Anisotropy of Phase Transformation in Aluminum and Copper under Shock Compression: Atomistic Simulations and Neural Network Model
Evgenii V. Fomin1,2, Ilya A. Bryukhanov1, Natalya A. Grachyova2, Alexander E. Mayer2,*
1 Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192, Russia
2 Department of General and Theoretical Physics, Chelyabinsk State University, Chelyabinsk, 454001, Russia
* Corresponding Author: Alexander E. Mayer. Email: 
Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.071952
Received 16 August 2025; Accepted 23 December 2025; Published online 21 January 2026
Abstract
It is well known that aluminum and copper exhibit structural phase transformations in quasi-static and dynamic measurements, including shock wave loading. However, the dependence of phase transformations in a wide range of crystallographic directions of shock loading has not been revealed. In this work, we calculated the shock Hugoniot for aluminum and copper in different crystallographic directions ([100], [110], [111], [112], [102], [114], [123], [134], [221] and [401]) of shock compression using molecular dynamics (MD) simulations. The results showed a high pressure (>160 GPa for Cu and >40 GPa for Al) of the FCC-to-BCC transition. In copper, different characteristics of the phase transition are observed depending on the loading direction with the [100] compression direction being the weakest. The FCC-to-BCC transition for copper is in the range of 150–220 GPa, which is consistent with the existing experimental data. Due to the high transition pressure, the BCC phase transition in copper competes with melting. In aluminum, the FCC-to-BCC transition is observed for all studied directions at pressures between 40 and 50 GPa far beyond the melting. In all considered cases we observe the coexistence of HCP and BCC phases during the FCC-to-BCC transition, which is consistent with the experimental data and atomistic calculations; this HCP phase forms in the course of accompanying plastic deformation with dislocation activity in the parent FCC phase. The plasticity incipience is also anisotropic in both metals, which is due to the difference in the projections of stress on the slip plane for different orientations of the FCC crystal. MD modeling results demonstrate a strong dependence of the FCC-to-BCC transition on the crystallographic direction, in which the material is loaded in the copper crystals. However, MD simulations data can only be obtained for specific points in the stereographic direction space; therefore, for more comprehensive understanding of the phase transition process, a feed-forward neural network was trained using MD modeling data. The trained machine learning model allowed us to construct continuous stereographic maps of phase transitions as a function of stress in the shock-compressed state of metal. Due to appearance and growth of multiple centers of new phase, the FCC-to-BCC transition leads to formation of a polycrystalline structure from the parent single crystal.
Keywords
Molecular dynamics (MD); aluminum; copper; shock wave; polymorphic phase transformation; polycrystalline structure; neural network model
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