The mechanical properties of a single crystal or a grain in a polycrystalline material are highly dependent on the direction of the applied load. Key properties of interest are the Young’s modulus and the Poisson ratio in the small strain limit, and the ideal tensile strength in the large strain regime. Prior atomistic computations of these properties interchangeably used two approaches. In one approach the stress-strain response is explicitly calculated via a numerical tensile test experiment. In the second approach the second order single crystal elastic constants are computed via small deformations and then used in analytical equations to derive the remaining mechanical properties. No prior attempts in the literature neither computational nor experimental attempted to evaluate the equivalence of the two approaches. Herein, we adopt the hypothesis that the brute-force approach to calculate the stress-strain curve is more robust since it accounts for all the higher orders effects not captured by second order elastic constants. We further prove this hypothesis by systematically computing the mechanical properties of 13 BCC metals and 12 FCC metals via the two approaches. These computations were performed using first principles density functional theory calculations. Our analysis revealed that calculations of direction dependent properties based on values of SECs do not capture instabilities detected by FPCTTs. Large relative discrepancies have been reported herein for Young’s moduli calculated using SECs relative to values from the stress-strain curves. Similarly, values of Poisson’s ratio calculated from SECs were unable to capture unpredicted auxetic responses for some transition metals nor large transverse contraction ratios for one of the three directions reported in this study. The detailed analyses and data presented in this work are aimed to be a future reference for the detailed studies of direction dependent mechanical properties of materials. Also, our thorough analysis of the lateral strains and the discovery of auxetic effect in certain metals in specific crystallographic directions can open the floor to applications that require such effect.


School of Sciences and Engineering


Mechanical Engineering Department

Degree Name

MS in Mechanical Engineering

Graduation Date

Winter 2-15-2023

Submission Date


First Advisor

Mostafa Youssef

Committee Member 1

Mostafa Youssef

Committee Member 2

Khalil ElKhodary

Committee Member 3

Ahmed Saleh



Document Type

Master's Thesis

Institutional Review Board (IRB) Approval

Not necessary for this item