Extracting flow stress surfaces of pristine materials using deformation paths in MD simulations

Accurate simulation of deformation processes at the atomic scale is critical for predicting the mechanical response of materials and particularly the calculation of directional flow stresses. This work presents a method for applying arbitrary deformation paths in LAMMPS while adhering to its convention that supercell periodic vectors a, b are aligned such that a coincides with the x-axis and b lies in the (x,y) plane. This method is particularly relevant for materials with low crystal symmetry and also for exploring non uniaxial deformations. The first step of the method consists in generating the simulation frame tensor's time evolution upon any deformation, which may initially violate LAMMPS alignment constraints. This constraint is then overcome by the application of a rigid body rotation to realign the tensor with LAMMPS's convention, ensuring valid periodic boundary conditions. The resulting lengths and tilt factors from the rotated tensor are expressed analytically using third-order polynomials and applied to the simulation cell using the fix deform command. The present approach versatility is validated with the calculation of directional flow stresses for various materials upon constant volume shear, tension and compression, demonstrating its effectiveness in simulations involving complex deformation scenarios and diverse crystal structures. The flow stress surface extracted from these simulations are finally analyzed as the fingerprint of all deformation mechanisms occurring in the material.