An efficient parameterized neural network enhanced multiscale finite element modeling for triply periodic minimal surface meta-structures and its applications for femur

Abstract

Triply periodic minimal surface (TPMS) multiscale structures are meta-structures known for their low-weight-high-strength property. Because of their delicate geometry and sheet-networks feature, a fine mesh is required for finite element analysis, which is computationally expensive for conventional direct numerical simulation. To resolve this issue, this study develops a neural network enhanced finite element method (NN-FEM) for parameterized TPMS multiscale meta-structures. The multiscale homogenization approach replaces the complicated representative volume elements (RVEs) with a surrogate homogenized material model. The surrogate process is accomplished by deep learning of artificial neural networks (NN) with an effective boundary displacement gradient and the Helmholtz free energy of RVEs. The NN-trained surrogate material model is deployed on the macroscale Galerkin finite element model for various field tests. The parameterized structural information of TPMS can also be embedded into the NN model to resolve the hidden constitutive relation of RVEs with unique geometries. Numerical examples are provided to benchmark the efficacy and efficiency of NN-FEM on the parameterized TPMS structure. The proposed model can be applied to femurs for rapid stress analysis and osteoporosis detection.

Keywords

• Multiscale homogenization method
• Meta-structures
• Neural network enhanced finite element method
• Parameterized triply periodic minimal surface
• Femur