A data-driven constitutive model for Al-Mg-Zn alloys: Embedding neural networks in crystal plasticity finite element analysis

Machine learning technology is increasingly becoming an important tool for material constitutive modeling with its inherent advantage in capturing the nonlinear behavior of materials under various loading conditions. In this study, a novel surrogate model framework that embeds artificial neural network in finite element analysis is proposed for the age-hardened aluminum alloy Al-7.02Mg-1.78Zn. This framework is based on data-driven principles and retains the solution framework for crystal slip. By decoupling the solution process of crystal plasticity finite element analysis and using neural networks to replace the Newton-Raphson iterative method for handling the core steps in crystal plasticity finite element analysis. Specifically, the state variables associated with the 12 slip systems of the face-centered cubic crystal structure are selected as inputs, while the slip system shear strain increments serve as the outputs to construct the artificial neural network. The weights and biases parameters of the model are saved and subsequently converted into finite element program code through custom scripting. Subsequently, matrix operations are employed within the finite element analysis to reconstruct the neural network prediction model, achieving data-driven constitutive modeling. In the numerical simulation of polycrystalline materials, the surrogate model replaces the complex iterative process of phenomenological crystal plasticity constitutive model, accurately forecasts the mechanical behavior of the material. Its computational efficiency is approximately twice that of traditional models under uniaxial loading and approximately seven times faster under cyclic loading. The neural network-based surrogate modeling framework improves the deficiencies of crystal plasticity constitutive model in terms of computational efficiency and convergence.