Machine-Learning-Based Model of Elastic—Plastic Deformation of Copper for Application to Shock Wave Problem

Alexander E Mayer,Eugeniy V Fomin,Mikhail V Lekanov,Natalya A Grachyova

doi:10.3390/met12030402

Abstract

Molecular dynamics (MD) simulations explored the deformation behavior of copper single crystal under various axisymmetric loading paths. The obtained MD dataset was used for the development of a machine-learning-based model of elastic–plastic deformation of copper. Artificial neural networks (ANNs) approximated the elastic stress–strain relation in the form of tensor equation of state, as well as the thresholds of homogeneous nucleation of dislocations, phase transition and the beginning of spall fracture. The plastic part of the MD curves was used to calibrate the dislocation plasticity model by means of the probabilistic Bayesian algorithm. The developed constitutive model of elastic–plastic behavior can be applied to simulate the shock waves in thin copper samples under dynamic impact.

Highlights

The structure and evolution of shock waves in pure metals [1–5], alloys [6] and microstructured material [7–10] still attract an increased attention, due to both the fundamental interest in dynamic behavior of materials and the practical issues related to high-energy-density technologies, aerospace and defense applications
The obtained parameters are collected in the file “Cu.TEOS1.ANNp”, which is attached to the paper as Supplementary
The dislocation nucleation triggers the plasticity, while further kinetics is determined by the dislocation multiplication and annihilation; the system behavior is not very sensitive to the dislocation nucleation rate controlled by the coefficient kn

Summary

Introduction

The structure and evolution of shock waves in pure metals [1–5], alloys [6] and microstructured material [7–10] still attract an increased attention, due to both the fundamental interest in dynamic behavior of materials and the practical issues related to high-energy-density technologies, aerospace and defense applications. The structure and evolution are closely related with plasticity, phase transformations and other processes of defect formation, as well as with the response of the existing microstructure of material. The application of short [12,13] and ultra-short powerful laser pulses for the irradiation of thin metal samples expands the range of strain rates investigated in experiments up to 107 –109 s–1 [14–17]. These strain rates can be realized in molecular dynamics (MD) simulations for representative volume elements, but direct MD simulation of the shock-wave processes [18–20]. Continuum mechanics models are used to investigate the shock-wave problem numerically [21–24]. It makes essential a transfer of information from the MD, which allows one to study the rich physics of inelastic deformation, to continuum models applicable for realistic spatial and temporal scales

Methods

Results

Discussion

Conclusion