Accelerated Continuum Crystal Plasticity and Phase Field Microstructure Modeling using U-Net

An overview of various continuum-level machine learning based models for microstructure evolution is presented, focussing on crystal plasticity and phase field methods [1, 2].<br/>For accelerating mechanical boundary condition treatment for heterogeneous solids we propose a deep neural network as a fast surrogate model for local stress calculations in inhomogeneous linear or non-linear elasto-viscoplastic materials, using U-Net. We show that the surrogate model predicts the local stresses with &lt;4% mean absolute percentage error for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 100-500 times faster than spectral solvers. The model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical finite element solvers.<br/>A similar approach was chosen for phase-field models: these are costly when applied to large, complex systems [3,4]. To reduce the computational costs, a U-Net surrogate model has been developed. Training input is obtained from the results of the numerical solution of initial-boundary-value problems based on the Fan-Chen model for grain microstructure evolution. The trained network is applied recursively on initial order parameters to calculate the time evolution of the phase fields. The results are compared to the ones obtained from the conventional numerical solution in terms of the errors in order parameters and the system's free energy. The resulting order parameter error averaged over all points and all simulation cases is 0.005 and the relative error in the total free energy in all simulation boxes does not exceed 1%.<br/><br/>1. J.R. Mianroodi, et al., npj Computational Materials 7 (2021)<br/>2. M.S. Khorrami, et al. npj Computational Materials 9 (2023)<br/>3. D. Raabe et al. Nature Comput. Sci. 3 (2023)<br/>4. I. Peivaste et al. Comput. Mater. Sci. 214 (2022)