For the final project, your goal is to predict the elastic response of a hypothetical metal matrix composite (MMC) using computational tools. Your metal matrix will be aluminum, whose elastic constants you have already computed. The reinforcement will be tantalum carbide (TaC), which forms in the rocksalt (\(\text{Fm}\bar3\text{m}\)) structure. You will need to (a) compute the elastic constants for TaC from first principles, and (b) investigate the effect of spatial distribution and orientation on the elastic properties of this MMC.

Successful completion of this work will demonstrate competence in using both DFT and FEM software to analyze material elastic response, and the ability to design your own computational study.

You will produce a detailed (5–8) page report that includes an Abstract, Introduction, Methods, Results and Discussion, Conclusions, and Bibliography. This will be graded on your

- design of computational materials research project (20%),
- appropriate and competent use of computational tools (50%), and
- clarity of the report (30%)

Your report should be formatted as a single pdf document comprising
your report. You may wish to write your report in latex and convert
using `pdflatex`

, or in markdown and convert using
`pandoc report.text --to latex --out report.pdf`

.
(`module load pandoc`

and `module load texlive`

to
have the most up-to-date versions of each).

You should creating a subdirectory called
`/class/mse404ela/sp22/<your_net_id>/FinalProject`

and
copying your work into that directory by **11:59pm on 14 March
2022. Late submissions will not be accepted; let me know in advance if
you will have difficulty with completion.**

You will need to compute the elastic constants of TaC using
`QuantumEspresso`

. You should use the PAW potentials with the
PBE exchange-correlation potential, with a scalar relativistic
treatment. As with aluminum, you will need to (a) perform and
demonstrate convergence with respect to computational parameters, (b)
determine the relaxed structural parameters, and (c) compute the
anisotropic elastic constants for TaC.

You will investigate the effect of shape and orientation on the
elastic response of a hypothetical MMC. A simple generalization of the
volume fraction rule includes an empirical prefactor corresponding to
geometric effects: \[E_\text{composite} =
E_\text{matrix}(1-V_\text{f}) + \alpha
E_\text{reinforcement}V_\text{f}\] where \(V_\text{f}\) is the volume fraction of
reinforcement, \(E_\text{matrix}\) and
\(E_\text{reinforcement}\) are the
corresponding Young’s moduli, and \(0<\alpha<1\) is an empirical
parameter that captures the geometric contributions. In
`/class/mse404ela/FinalProject`

, you will find four different
“microstructures” corresponding to regular arrays of circular and
rectangular reinforcements as well as random arrangements of the same.
Use these images as your basis to study the effect of shape,
arrangement, and orientation on the elastic response. As you did
previously, you will need to (a) develop and critique your choice of
skeleton, (b) determine elastic response, and (c) investigate the
distribution of stress in your material.

Conclude your assessment with a recommendation of preferred reinforcement structure to optimize the elastic response based on your findings.