Skip to main content


  • Lorenzo Valdevit (a1), Katia Bertoldi (a2), James Guest (a3) and Christopher Spadaccini (a4)
  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Available formats
Hide All
1. Fleck, N.A., Deshpande, V.S., and Ashby, M.F.: Micro-architectured materials: Past, present and future. Proc. R. Soc. A 466, 24952516 (2011).
2. Valdevit, L., Jacobsen, A.J., Greer, J.R., and Carter, W.B.: Protocols for the optimal design of multi-functional cellular structures: From hypersonics to micro-architected materials. J. Am. Ceram. Soc. 94, s15s34 (2011).
3. Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F., and Wadley, H.N.G.: The topological design of multifunctional cellular metals. Prog. Mater. Sci. 46, 309328 (2001).
4. Bauer, J., Meza, L.R., Schaedler, T.A., Schwaiger, R., Zheng, X., and Valdevit, L.: Nanolattices: An emerging class of mechanical metamaterials. Adv. Mater. 15, 17018501701926 (2017).
5. O’Masta, M.R., Dong, L., St-Pierre, L., Wadley, H.N.G., and Deshpande, V.S.: The fracture toughness of octet-truss lattices. J. Mech. Phys. Solids 98, 271289 (2016).
6. Lee, J-H., Wang, L., Boyce, M.C., and Thomas, E.L.: Periodic bicontinuous composites for high specific energy absorption. Nano Lett. 12, 43924396 (2012).
7. Landy, N.I., Sajuyigbe, S., Mock, J.J., Smith, D.R., and Padilla, W.J.: Perfect metamaterial absorber. Phys. Rev. Lett. 100, 207402 (2008).
8. Vakil, A. and Engheta, N.: Transformation optics using graphene. Science 332, 12911294 (2011).
9. Valentine, J., Zhang, S., Zentgraf, T., Ulin-Avila, E., Genov, D.A., Bartal, G., and Zhang, X.: Three-dimensional optical metamaterial with a negative refractive index. Nature 455, 376U32 (2008).
10. Shelby, R.A., Smith, D.R., and Schultz, S.: Experimental verification of a negative index of refraction. Science 292, 7779 (2001).
11. Schurig, D., Mock, J.J., Justice, B.J., Cummer, S.A., Pendry, J.B., Starr, A.F., and Smith, D.R.: Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977980 (2006).
12. Mullin, T., Deschanel, S., Bertoldi, K., and Boyce, M.C.: Pattern transformation triggered by deformation. Phys. Rev. Lett. 99, 084301 (2007).
13. Zhang, Y., Matsumoto, E.A., Peter, A., Lin, P-C., Kamien, R.D., and Yang, S.: One-step nanoscale assembly of complex structures via harnessing of elastic instability. Nano Lett. 8, 11921196 (2008).
14. Liu, J., Gu, T., Shan, S., Kang, S.H., Weaver, J.C., and Bertoldi, K.: Harnessing buckling to design architected materials that exhibit effective negative swelling. Adv. Mater. 28, 66196624 (2016).
15. Lazarus, A. and Reis, P.M.: Soft actuation of structured cylinders through auxetic behavior. Adv. Eng. Mater. 17, 815820 (2015).
16. Yang, D., Mosadegh, B., Ainla, A., Lee, B., Khashai, F., Suo, Z., Bertoldi, K., and Whitesides, G.M.: Buckling of elastomeric beams enables actuation of soft machines. Adv. Mater. 27, 6323 (2015).
17. Li, J., Shim, J., Deng, J., Overvelde, J.T.B., Zhu, X., Bertoldi, K., and Yang, S.: Switching periodic membranes via pattern transformation and shape memory effect. Soft Matter 8, 1032210328 (2012).
18. Zhu, X., Wu, G., Dong, R., Chen, C-M., and Yang, S.: Capillarity induced instability in responsive hydrogel membranes with periodic hole array. Soft Matter 8, 80888093 (2012).
19. Wang, P., Casadei, F., Shan, S., Weaver, J.C., and Bertoldi, K.: Harnessing buckling to design tunable locally resonant acoustic metamaterials. Phys. Rev. Lett. 113, 014301 (2014).
20. Bertoldi, K. and Boyce, M.C.: Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Phys. Rev. B 77, 052105 (2008).
21. Shan, S., Kang, S.H., Wang, P., Qu, C., Shian, S., Chen, E.R., and Bertoldi, K.: Harnessing multiple folding mechanisms in soft periodic structures for tunable control of elastic waves. Adv. Funct. Mater. 24, 49354942 (2014).
22. Celli, P., Gonella, S., Tajeddini, V., Muliana, A., Ahmed, S., and Ounaies, Z.: Wave control through soft microstructural curling: Bandgap shifting, reconfigurable anisotropy and switchable chirality. Smart Mater. Struct. 26, 035001 (2017).
23. Haghpanah, B., Salari-Sharif, L., Pourrajab, P., Hopkins, J., and Valdevit, L.: Multistable shape-reconfigurable architected materials. Adv. Mater. 28, 79157920 (2016).
24. Shan, S., Kang, S.H., Raney, J.R., Wang, P., Fang, L., Candido, F., Lewis, J.A., and Bertoldi, K.: Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27, 42964301 (2015).
25. Restrepo, D., Mankame, N.D., and Zavattieri, P.D.: Phase transforming cellular materials. Extreme Mech. Lett. 4, 5260 (2015).
26. Raney, J.R., Nadkarni, N., Daraio, C., Kochmann, D.M., Lewis, J.A., and Bertoldi, K.: Stable propagation of mechanical signals in soft media using stored elastic energy. Proc. Natl. Acad. Sci. U. S. A. 113, 97229727 (2016).
27. Zheng, X., DeOtte, J., Alonso, M.P., Farquar, G.R., Weisgraber, T.H., Gemberling, S., Lee, H., Fang, N., and Spadaccini, C.M.: Design and optimization of a light-emitting diode projection micro-stereolithography three-dimensional manufacturing system. Rev. Sci. Instrum. 83, 125001 (2012).
28. Tumbleston, J.R., Shirvanyants, D., Ermoshkin, N., Janusziewicz, R., Johnson, A.R., Kelly, D., Chen, K., Pinschmidt, R., Rolland, J.P., Ermoshkin, A., Samulski, E.T., and DeSimone, J.M.: Continuous liquid interface production of 3D objects. Science 347, 13491352 (2015).
29. Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit, L., and Carter, W.B.: Ultralight metallic microlattices. Science 334, 962 (2011).
30. Lee, K-S., Kim, R.H., Yang, D-Y., and Park, S.H.: Advances in 3D nano/microfabrication using two-photon initiated polymerization. Prog. Polym. Sci. 33, 631681 (2008).
31. Eckel, Z.C., Zhou, C., Martin, J.H., Jacobsen, A.J., Carter, W.B., and Schaedler, T.A.: Additive manufacturing of polymer-derived ceramics. Science 351, 5862 (2016).
32. Zheng, X., Lee, H., Weisgraber, T.H., Shusteff, M., DeOtte, J., Duoss, E.B., Kuntz, J.D., Biener, M.M., Ge, Q., Jackson, J.A., Kucheyev, S.O., Fang, N.X., and Spadaccini, C.M.: Ultralight, ultrastiff mechanical metamaterials. Science 344, 13731377 (2014).
33. Wang, Q., Jackson, J.A., Ge, Q., Hopkins, J.B., Spadaccini, C.M., and Fang, N.X.: Lightweight mechanical metamaterials with tunable negative thermal expansion. Phys. Rev. Lett. 117, 175901175906 (2016).
34. Smay, J.E., Cesarano, J., and Lewis, J.A.: Colloidal inks for directed assembly of 3-D periodic structures. Langmuir 18, 54295437 (2002).
35. Duoss, E.B., Twardowski, M., and Lewis, J.A.: Sol–gel inks for direct-write assembly of functional oxides. Adv. Mater. 19, 3485 (2007).
36. Hansen, C.J., Saksena, R., Kolesky, D.B., Vericella, J.J., Kranz, S.J., Muldowney, G.P., Christensen, K.T., and Lewis, J.A.: High-throughput printing via microvascular multinozzle arrays. Adv. Mater. 25, 96102 (2013).
37. Valdevit, L., Godfrey, S.W., Schaedler, T.A., Jacobsen, A.J., and Carter, W.B.: Compressive strength of hollow microlattices: Experimental characterization, modeling, and optimal design. J. Mater. Res. 28, 24612473 (2013).
38. Osanov, M. and Guest, J.K.: Topology optimization for architected materials design. Annu. Rev. Mater. Res. 46, 211233 (2016).
39. Sigmund, O.: Materials with prescribed constitutive parameters: An inverse homogenization problem. Int. J. Solids Struct. 31, 23132329 (1994).
40. Sigmund, O. and Torquato, S.: Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45, 10371067 (1997).
41. Challis, V.J., Roberts, A.P., and Wilkins, A.H.: Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int. J. Solids Struct. 45, 41304146 (2008).
42. Guest, J.K. and Prevost, J.H.: Design of maximum permeability material structures. Comput. Meth. Appl. Mech. Eng. 196, 10061017 (2007).
43. Challis, V.J., Guest, J.K., Grotowski, J.F., and Roberts, A.P.: Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization. Int. J. Solid Struct. 49, 33973408 (2012).
44. Sigmund, O. and Jensen, J.S.: Systematic design of phononic band-gap materials and structures by topology optimization. Philos. Trans. R. Soc. London, Ser. A 361, 10011019 (2003).
45. Rupp, C.J., Evgrafov, A., Maute, K., and Dunn, M.L.: Design of phononic materials/structures for surface wave devices using topology optimization. Struct. Multidiscip. Optim. 34, 111121 (2007).
46. Prasad, J. and Diaz, A.R.: Viscoelastic material design with negative stiffness components using topology optimization. Struct. Multidiscip. Optim. 38, 583597 (2008).
47. Andreassen, E. and Jensen, J.S.: Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials. Struct. Multidiscip. Optim. 49, 695705 (2013).
48. Asadpoure, A., Tootkaboni, M., and Valdevit, L.: Topology optimization of multiphase architected materials for energy dissipation. Comput. Method. Appl. M. 325, 314329 (2017).
49. Diaz, A.R. and Sigmund, O.: A topology optimization method for design of negative permeability metamaterials. Struct. Multidiscip. Optim. 41, 163177 (2010).
50. Zhou, S., Li, W., Chen, Y., Sun, G., and Li, Q.: Topology optimization for negative permeability metamaterials using level-set algorithm. Acta Mater. 59, 26242636 (2011).
51. Carstensen, J.V., Lotfi, R., Guest, J.K., Chen, W., and Schroers, J.: Topology optimization of cellular materials with maximized energy absorption. In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (ASME, Boston, Massachusetts, 2015); p. V02BT03A014.
52. Clausen, A., Wang, F., Jensen, J.S., Sigmund, O., and Lewis, J.A.: Topology optimized architectures with programmable Poisson’s ratio over large deformations. Adv. Mater. 27, 55235527 (2015).
53. Cadman, J.E., Zhou, S., Chen, Y., and Li, Q.: On design of multi-functional microstructural materials. J. Mater. Sci. 48, 5166 (2013).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 12
Total number of PDF views: 172 *
Loading metrics...

Abstract views

Total abstract views: 189 *
Loading metrics...

* Views captured on Cambridge Core between 14th February 2018 - 20th August 2018. This data will be updated every 24 hours.