Neural network constitutive model for crystal structures

Neural network constitutive models (NNCMs) for crystal structures are proposed based on computationally generated high-fidelity data. Stress, and tangent modulus data are generated under various strain states using empirical potentials and first-principles calculations. Strain-stress artificial neural network and strain-tangent modulus ANN are constructed. The symmetry conditions are considered for cubic, tetragonal, and hexagonal structures. The NNCMs of six face-centered cubic materials (Cu, Ni, Pd, Pt, Ag, and Au), two diamond cubic materials (Si, Ge), two tetragonal crystal materials (TiO2, ZnO), and two hexagonal crystal materials (ZnO, GaN) are constructed and tested under the untrained strain state. In particular, the performance of NNCM for cubic structure is better compared with that of the classical model. The suggested NNCM can be embedded into a nonlinear finite element method, and numerical examples are performed to verify the proposed NNCM.

Automated summary

Neural network constitutive models (NNCMs) for crystal structures based on computationally generated high-fidelity data were proposed, demonstrating better performance for cubic structures compared to classical models. Constructed artificial neural networks were tested under various strain states, with consideration of symmetry conditions, showcasing the potential for embedding into a nonlinear finite element method.