Dynamic behaivour seems often overlooked when new materials are invented. Prof Qingming Li and I have published a long review paper on the dynamic compressive behaivour of cellular mateirals in International Journal of Impact Engineering, which may be of interest for those who work on foams, honeycombs, wood, architected lattices, metamaterials and so on. (free download via https://authors.elsevier.com/c/1V~wn,GjCIbJUX)

Dear Nick,

Thank you very much for sharing your thoughts. I agree with you that we need to consider fabrication constraints for design and optimization process. There are some efforts to do that as it's mentioned in the review paper by Jamie Guest (reference #3). I appreciate your kind encouragement and the helpful reference.

From fabrication and test point of view, I am particularly intrigued of the combinatorial design of tileable unit cells illustrated in Figure 4. It is desirable to consider fabrication constraints (such as, edge thickness and need of support structures for 3D printing) into the design and optimization process. A related work is from Denis Zorin group at NYU:

Elastic Textures
Julian Panetta, Qingnan Zhou, Luigi Malmo, Nico Pietroni, Paolo Cignoni, Denis Zorin
ACM Transactions on Graphics (TOG) vol. 34, 4, 2015 (Proceedings of SIGGRAPH 2015), 135

Dear Ling,

Many thanks for sharing this with us. I know little about topology optimization. It is a good opportunity for me to learn.

Best

shengqiang

Dear Ling,

Thank you very much for sharing references about concurrently optimizing structures and materials.

Shengqiang,

We developed a multiscale topology optimization concept for cocurrently optimizing structures and materials. The original algorithsm was developed for structural compliance design. The concept was later extended to frequency design and multiobjective design. Key publications include:

Optimum structure with homogeneous optimum truss-like material (http://www.sciencedirect.com/science/article/pii/S0045794908000308)

Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency (https://link.springer.com/article/10.1007/s00158-008-0334-4)

Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material (https://link.springer.com/article/10.1007/s00158-012-0849-6)

Thank you for sharing the information. Yes, it looks like a part of the Eiffel tower.

Greer group at Caltech has published a number of seminal papers in this area including the work that you mentioned. For the PNAS paper, they reported a fractal-like multilevel hierarchal structures for a resilsent architected material.

The following paper that I mentioned in the article is also a recent related effort.

Zheng, X. et al. Multiscale metallic metamaterials. Nature Materials 15, 1100–1106 (2016).

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Resilient 3D hierarchical architected metamaterials

Dear Mike,

I agree with you that not many have read the original Eiffel paper. I appreciate your kind introduction of the classic work. From recent papers, I saw a work like the following example that people modify the arrangement of materials for desired deformation behaviors.

http://onlinelibrary.wiley.com/doi/10.1002/adfm.201400451/abstract

For the case of topology optimization, to the best of my knowledge, it's about what would be the optimal geometry that can maximize/minimize the objective function(s) based on constraints (boundary conditions and loading conditions). There are some softwares that you can play with in the following site by Ole Sigmund group.

http://www.topopt.dtu.dk/?q=node/792

If you are interested in the topic, I would suggest you to check the recent review paper by Jamie Guest that is mentioned in the article as below.

Osanov, M. & Guest, J. K. Topology optimization for architected materials design. Annual Review of Materials Research 46, 211–33 (2016).

Again, thank you very much for your comments.

dear Sung

you know the literature on architectured materials better than I do, so it is interesting if you are able to tell me if you find interesting what Eiffel did in 19th century and is known even to few design engineers, as it was discussed deeply only recently (the English translation of Eiffel's 1885 communication to the Society of French Engineers by Weidman and Roland recently was accepted for publication in the Architectural Research Quarterly published in Great Britain).

Essentially, Eiffell was worried about wind. The structure is made with the famous profile in order to limit the need for lattice truss members, because simple considerations show that they are in principle free from stress. The full solution Eiffell found by graphical methods was due to him being a genius engineer, and was only understood by very complex non-linear integral equation recently.

So do you know anything similar? I guess with materials, people worry about reducing bending stresses, and obtain the highest possible strength/density. In other words, there is no optimization with respect to given loads. But your comment that topological optimization should be done, reminds me that you need loads and boundary conditions to do topological optimization. So the matter is unclear to me.

As with any review, your task is very difficult! But try......

Model equations for the Eiffel Tower profile: historical perspective and new resultsP Weidman, I Pinelis - Comptes Rendus Mecanique, 2004 - Elsevier

Dear Mike,

Thank you very much for sharing the great historic example.
Yes, Eiffel tower is an example of an architected multiscale structure.

Actually, a number of people show the Eiffel tower when they give introduction about architected materials. With the progress of fabrication technologies such as 3D printing, we can make small scale architectures that look like "material" and show tailored and/or intriguing new properties that are different from those of constituents.

Regarding your great follow-up question, I am not a good person to answer because it's more about design side. But, in a way, the examples shown in the Fig. 1 of my article provide new designs that take advantage of recent findings.

Thank you for sharing your comment.

dear Sung

just to say something of historical interest. Is Eiffel tower an example of a (linear) architectured multiscale structure?

How would you take advantage of recent findings in designing it today?

Mike

Dear Lifeng,

Thanks for your comment. As you actively work on architected materials, it will be great to hear your thoughts about the field.
Thank you again.

Dear Shengqiang and Sung Hoon,

That's a great question. Topology optimization of Architected Materials is of great importance in design. Nonlinearity and multimaterial capability are of particular interest. I will read Guest's paper carefully. Thank you for the information.

Lifeng

Dear Shengqiang,

Thanks a lot for your kind encouragement. I am happy to hear that you enjoyed reading the article.

While I am not an expert in the field, I communicated with my colleague, Jamie Guest who is an expert in the field. There are many people working on the field. For the topology optimization, there are a number of works demonstrating inverse design capability for architected materials as mentioned in the journal clua article by Jamie (//m.limpotrade.com/node/17756) and his recent review article that I cited as below.

Osanov, M. & Guest, J. K. Topology optimization for architected materials design. Annual Review of Materials Research 46, 211–33 (2016).

As far as I heard, incorporating nonlinearity to topology optimization is still a challenge.

Dear Sung,

Many thanks for the prompt review of this vibrant field. I enjoyed reading your review.

I am not sure if currently developed topological optimization algorithm can be used to do inverse design of architected material. Maybe some one working on topological optimization can comment on this.

shengqiang