to be studied by the BFEM model. When the constitutive relationships of different incompressible hyperelastic materials were described, only two parameters needed to be changed. The governing equations of the BFEM model are general and concise, and its derivation process does not involve an approximate representation of shape functions. The calculation results of the examples indicate that the model has high accuracy. This new numerical method fills the gap in using the complementary energy finite element method to calculate the finite strain problem of incompressible hyperelastic materials.