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Journal Club for March 2017: Architected Materials

Sung Hoon Kang's picture

Architected Materials


           Architected material (or architectured material) is a class of materials that show new and/or customized behaviors by the interplay between material properties and geometry [1,2,3]. There have been active studies in this area with the progress of computational modeling that can predict the behaviors of materials and structures and advanced manufacturing methods such as 3D printing that can spatially control material constituents. There were related articles in the journal club in the past including “Negative Poisson’s Ratio Materials” (April 2010, Katia Bertoldi), “Harnessing Instabilities in Response to Stimuli” (November 2012, Xuanhe Zhao), “Metamaterials Inspired by Concepts for Elastic Wave Energy Harvesting” (December 2012, Massimo Ruzzene), “Mechanical Metamaterials” (April 2013, Jongmin Shim) and “Nano-architected Nanolattice Structures” (November 2013, Lucas Meza, Lauren Montemayor, Julia Greer). Since then, there were many exciting development in the field in terms of investigating design principles, developing new fabrication approaches, and exploring new properties and applications. So, it is good time to summarize recent findings in the field and explore future opportunities. The article is not intended as a comprehensive review of the field due to limited space. Rather, it is intended as a living document that can facilitate the discussion among researchers in the field and a broad iMechanica community so that one can add thoughts and references about this growing field. After introduction, some of the recent examples in architected materials will be described followed by current challenges in the field and potential future directions as a starting point for further discussion.  

Recent progress in architected materials

            Since 2014, there have been exciting new studies in the field that significantly expanded available property spaces (or filled “white spaces” in Ashby plot) as well as introduced new properties not available before. Figure 1 shows some of the examples of the recent developments. Based on rational design of architecture followed by high resolution 3D printing, Zheng et al. reported ultralight and ultrastiff materials (Figs. 1A-B) with the minimum density of 0.87 kg/m3 (c.f. density of water ~1000 kg/m3) and the modulus of ~ 1 MPa [4]. The architected material has 0.025% relative density (i.e. 99.75% air), but it has substantial load bearing capability. In the same year, Meza et al. reported 3D ceramic lattices (Figs. 1C-D) with high specific stiffness and shape recovery after large deformation. While ceramics tend to undergo plastic deformation or fracture under large deformation, the reported architected ceramic lattices could recover their original shapes after compressions in excess of 50% strain [5]. Since then, there have been many studies that expanded available material property spaces. However, there was no geometry or architecture that achieved a theoretical upper bound of material properties such as isotropic elastic stiffness. The recent study by Berger et al. addressed this challenge by reporting architected materials (Figs. 1E-F) with isotropic elastic stiffness at the theoretical limit of Hashin–Shtrikman upper bounds [6]. Beyond expanding available property spaces, there have been also works to generate new properties or behaviors that are not observed in bulk forms.

Fig. 1. (A) Mechanical response to compressive loading of a stretch-dominated octet-truss unit cell [4]. (B) Octet-truss unit cells packed into a cubic microlattice [4]. © 2014 American Association for the Advancement of Science. (C) Cutaway of hollow octet-truss unit cell [5]. (D) SEM image of alumina octet-truss nanolattice [5]. © 2014 American Association for the Advancement of Science. (E) A representative topology of cubic-octet foam (Isomax™) [6]. © 2017 Nature Publishing Group. (F) A 3D-printed model of the foam's cellular structure with isotropic elastic stiffness at theoretical limit. (Photo Credit: Sonia Fernandez)

            In particular, there have been active studies that harness elastic deformation for novel reversible and/or tunable mechanical behaviors. For example, Shan et al. (Fig. 2A) and Frenzel et al. reported architected materials with reusable energy absorption by harnessing mechanical instability [7,8]. Restrepo et al. and Haghpanah et al. (Fig. 2B) reported shape reconfigurable materials with energy dissipation by elastic deformation [9,10]. Beyond quasi-static loading conditions, there were also studies reporting architected materials for dynamic loadings such as elastic wave propagation. Shan et al. reported an architected material (Fig. 2C) with tunable vibration propagation and absorption by triggering different mechanical instability-induced pattern formation [11]. Matlack et al. reported an architected material (Fig. 2D) with low frequency broad band vibration absorption [12]. Raney et al. reported stable propagation of mechanical signals in soft media (Fig. 2E) by storing elastic strain energy using mechanical instability [13].

Fig. 2.
(A) A photo of an architected material with reversible energy absorption [7] © 2015 Wiley-VCH. (B) Images of multistable shape-reconfigurable architected materials [10]. © 2016 Wiley-VCH. (C) A photo of an architected material with tunable control of elastic wave propagation by harnessing multiple folding mechanisms in soft periodic structures [11]. © 2014 Wiley-VCH. (D) One-dimensional chain of mesoscale unit cells with periodicity in the x direction (Top). Photograph of a metastructure during 3D printing, with polycarbonate lattice (white), support material (brown), and embedded steel resonators (gray) (middle). Final 3D-printed metastructure with embedded resonators (bottom) [12] © 2016 National Academy of Sciences. (E) A 1D series of bistable elements connected by soft coupling elements for stable propagation of mechanical signals in soft media using stored elastic energy [13]. © 2016 National Academy of Sciences.

           Moreover, there have been also studies that reported architected materials with unusual or exotic properties such as negative effective swelling (Fig. 3A) [14], negative thermal expansion (Fig. 3B) [15] and static non-reciprocity (Fig. 3C) [16]. These examples demonstrate the cases that the architected materials show in a way opposite properties of those of constituents and give us intriguing new opportunities for design of materials and structures.

Fig. 3. (A) Experimental snapshots of an architected material with effective negative swelling during the swelling process. The dashed red square indicates the cells that are used to calculate εsw (strain by swelling) [14]. © 2016 Wiley-VCH. (B) Experimental sequences of a unit cell with increasing temperature that show negative thermal expansion behaviors. The red arrows indicate the inward bending of the reinforced PEGDA beams [15]. © 2016 American Physical Society. (C) A 3D printed architected material with static non-reciprocity [16] © 2017 Nature Publishing Group.

Challenges & perspectives

              While there have been many exciting progress in architected materials, there are also challenges such as inverse design capability and fabrication of hierarchical architectures across different length scales. To design architected materials, unit cell-based parametric approaches are most common methods. Other methods include combinatorial approach (Fig. 4B) [17] and searching mechanical analogues of physical principles as the case of the architected materials with static non-reciprocity [16]. However, there are challenges of guiding the inverse design of architecture for desired applications based on these approaches. In this sense, recent developments in topology optimization (Fig. 4A) [3] provide design algorithms for architected materials with desired properties with consideration of other conditions such as manufacturing constraints and tolerance, making them suitable as guidance for fabricating architected materials. Nevertheless, there are also challenges in this approach such as considering instability in the optimization algorithms for rational design of tunable architectures with changing properties. To the best of my knowledge, currently, there is no algorithm or tool that provides us inverse design capability of architected materials with nonlinear behaviors of materials and/or structures.

Fig. 4. (A) An example of the topology optimization design framework for architected materials. The optimized unit cell architecture is then repeated in all directions and manufactured to form the bulk material [3]. © 2016 Annual Reviews. (B) (1st Row)(Left)Bricks (top) and their schematic representation (bottom), with the color indicating orientation, and black dents and white protrusions representing deformations. (Right)Two examples where appropriately polarized, adjacent bricks fit together. (2nd Row) Periodic (left), complex (middle) and frustrated (right) 2 × 2 × 2 stackings—for the frustrated stacking, no consistent brick configurations exist (grey/dashed). Schematic symbols are separated from one another for ease of visualization [17].  © 2016 Nature Publishing Group.

             In terms of fabrication, there are still limitations in terms of available materials and fabrication approaches for different length scales. Most of fabrication approaches are effective for particular class of materials and/or length scales. There is no single tool that can allow us to fabricate arbitrary 3D structures made of any material from sub micro to macro scale hierarchically. The recent demonstration of fabricating multiscale materials (Fig. 5A) [18] using a single fabrication tool provides a potential fabrication path to connect different length scales. We can also expand the design space of architected materials by using various stimuli-responsive materials including shape memory materials and gels.

             Beyond controlling external geometry, one can further expand the design space and the resulting performance space of architected materials by coupling geometry with printing path [19] or microstructures in addition to materials properties. Recent progress in 3D printing provides such opportunities by enabling microstructure control within the printed geometry (Figs. 5B-C) [20,21]. The additional control of microstructures can allow us to have architected materials with different responses based on microstructures while they have the same geometries and material compositions.

Fig. 5. (A) Scanning electron micrographs showing cross-section breakdown of structural hierarchy of the multiscale architected material shown down to tens of nanometers in wall thickness [18]. © 2016 Nature Publishing Group. (B) (Left) Optical image of 3D printing of a triangular honeycomb composite. (Right) Schematic illustration of the progressive alignment of high aspect ratio fillers within the nozzle during composite ink deposition [20]. © 2014 Wiley-VCH. (C) Schematics showing the 3D magnetic printing process systematically aligns and selectively polymerizes groupings of voxels programmed to have specific reinforcement orientation within each layer of printed material based upon a shifting field [21]. © 2015 Nature Publishing Group.

              As a closing remark, architected material is an exciting field that opens new opportunities by coupling various disciplines including mechanics, materials science/engineering, physics, chemistry, and biology. It is also a field that needs further studies in many areas including analytical and numerical modeling as well as advanced fabrication methods with expanded palettes of materials, length scales, and microstructures. Beyond scientific community, industries are also active in this field for applications such as aerospace, automotive and sportswear. Architected material is a field that researchers across disciplines and sectors can work together to bring new understanding of behaviors of materials and structures and open new opportunities for materials and structures with tailored and/or intriguing characteristics. 


1.        Valdevit, L., Jacobsen, A. J., Greer, J. R. & Carter, W. B. Protocols for the optimal design of multi-functional cellular structures: From hypersonics to micro-architected materials. Journal of the American Ceramic Society 94, 15–34 (2011).

2.        Schaedler, T. A. & Carter, W. B. Architected cellular materials. Annual Review of Materials Research 46, 187–210 (2016).

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

4.        Zheng, X. Y. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373–1377 (2014).

5.        Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322–1326 (2014).

6.        Berger, J. B., Wadley, H. N. G. & McMeeking, R. M. Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness. Nature (2017). doi:10.1038/nature21075

7.        Shan, S. et al. Multistable architected materials for trapping elastic strain energy. Advanced Materials 27, 4296–4301 (2015).

8.        Frenzel, T., Findeisen, C., Kadic, M., Gumbsch, P. & Wegener, M. Tailored buckling microlattices as reusable light-eeight shock absorbers. Advanced Materials 5865–5870 (2016).

9.        Restrepo, D., Mankame, N. D. & Zavattieri, P. D. Phase transforming cellular materials. Extreme Mechanics Letters 4, 52–60 (2015).

10.      Haghpanah, B., Salari-Sharif, L., Pourrajab, P., Hopkins, J. & Valdevit, L. Multistable shape-reconfigurable architected materials. Advanced Materials 28, 8065 (2016).

11.      Shan, S. C. et al. Harnessing multiple folding mechanisms in soft periodic structures for tunable control of elastic waves. Advanced Functional Materials 24, 4935–4942 (2014).

12.      Matlack, K. H., Bauhofer, A., Krödel, S., Palermo, A. & Daraio, C. Composite 3D-printed meta-structures for low frequency and broadband vibration absorption. Proceedings of National Academy of Sciences, USA 113, 8386–8390 (2016).

13.      Raney, J. R. et al. Stable propagation of mechanical signals in soft media using stored elastic energy. Proceedings of National Academy of Sciences, USA 113, 201604838 (2016).

14.      Liu, J. et al. Harnessing buckling to design architected materials that exhibit effective negative swelling. Advanced Materials 28, 6619–6624 (2016).

15.      Wang, Q. et al. Lightweight mechanical metamaterials with tunable negative thermal expansion. Physical Review Letters 117, (2016).

16.      Coulais, C., Sounas, D. & Alù, A. Static non-reciprocity in mechanical metamaterials. Nature 542, 461–464 (2017).

17.      Coulais, C., Teomy, E., de Reus, K., Shokef, Y. & van Hecke, M. Combinatorial design of textured mechanical metamaterials. Nature 535, 529–532 (2016).

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

19.      Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nature Materials 15, 413–8 (2016).

20.      Compton, B. G. & Lewis, J. A. 3D-printing of lightweight cellular composites. Advanced Materials 26, 5930–5935 (2014).

21.      Martin, J. J., Fiore, B. E. & Erb, R. M. Designing bioinspired composite reinforcement architectures via 3D magnetic printing. Nature Communications 6, 8641 (2015).

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Cai Shengqiang's picture

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. 


Ling Liu's picture


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 (

Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency (

Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material (

Sung Hoon Kang's picture

Dear Ling,

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

Cai Shengqiang's picture

Dear Ling, 

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



Sung Hoon Kang's picture

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 ( 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.

Lifeng Wang's picture

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.


Sung Hoon Kang's picture

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.

Mike Ciavarella's picture

dear Sung

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

 Immagine correlata

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



Sung Hoon Kang's picture

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.

Mike Ciavarella's picture

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

Sung Hoon Kang's picture

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.

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.

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.

Sung Hoon Kang's picture

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).

nicfang's picture

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



Sung Hoon Kang's picture

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.

Yongle Sun's picture

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,GjCIbJUX)

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