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What did I do?
MADAM project: Material design (MAD) for additive manufacturing (AM).
Objectives:
Develop numerical algorithms to solve the material design problems when considering addittive manufacturing constraints.
Develop numerical algorithms to solve the MAD problem when considering stress constraints.
Develop second order optimization algorithms to efficiently solve the MAD problem.
Outcomes:
Design of optimal microstructure for stress minimization through a periodically repeated lattice net with an spatially varying optimal superellipsoidal hole.
Computation of amplificators for solving the macroscopic stress minimization problem
Validation of optimal microstructure with Vigdergauz microstructure.
Where did I do it?
I had the opportunity during 2018-2020 to join the wonderfull group of MMOF at the applied mathematics department CMAP of Ecole Polytechnique in Palaiseau, France.
The research group of "Mécanique, matériaux et optimisation de formes (MMOF)" was formed by amazing researchers like Grégoire Allaire, Samuel Amstutz, Benjamin Bogosel, Mathilde Boissier, Florian Feppon, Perle Geoffroy Donders, Matias Godoy and many others.
We had great scienfitic discussions, weekly meetings and we shared many interesting personal expiriencies during lunch time, coffee braeaks and conferences.
The department of applied Mathematics, or in French "Centre de mathématiques appliquées" is an outstanding center both in the scientific and in the personal side. Seminars and courses were really interesting, not to mention the mathematical discussions that arise in the coffee room. I felt lucky to get surrounded by great mathematicians.
L'X, the way French people refers to École Polytechnique, is considered the best École in France. You can feel the top research level just walking around and watching the ancient professors of the University: Lagrange, Cauchy, Schwartz, Fourier, Navier, Stokes, Lions.....among others. In addition, the cantine offers many good options at a reasonable price and the sport facilities are wonderful: it was really nice to play football with CMAP against other departments.
I am grateful to become part of the community of l'X.
Cite Universitaire
Although l'X is placed in Palaisau, I lived in Cité Universitare in Paris. Even if I had to take every morning the crowded RerB, the CitéU is a perfect place for a researcher, specially at Collegue d'Espagne. I met wonderful people that will lay in my heart forever.
Paris
For someone comming from the mediterranen weather, Paris has a really rainy weather. However, the city is wonderful: full of museums, restaurants, activities. Food is delitious! Also the surrunders are great and offers incredible picnique-days! What a great expirience!
What did I learn?
In the scientific side, the training has been enourmes. I learnt many technical aspects like:
Homogenization: I attended to the course of Prof. Allouges of Homogenization where I learnt not only its mathematical aspects but also many numerical techniques. Correctos, amplificators, two-scale convergence among other concepts
Optimization: The course of Prof. Chambolle is really great. I learnt a lot on convexity, dualty, primal-dual algorithms, proximal algorithms, monotone operators, ADMM and a really general framework to explain all the modern algortihms.
Optimal transport: I also attended to the course of Prof. Peyre where I learnt a lot on transport, Wasserstein distance, Kantorovich-Monge approaches.
Functional analysis: Through semanal meetings with Prof. Allaire I learnt about compactness, embeddings, weak convergence and many other necessary concepts on applied mathematics.
De-homogenization: With Perle and Grégoire, I learnt the process of de-homogenization, amplificators and new techniques on lattice structures.
Additive manufacturing: Since during this time I joint the Sofia project, I learnt the needs and applications that the industry require when manufacturing an optimal shape using addittive manufacturing techniques.
I still work in the topic of topology optimization, but I feel now that I see the topic from a completely new perspective! As a researcher: I fully recommend to have an abroad research expirience!
Finally, during this period I met many scientists and different researchers, I organized workshops and conference and I manged my own research project. Last but not least, I learnt French!! :) :) Voilà!!!!
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