Density Functional Theory as a Powerful Tool for Predicting Mechanical Properties of Materials: From Elastic Constants to Alloy Behavior

Key Methodologies

•     Integrated Modeling: DFT is combined with vibrational spectroscopy and finite element modeling (FEM) to recover Young’s modulus from resonance frequency relations.
•     Alloy & Phase Analysis: For binary and multiphase systems—including structural alloys (Ti–Al, Fe–Al) and shape memory alloys (Cu–Al–Be)—DFT calculates the properties of individual phases, which are then integrated using the rule of mixtures.
•     Anisotropy Evaluation: The framework analyzes the directional dependence of Young’s modulus using crystallographic directional cosines, helping explain discrepancies between theoretical and experimental data.

Conclusion: This comprehensive approach highlights the strength of DFT as a predictive tool that, when combined with experimental characterization and computational modeling, provides a robust foundation for understanding and designing materials with tailored mechanical properties.

The ab initio computational method based on Density Functional Theory (DFT) has become a powerful framework for predicting and understanding the physical properties of materials at the atomic scale. Without relying on empirical parameters, DFT enables the calculation of a wide range of material properties, including electronic structure, electrical behavior, mechanical response, thermal and thermoelectric properties, and magnetic properties, making it a formidable tool in modern materials science for both fundamental research and the design of advanced materials. In particular, DFT can be used to determine elastic constants and Young’s modulus through the stress–strain method, where small strains are applied to a crystal structure and the resulting stresses are calculated according to Hooke’s law. The slope of the stress–strain curve yields the elastic stiffness constants (c_ij), from which the elastic compliance constants (S_ij) are derived. These parameters enable the computation of bulk and shear moduli using the Voigt and Reuss approximations, with their averages giving the Hill approximation, from which the effective Young’s modulus and Poisson’s ratio of crystals are obtained. Furthermore, DFT can be integrated with vibrational spectroscopy and finite element modeling (FEM) to evaluate the mechanical behavior of materials, where resonance frequencies measured experimentally using a piezoelectric transducer are compared with those predicted by quasi-analytical models and FEM simulations. In this approach, Young’s modulus is recovered from resonance frequency relations, while density and Poisson’s ratio are obtained from first-principles calculations. The methodology can also be applied to binary alloys and multiphase materials, where phase diagrams, scanning electron microscopy (SEM) micrographs, and energy-dispersive spectroscopy (EDS) compositions are used to determine phase fractions. The elastic properties of individual phases are calculated using DFT and combined using the rule of mixtures to estimate the effective Young’s modulus of the alloy. Case studies involving Ti–Al alloys, Cu–Al–Be shape memory alloys, and Fe–Al binary alloys demonstrate that the computed values show good agreement with experimental measurements. In addition, DFT provides a powerful means of analyzing elastic anisotropy by evaluating the directional dependence of Young’s modulus through crystallographic directional cosines. Three-dimensional and two-dimensional representations of directional Young’s modulus reveal significant anisotropy in certain alloys, helping to explain discrepancies between theoretical predictions and experimental observations. Overall, this presentation highlights the strength of DFT as a predictive tool that, when combined with experimental characterization and computational modeling, provides a comprehensive approach for understanding and designing materials with tailored mechanical properties.

References
1.    Benlachemi, R., Ogam, E., Ongwen, N., Boudour, A., & Fellah, Z. E. A. (2024). Investigating the Young's modulus of Cu-Al-Be shape memory alloy using a phase diagram, vibration spectroscopy and ultrasonic waves. Journal of Alloys and Compounds, 976, 173010. https://doi.org/10.1016/j.jallcom.2023.173010. 
2.    Chanbi, D., Amara, L. A.m Ogam, E., Amara, S. E., & Fella, Z.E.A. (2019). Microstructural and mechanical properties of binary Ti-Rich Fe–Ti, Al-Rich Fe–Al, and Ti–Al Alloys. Materials, 12(3), 433. https://doi.org/10.3390/ma12030433. 
3.    Ongwen, N., Ogam, E. Fellah, Z. E. A., Otunga, H. Oduor, A., & Mageto, M. (2022). Accurate Ab-initio calculation of elastic constants of anisotropic binary alloys: A case of Fe–Al. Solid State Communications, 353, 114879. https://doi.org/10.1016/j.ssc.2022.114879. 
4.    Ongwen, N., Chanbi, D., Ogam, E., Otunga, H., Oduor, A., & Fellah, Z.E.A. (2021). Microstructural and elastic properties of stable aluminium-rich TiAl and TiAl2 formed phase Intermetallics. Materials Letters. 287, 129295. https://doi.org/10.1016/j.matlet.2020.129295. 

Le lundi 16 mars 2026 à 14h00 / Amphithéâtre François Canac, LMA

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