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.

中文翻译：

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晶体结构的神经网络本构模型

基于计算生成的高保真数据提出了晶体结构的神经网络本构模型 (NNCM)。应力和切线模量数据是使用经验势和第一性原理计算在各种应变状态下生成的。构建了应变-应力人工神经网络和应变-切线模量人工神经网络。对称条件被考虑用于立方、四方和六方结构。六种面心立方材料（Cu、Ni、Pd、Pt、Ag和Au）、两种金刚石立方材料（Si、Ge）、两种四方晶材料（TiO2、ZnO）和两种六方晶材料（ ZnO、GaN) 在未经训练的应变状态下构建和测试。特别是，与经典模型相比，NNCM 对立方结构的性能更好。