Hostname: page-component-76c49bb84f-65mhm Total loading time: 0 Render date: 2025-07-11T21:00:40.717Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiscale modeling and optimization of the mechanics of hierarchical metamaterials

Published online by Cambridge University Press:  10 October 2019

Dennis M. Kochmann ,
Jonathan B. Hopkins  and
Lorenzo Valdevit
Dennis M. Kochmann
Affiliation:
ETH Zürich, Switzerland; dmk@ethz.ch
Jonathan B. Hopkins
Affiliation:
University of California, Los Angeles, USA; hopkins@seas.ucla.edu
Lorenzo Valdevit
Affiliation:
University of California, Irvine, USA; valdevit@uci.edu
Get access

Abstract

We present a survey of modeling techniques used to describe and predict architected cellular metamaterials, and to optimize their topology and geometry toward tailoring their mechanical properties such as stiffness, strength, fracture toughness, and energy absorption. Architectures of interest include truss-, plate-, and shell-based networks with and without periodicity, whose effective mechanical behavior is simulated by tools such as classical finite elements, further scale-bridging techniques such as homogenization and concurrent scale-coupling, and effective continuum descriptions of the underlying discrete networks. In addition to summarizing advances in applying the latter techniques to improve the properties of metamaterials and featuring prominent examples of structure–property relations achieved this way, we also present recently introduced techniques to improve the optimization process toward a full exploitation of the available design space, accounting for both linear and nonlinear material behavior.

Information

Type
Three-Dimensional Architected Materials and Structures
Information
MRS Bulletin , Volume 44 , Issue 10: Three-Dimensional Architected Materials and Structures , October 2019 , pp. 773 - 781
Copyright
Copyright © Materials Research Society 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Veselago, V.G., Sov. Phys. Usp. 10, 509 (1968).CrossRefGoogle Scholar
Shelby, R.A., Smith, D.R., Shultz, S., Science 292, 77 (2001).CrossRefGoogle Scholar
Gibson, I., Rosen, D.W., Stucker, B., Additive Manufacturing Technologies (Springer, New York, 2014).Google Scholar
Meza, L., Zelhofer, A.J., Clarke, N., Mateos, A.J., Kochmann, D.M., Greer, J.R., Proc. Natl. Acad. Sci. U.S.A. 112, 11502 (2015).CrossRefGoogle Scholar
Li, X., Gao, H., Nat. Mater. 15, 373 (2016).CrossRefGoogle Scholar
Greer, J.R., De Hosson, J.T.M., Prog. Mater. Sci. 56, 654 (2011).CrossRefGoogle Scholar
Pasini, D., Guest, J., MRS Bull . 44 (10), 766 (2019).Google Scholar
Gibson, L.J., Ashby, M.F., Cellular Solids: Structure and Properties (Cambridge University Press, 1999).Google Scholar
Coulais, C., Teomy, E., de Reus, K., Shokef, Y., van Hecke, M., Nature 535, 529 (2016).CrossRefGoogle Scholar
Deshpande, V.S., Fleck, N.A., Ashby, M.F., J. Mech. Phys. Solids 49, 1747 (2001).CrossRefGoogle Scholar
Gibson, L., Ashby, M., Cellular Solids: Structure and Properties (Pergamon Press, Oxford, UK, 1988).Google Scholar
Wicks, N., Hutchinson, J.W., Int. J. Solids Struct. 38, 5165 (2001).CrossRefGoogle Scholar
Zok, F.W., Waltner, S.A., Wei, Z., Rathbun, H.J., McMeeking, R.M., Evans, A.G., Int J. Solids Struct. 41, 6249 (2004).CrossRefGoogle Scholar
Zok, F.W., Rathbun, H.J., Wei, Z., Evans, A.G., Int. J. Solids Struct. 40, 5707 (2003).CrossRefGoogle Scholar
Tancogne-Dejean, T., Diamantopoulou, M., Gorji, M.B., Bonatti, C., Mohr, D., Adv. Mater. 30, 1803334 (2018).CrossRefGoogle Scholar
Fleck, N.A., Deshpande, V.S., Ashby, M.F., Proc. R. Soc. Lond. A 466, 2495 (2011).CrossRefGoogle Scholar
Triantafyllidis, N., Bardenhagen, S., J. Elast. 33, 259 (1993).CrossRefGoogle Scholar
Wang, Y., Cuitiño, A., J. Mech. Phys. Solids 48, 961 (2000).CrossRefGoogle Scholar
Chen, J.Y., Huang, Y., Ortiz, M., J. Mech. Phys. Solids 46, 789 (1998).CrossRefGoogle Scholar
Kumar, R.S., McDowell, D.L., Int. J. Solids Struct. 41, 7399 (2004).CrossRefGoogle Scholar
Glaesener, R., Lestringant, C., Telgen, B., Kochmann, D.M., Int. J. Solids Struct. 171, 117 (2019).CrossRefGoogle Scholar
Valdevit, L., Wei, Z., Mercer, C., Zok, F., Evans, A., Int. J. Solids Struct. 43, 4888 (2006).CrossRefGoogle Scholar
Zok, F.W., Rathbun, H., He, M., Ferri, E., Mercer, C., McMeeking, R.M., Evans, A.G., Philos. Mag. 85, 3207 (2005).CrossRefGoogle Scholar
O’Masta, M.R., Dong, L., St.-Pierre, L., Wadley, H.N.G., Deshpande, V.S., J. Mech. Phys. Solids 98, 271 (2016).CrossRefGoogle Scholar
Valdevit, L., Godfrey, S.W., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., J. Mater. Res. 28, 2461 (2013).CrossRefGoogle Scholar
Meza, L.R., Phlipot, G., Portela, C.M., Maggi, A., Montemayor, L.C., Comella, A., Kochmann, D.M., Greer, J.R., Acta Mater . 140, 424 (2017).CrossRefGoogle Scholar
Hsieh, M.-T., Endo, B., Zhang, Y., Bauer, J., Valdevit, L., J. Mech. Phys. Solids 125, 401 (2019).CrossRefGoogle Scholar
Vidyasagar, A., Krödel, S., Kochmann, D.M., Proc. R. Soc. Lond. A 47, 20180535 (2018).CrossRefGoogle Scholar
Andreassen, E., Andreasen, C.S., Comput. Mater. Sci. 83, 488 (2014).CrossRefGoogle Scholar
Torquato, S., Random Heterogeneous Materials (Springer, New York, 2002).CrossRefGoogle Scholar
Portela, C.M., Greer, J.R., Kochmann, D.M.. Extreme Mech. Lett. 22, 138 (2018).CrossRefGoogle Scholar
Berger, J.B., Wadley, H.N.G., McMeeking, R.M., Nature 543, 533 (2017).CrossRefGoogle Scholar
Sigmund, O., Torquato, S., J. Mech. Phys. Solids 45, 1037 (1997).CrossRefGoogle Scholar
Guest, J.K., Prévost, J.H., Int. J. Solids Struct. 43, 7028 (2006).CrossRefGoogle Scholar
Kochmann, D.M., Venturini, G.N., Smart Mater. Struct. 22, 084004 (2013).CrossRefGoogle Scholar
Shan, S., Kang, S.H., Wang, P., Qu, C., Shian, S., Chen, E.R., Bertoldi, K., Adv. Funct. Mater. 24, 4935 (2014).CrossRefGoogle Scholar
Valdevit, L., Hutchinson, J.W., Evans, A.G., Int. J. Solids Struct. 41, 5105 (2004).CrossRefGoogle Scholar
Vigliotti, A., Pasini, D., Mech. Mater. 46, 57 (2012).CrossRefGoogle Scholar
Vigliotti, A., Pasini, D., Comput. Methods Appl. Mech. Eng. 229, 27 (2012).CrossRefGoogle Scholar
Geymonat, G., Müller, S., Triantafyllidis, N., Arch. Ration. Mech. Anal. 122, 231 (1993).CrossRefGoogle Scholar
Bertoldi, K., Boyce, M.C., Phys. Rev. B 78, 184107 (2008).CrossRefGoogle Scholar
Hutchinson, R.G., Fleck, N.A., J. Mech. Phys. Solids 54, 756 (2006).CrossRefGoogle Scholar
Hussein, M.I., Leamy, M.J., Ruzzene, M., Appl. Mech. Rev. 66, 040802 (2014).CrossRefGoogle Scholar
Asadpoure, A., Tootkaboni, M., Valdevit, L., Comput. Methods Appl. Mech. Eng. 325, 314 (2017).CrossRefGoogle Scholar
Salari-Sharif, L., Haghpanah, B., Guell Izard, A., Tootkaboni, M., Valdevit, L., Phys. Rev. Appl. 11, 024062 (2019).CrossRefGoogle Scholar
Zelhofer, A., Kochmann, D.M., Int. J. Solids Struct. 115–116, 248 (2017).CrossRefGoogle Scholar
Kochmann, D.M., Bertoldi, K., Appl. Mech. Rev. 69, 050801 (2017).CrossRefGoogle Scholar
Kashdan, L., Seepersad, C.C., Haberman, M., Wilson, P.S., Rapid Prototyp. J. 18, 194 (2012).CrossRefGoogle Scholar
Kalathur, H., Lakes, R.S., Smart Mater. Struct. 22, 084013 (2013).CrossRefGoogle Scholar
Dong, L., Lakes, R.S., Int. J. Solids Struct. 50, 2416 (2013).CrossRefGoogle Scholar
Kochmann, D.M.. Mech. Res. Commun. 58, 36 (2014).CrossRefGoogle Scholar
Shan, S., Kang, S.H., Raney, J.R., Wang, P., Fang, L., Candido, F., Lewis, J.A., Bertoldi, K., Adv. Mater. 27, 4296 (2015).CrossRefGoogle Scholar
Bertoldi, K., Vitelli, V., Christensen, J., van Hecke, M., Nat. Rev. Mater. 2, 17066 (2017).CrossRefGoogle Scholar
Harne, R.L., Wang, K.-W., Harnessing Bistable Structural Dynamics: For Vibration Control, Energy Harvesting and Sensing (Wiley, Chichester, West Sussex, UK, 2017).CrossRefGoogle Scholar
Haghpanah, B., Shirazi, A., Salari-Sharif, L., Izard, A.G., Valdevit, L., Extreme Mech. Lett. 17, 56 (2017).CrossRefGoogle Scholar
Haghpanah, B., Salari-Sharif, L., Pourrajab, P., Hopkins, J., Valdevit, L., Adv. Mater. 28, 7915 (2016).CrossRefGoogle Scholar
Izard, A.G., Alfonso, R.F., McKnight, G., Valdevit, L., Mater. Des. 135, 37 (2017).CrossRefGoogle Scholar
Quintana-Alonso, I., Fleck, N.A., in Major Accomplishments in Composite Materials and Sandwich Structures, Daniel, I.M., Gdoutos, E.E., Rajapakse, Y.D.S., Eds. (Springer, Dordrecht, The Netherlands, 2010), pp. 799–816.Google Scholar
Tankasala, H.C., Deshpande, V.S., Fleck, N.A., J. Appl. Mech. 82, 091004 (2015).CrossRefGoogle Scholar
Fleck, N.A., Qiu, X., J. Mech. Phys. Solids 55, 562 (2007).CrossRefGoogle Scholar
Tadmor, E.B., Ortiz, M., Phillips, R., Philos. Mag. A 73, 1529 (1996).CrossRefGoogle Scholar
Beex, L.A.A., Peerlings, R.H.J., Geers, M.G.D., Int. J. Numer. Methods Eng. 87, 701 (2011).CrossRefGoogle Scholar
Beex, L.A.A., Peerlings, R.H.J., Geers, M.G.D., J. Mech. Phys. Solids 64, 154 (2014).CrossRefGoogle Scholar
Beex, L.A.A., Peerlings, R.H.J., Geers, M.G.D., Comput. Methods Appl. Mech. Eng. 269, 108 (2014).CrossRefGoogle Scholar
Phlipot, G.P., Kochmann, D.M., J. Mech. Phys. Solids 124, 758 (2019).CrossRefGoogle Scholar
Vigliotti, A., Deshpande, V., Pasini, D., J. Mech. Phys. Solids 64, 44 (2014).CrossRefGoogle Scholar
Bauer, J., Meza, L.R., Schaedler, T.A., Schwaiger, R., Zheng, X., Valdevit, L., Adv. Mater. 29, 1701850 (2017).CrossRefGoogle Scholar
Torrents, A., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., Valdevit, L., Acta Mater. 60, 3511 (2012).CrossRefGoogle Scholar
Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit, L., Carter, W.B., Science 334, 962 (2011).CrossRefGoogle Scholar
Vyatskikh, A., Delalande, S., Kudo, A., Zhang, X., Portela, C.M., Greer, J.R., Nat. Commun. 9, 593 (2018).CrossRefGoogle Scholar
Zhang, X., Vyatskikh, A., Gao, H., Greer, J.R., Li, X., Proc. Natl. Acad. Sci. U.S.A. 116, 6665 (2019).CrossRefGoogle Scholar
Zhang, X., Zhong, L., Mateos, A., Kudo, A., Vyatskikh, A., Gao, H., Greer, J.R., Li, X., Nat. Nanotechnol. 14, 762 (2019).CrossRefGoogle Scholar
Meza, L.R., Das, S., Greer, J.R., Science 345, 1322 (2014).CrossRefGoogle Scholar
Bauer, J., Schroer, A., Schwaiger, R., Tesari, I., Lange, C., Valdevit, L., Kraft, O., Extreme Mech. Lett. 3, 105 (2015).CrossRefGoogle Scholar
Zhu, M., Yang, Y., Guest, J.K., Shields, M.D., Struct. Saf. 67, 116 (2017).CrossRefGoogle Scholar
Sigmund, O., Mech. Struct. Mach. 25, 493 (1997).CrossRefGoogle Scholar
Shaw, L.A., Sun, F., Portela, C.M., Barranco, R.I., Greer, J.R., Hopkins, J.B., Nat. Commun. 10, 291 (2019).CrossRefGoogle Scholar
Hopkins, J.B., “Chapter 6: Synthesis Through Freedom and Constraint Topologies,” in Handbook of Compliant Mechanisms, Howell, L.L., Magleby, S.P., Olsen, B.M., Eds. (Wiley, Oxford, UK, 2013), pp. 79–92.Google Scholar
Hopkins, J.B., Culpepper, M.L., Precis. Eng. 34, 259 (2010).CrossRefGoogle Scholar
Hopkins, J.B., Culpepper, M.L., Precis. Eng. 34, 271 (2010).CrossRefGoogle Scholar
Ball, R.S., A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, UK, 1900).Google Scholar
Hopkins, J.B., Vericella, J.J., Harvey, C.D., Precis. Eng. 38, 525 (2014).CrossRefGoogle Scholar
Hopkins, J.B., Culpepper, M.L., Precis. Eng. 35, 638 (2011).CrossRefGoogle Scholar
Hopkins, J.B., J. Mech. Robot. 7, 031011 (2015).CrossRefGoogle Scholar
Hopkins, J.B., Mech. Sci. 4, 319 (2013).CrossRefGoogle Scholar
Sun, F., Hopkins, J.B., J. Mech. Robot. 9, 031018 (2017).CrossRefGoogle Scholar
Hatamizadeh, A., Song, Y., Hopkins, J.B., Math. Probl. Eng. 2018, 1058732 (2018).CrossRefGoogle Scholar
LeCun, Y., Bengio, Y., Hinton, G., Nature 521, 436 (2015).CrossRefGoogle Scholar