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On design of multi-functional microstructural materials

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Abstract

The design of periodic microstructural composite materials to achieve specific properties has been a major area of interest in material research. Tailoring different physical properties by modifying the microstructural architecture in unit cells is one of the main concerns in exploring and developing novel multi-functional cellular composites and has led to the development of a large variety of mathematical models, theories and methodologies for improving the performance of such materials. This paper provides a critical review on the state-of-the-art advances in the design of periodic microstructures of multi-functional materials for a range of physical properties, such as elastic stiffness, Poisson’s ratio, thermal expansion coefficient, conductivity, fluidic permeability, particle diffusivity, electrical permittivity and magnetic permeability, etc.

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References

  1. Zhou S, Li Q (2007) J Phys D 40:6083

    Article  CAS  Google Scholar 

  2. Wiener O (1912) Abh. Math. Phys. Kl. Koniglich Saechs Akad. Wiss. 32:509

    Google Scholar 

  3. Hashin Z, Shtrikman S (1963) J Mech Phys Solids 11:127

    Article  Google Scholar 

  4. Hashin Z, Shtrikman S (1961) J Frankl Inst Eng Appl Math 271:336

    Article  Google Scholar 

  5. Hashin Z, Shtrikman S (1962) J Mech Phys Solids 10:335

    Article  Google Scholar 

  6. Walpole LJ (1966) J Mech Phys Solids 14:151

    Article  Google Scholar 

  7. Berryman JG, Milton GW (1988) J Phys D-Appl Phys 21:87

    Article  Google Scholar 

  8. Milton GW, Phan-Thien N (1982) Proc R Soc Lond A Math Phys Eng Sci 380:305

    Article  Google Scholar 

  9. Cherkaev AV, Gibiansky LV (1993) J Mech Phys Solids 41:937

    Article  Google Scholar 

  10. Hashin Z, Shtrikman S (1962) J Appl Phys 33:3125

    Article  CAS  Google Scholar 

  11. Milton GW, Kohn RV (1988) J Mech Phys Solids 36:597

    Article  Google Scholar 

  12. Rosen BW, Hashin Z (1970) Int J Eng Sci 8:157

    Article  Google Scholar 

  13. Torquato S, Pham DC (2004) Phys Rev Lett 92:255505

    Article  CAS  Google Scholar 

  14. Pham DC, Torquato S (2005) J Appl Phys 97:013535

    Article  CAS  Google Scholar 

  15. Golden KM, Heaton AL, Eicken H, Lytle VI (2006) Mech Mater 38:801

    Article  Google Scholar 

  16. Gibiansky LV, Torquato S (1996) Proc R Soc Lond A 452:253

    Article  Google Scholar 

  17. Bergman DJ (1978) Phys Rep 43:378

    Article  Google Scholar 

  18. Milton GW (1981) J Appl Phys 52:5294

    Article  Google Scholar 

  19. Avellaneda M, Cherkaev AV, Lurie KA, Milton GW (1988) J Appl Phys 63:4989

    Article  CAS  Google Scholar 

  20. Torquato S, Hyun S, Donev A (2003) J Appl Phys 94:5748

    Article  CAS  Google Scholar 

  21. Bendsoe MP, Sigmund O (1999) Arch Appl Mech 69:635

    Article  Google Scholar 

  22. Bendsoe MP, Sigmund O (2003) Topology, optimization: theory, methods, and applications. Springer, Berlin

    Google Scholar 

  23. Sigmund O, Petersson J (1998) Struct Optim 16:68

    Article  Google Scholar 

  24. Diaz A, Sigmund O (1995) Struct Optim 10:40

    Article  Google Scholar 

  25. Jog CS, Haber RB, Bendsoe MP (1994) Int J Numer Meth Eng 37:1323

    Article  Google Scholar 

  26. Rodrigues H, Fernandes P (1995) Int J Numer Meth Eng 38:1951

    Article  Google Scholar 

  27. Bendsoe MP, Kikuchi N (1988) Comput Methods Appl Mech Eng 71:197

    Article  Google Scholar 

  28. Bendsoe MP (1989) Struct Optim 1:193

    Article  Google Scholar 

  29. Haber RB, Jog CS, Bendsoe MP (1996) Struct Optim 11:1

    Article  Google Scholar 

  30. Kim H, Querin OM, Steven GP, Xie YM (2000) Struct Multidisc Optim 19:140

    Article  Google Scholar 

  31. Fernandes P, Guedes JM, Rodrigues H (1999) Comput Struct 73:583

    Article  Google Scholar 

  32. Petersson J, Sigmund O (1998) Int J Numer Meth Eng 41:1417

    Article  Google Scholar 

  33. Neves MM, Sigmund O, Bendsoe MP (2002) Int J Numer Meth Eng 54:809

    Article  Google Scholar 

  34. Li Q, Steven GP, Querin OM, Xie YM (2000) Eng Comput 17:715

    Article  Google Scholar 

  35. Sigmund O (1997) Mech Struct Mach 25:493

    Article  Google Scholar 

  36. Guest JK, Prevost JH, Belytschko T (2004) Int J Numer Meth Eng 61:238

    Article  Google Scholar 

  37. Poulsen TA (2002) Struct Multidiscip Optim 24:396

    Article  Google Scholar 

  38. Poulsen TA (2003) Int J Numer Meth Eng 57:741

    Article  Google Scholar 

  39. Wang MY, Zhou S, Ding H (2004) Struct Multidiscip Optim 28:262

    Article  Google Scholar 

  40. Zhou SW, Cadman J, Chen YH, Li W, Xie YM, Huang XD, Appleyard R, Sun GY, Li Q (2012) Int J Heat Mass Transf (in press)

  41. Zhou SW, Li Q (2008) Mater Lett 62:4022

    Article  CAS  Google Scholar 

  42. Zhou S, Li Q (2008) J Mater Sci 43:5157. doi:10.1007/s10853-008-2722-y

    Article  CAS  Google Scholar 

  43. Zhou S, Li Q (2008) Comput Mater Sci 43:549

    Article  CAS  Google Scholar 

  44. Zhou SW, Li Q (2008) J Mater Res 23:798

    Article  CAS  Google Scholar 

  45. Nakasone PH, Silva ECN (2010) J Intell Mater Syst Struct 21:1627

    Article  Google Scholar 

  46. Swan CC, Kosaka I (1997) Comput Struct 64:603

    Article  Google Scholar 

  47. Guest JK, Igusa T (2008) Comput Methods Appl Mech Eng 198:116

    Article  Google Scholar 

  48. Schevenels M, Lazarov BS, Sigmund O (2011) Comput Methods Appl Mech Eng 200:3613

    Article  Google Scholar 

  49. Asadpoure A, Tootkaboni M, Guest JK (2011) Comput Struct 89:1131

    Article  Google Scholar 

  50. Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Struct Multidiscip Optim 43:1

    Article  Google Scholar 

  51. Wang FW, Lazarov BS, Sigmund O (2011) Struct Multidiscip Optim 43:767

    Article  Google Scholar 

  52. Sigmund O (2007) Struct Multidiscip Optim 33:401

    Article  Google Scholar 

  53. Sigmund O (2009) Acta Mech Sin 25:227

    Article  Google Scholar 

  54. Guest JK (2009) Comput Methods Appl Mech Eng 199:123

    Article  Google Scholar 

  55. Rozvany GIN, Zhou M (1991) Comput Methods Appl Mech Eng 89:281

    Article  Google Scholar 

  56. Zhou M, Rozvany GIN (1992) Struct Optim 5:12

    Article  Google Scholar 

  57. Zhou M, Rozvany GIN (1991) Comput Methods Appl Mech Eng 89:309

    Article  Google Scholar 

  58. Norato JA, Bendsoe MP, Haber RB, Tortorelli DA (2007) Struct Multidiscip Optim 33:375

    Article  Google Scholar 

  59. Hassani B, Hinton E (1998) Comput Struct 69:739

    Article  Google Scholar 

  60. Sigmund O (1995) Mech Mater 20:351

    Article  Google Scholar 

  61. Sigmund O (1994) Int J Solids Struct 31:2313

    Article  Google Scholar 

  62. Sigmund O (1994) J Intell Mater Syst Struct 5:736

    Article  Google Scholar 

  63. Yin LZ, Yang W (2001) Comput Struct 79:1839

    Article  Google Scholar 

  64. Svanberg K (1987) Int J Numer Meth Eng 24:359

    Article  Google Scholar 

  65. Zuo K-T, Chen L-P, Zhang Y-Q, Yang J (2007) Int J Manuf Technol 32:787

    Article  Google Scholar 

  66. Svanberg K (1999) A new globally convergent version of the method of moving asymptotes. Royal Institute of Technology, Stockholm

    Google Scholar 

  67. Patil S, Zhou S, Li Q (2008) Adv Mater Res 32:279

    Article  CAS  Google Scholar 

  68. Xie YM, Steven GP (1993) Comput Struct 49:885

    Article  Google Scholar 

  69. Xie YM, Steven GP (1997) Evolutionary structural optimization. Springer, London

    Book  Google Scholar 

  70. Li Q, Steven GP, Xie YM, Querin OM (2004) Int J Heat Mass Transf 47:5071

    Article  Google Scholar 

  71. Hussein MI, Hamza K, Hulbert GM, Scott RA, Saitou K (2006) Struct Multidiscip Optim 31:60

    Article  Google Scholar 

  72. Zohdi TI (2002) Int J Fract 118:L89

    Article  Google Scholar 

  73. Bruck HA, Gilat R, Aboudi J, Gershon AL (2007) Modell Simul Mater Sci Eng 15:653

    Article  CAS  Google Scholar 

  74. Sethian JA, Wiegmann A (2000) J Comput Phys 163:489

    Article  Google Scholar 

  75. Wang MY, Wang XM, Guo DM (2003) Comput Methods Appl Mech Eng 192:227

    Article  Google Scholar 

  76. Mei YL, Wang XM (2004) Acta Mech Solida Sin 17:239

    Google Scholar 

  77. Allaire G, Jouve F, Toader A-M (2004) J Comput Phys 194:363

    Article  Google Scholar 

  78. Challis VJ, Roberts AP, Wilkins AH (2008) Int J Solids Struct 45:4130

    Article  Google Scholar 

  79. Zhou SW, Li Q (2008g) J Comput Phys 227:10178

    Article  Google Scholar 

  80. Guedes JM, Kikuchi N (1990) Comput Methods Appl Mech Eng 83:143

    Article  Google Scholar 

  81. Hollister SJ, Lin CY (2007) Comput Methods Appl Mech Eng 196:2991

    Article  Google Scholar 

  82. Adachi T, Osako Y, Tanaka M, Hojo M, Hollister SJ (2006) Biomaterials 27:3964

    Article  CAS  Google Scholar 

  83. de Kruijf N, Zhou SW, Li Q, Mai YW (2007) Int J Solids Struct 44:7092

    Article  Google Scholar 

  84. Haug EJ, Choi KK, Komkov V (1986) Design sensitivity analysis of structural systems. Academic Press, Orlando

    Google Scholar 

  85. Bendsoe MP, Guedes JM, Haber RB, Pedersen P, Taylor JE (1994) J Appl Mech 61:930

    Article  Google Scholar 

  86. Fujii D, Chen BC, Kikuchi N (2001) Int J Numer Meth Eng 50:2031

    Article  Google Scholar 

  87. Neves MM, Rodrigues H, Guedes JM (2000) Comput Struct 76:421

    Article  Google Scholar 

  88. Zhang WH, Sun SP (2006) Int J Numer Meth Eng 68:993

    Article  Google Scholar 

  89. Sigmund O (2000) J Mech Phys Solids 48:397

    Article  Google Scholar 

  90. Gibiansky LV, Sigmund O (2000) J Mech Phys Solids 48:461

    Article  Google Scholar 

  91. Sigmund O, Torquato S (1997) J Mech Phys Solids 45:1037

    Article  CAS  Google Scholar 

  92. Huang X, Radman A, Xie YM (2011) Comput Mater Sci 50:1861

    Article  Google Scholar 

  93. Wadley HNG, Fleck NA, Evans AG (2003) Compos Sci Technol 63:2331

    Article  CAS  Google Scholar 

  94. Liu T, Deng ZC, Lu TJ (2006) Int J Solids Struct 43:7891

    Article  CAS  Google Scholar 

  95. Liu L, Yan J, Cheng G (2008) Comput Struct 86:1417

    Article  Google Scholar 

  96. Chen YH, Zhou SW, Li Q (2010) Comput Struct 88:806

    Article  Google Scholar 

  97. Huang X, Xie YM (2008) Struct Multidiscip Optim 36:597

    Article  Google Scholar 

  98. Bacigalupo A, Gambarotta L (2010) Zamm Z Angew Math Mech 90:796

    Article  Google Scholar 

  99. Kaczmarczyk L, Pearce CJ, Bicanic N (2010) Comput Struct 88:1383

    Article  Google Scholar 

  100. Kaczmarczyk L, Pearce CJ, Bicanic N (2008) Int J Numer Meth Eng 74:506

    Article  Google Scholar 

  101. Yuan X, Tomita Y, Andou T (2008) Mech Res Commun 35:126

    Article  Google Scholar 

  102. Diaz AR, Benard A (2003) Int J Numer Meth Eng 57:301

    Article  Google Scholar 

  103. Benard A, Diaz AR (2001) Commun Numer Methods Eng 17:543

    Article  Google Scholar 

  104. Barbarosie C (2003) Comput Mech 30:235

    Article  Google Scholar 

  105. Barbarosie C, Toader AM (2010) Struct Multidiscip Optim 40:393

    Article  Google Scholar 

  106. Barbarosie C, Toader AM (2010) Struct Multidiscip Optim 40:381

    Article  Google Scholar 

  107. Qi H, Kikuchi N, Mazumder J (2004) Struct Multidiscip Optim 26:326

    Article  Google Scholar 

  108. Hollister SJ, Brennan JM, Kikuchi N (1994) J Biomech 27:433

    Article  CAS  Google Scholar 

  109. Lin CY, Hsiao CC, Chen PQ, Hollister SJ (2004) Spine 29:1747

    Article  Google Scholar 

  110. Lin CY, Kikuchi N, Hollister SJ (2004) J Biomech 37:623

    Article  Google Scholar 

  111. Lin CY, Schek RM, Mistry AS, Shi XF, Mikos AG, Krebsbach PH, Hollister SJ (2005) Tissue Eng 11:1589

    Article  CAS  Google Scholar 

  112. Lin CY, Wirtz T, LaMarca F, Hollister SJ (2007) J Biomed Mater Res, Part A 83A:272

    Article  CAS  Google Scholar 

  113. Yin LZ, Elliott DM (2005) J Biomech 38:1674

    Article  Google Scholar 

  114. Sturm S, Zhou S, Mai Y-W, Li Q (2010) J Biomech 43:1738

    Article  Google Scholar 

  115. Steven GP, Li Q, Xie YM (2000) Comput Mech 26:129

    Article  Google Scholar 

  116. Chen YH, Zhou SW, Li Q (2009) Int J Mod Phys B 23:1345

    Article  Google Scholar 

  117. Torquato S, Hyun S (2001) J Appl Phys 89:1725

    Article  CAS  Google Scholar 

  118. Hyun S, Torquato S (2001) J Mater Res 16:280

    Article  CAS  Google Scholar 

  119. Bruggeman DAG (1935) Ann Phys 2(4):636

    Article  Google Scholar 

  120. Torquato S, Hyun S, Donev A (2002) Phys Rev Lett 89:266601

    Article  CAS  Google Scholar 

  121. Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties. Springer, Berlin

    Google Scholar 

  122. Song YS, Youn JR (2006) Carbon 44:710

    Article  CAS  Google Scholar 

  123. Zhou S, Li Q (2008f) Numerical Heat Transf A 54:686

    Article  Google Scholar 

  124. Torquato S, Donev A (2004) Proc R Soc Lond A 460:1849

    Article  Google Scholar 

  125. Vigdergauz S (1999) Struct Optim 17:104

    Google Scholar 

  126. Vigdergauz S (1994) J Appl Mech 61:390

    Article  Google Scholar 

  127. Lakes R (1987) Science 235:1038

    Article  CAS  Google Scholar 

  128. Greaves GN, Greer AL, Lakes RS, Rouxel T (2011) Nat Mater 10:823

    Article  CAS  Google Scholar 

  129. Lakes R (1991) J Mater Sci 26:2287. doi:10.1007/BF01130170

    Article  Google Scholar 

  130. Yang W, Li ZM, Shi W, Xie BH, Yang MB (2004) J Mater Sci 39:3269. doi:10.1023/B:JMSC.0000026928.93231.e0

    Article  CAS  Google Scholar 

  131. Baughman RH, Shacklette JM, Zakhidov AA, Stafstrom S (1998) Nature 392:362

    Article  CAS  Google Scholar 

  132. Hirotsu S (1991) J Chem Phys 94:3949

    Article  CAS  Google Scholar 

  133. Alderson A, Alderson KL (2007) Proc Inst Mech Eng G 221:565

    Article  CAS  Google Scholar 

  134. Alderson KL, Coenen VL (2008) Phys Status Solidi B 245:489

    Article  CAS  Google Scholar 

  135. Bezazi A, Scarpa F (2007) Int J Fatigue 29:922

    Article  CAS  Google Scholar 

  136. Alderson KL, Alderson A, Smart G, Simkins VR, Davies PJ (2002) Plast, Rubber Compos 31:344

    Article  CAS  Google Scholar 

  137. Larsen UD, Sigmund O, Bouwstra S (1997) J Microelectromech Syst 6:99

    Article  Google Scholar 

  138. Chen BC, Silva ECN, Kikuchi N (2001) Int J Numer Meth Eng 52:23

    Article  Google Scholar 

  139. Sigmund O, Torquato S, Aksay IA (1998) J Mater Res 13:1038

    Article  CAS  Google Scholar 

  140. Sigmund O, Torquato S (1999) Smart Mater Struct 8:365

    Article  CAS  Google Scholar 

  141. Silva ECN, Ono Fonseca JS, de Espinosa FM, Crumm AT, Brady GA, Halloran JW, Kikuchi N (1999) Arch Comput Method Eng 6:117

    Article  Google Scholar 

  142. Silva ECN, Ono Fonseca JS, Kikuchi N (1998) Comput Methods Appl Mech Eng 159:49

    Article  Google Scholar 

  143. Silva ECN, Ono Fonseca JS, Kikuchi N (1997) Comput Mech 19:397

    Article  Google Scholar 

  144. Xianfan C, Shutian L (2006) Acta Mech Solida Sin 19:95

    Google Scholar 

  145. Horrigan EJ, Smith CW, Scarpa FL, Gaspar N, Javadi AA, Berger MA, Evans KE (2009) Mech Mater 41:919

    Article  Google Scholar 

  146. Paulino GH, Silva ECN, Le CH (2009) Struct Multidiscip Optim 38:469

    Article  Google Scholar 

  147. Sigmund O, Torquato S (1996) Appl Phys Lett 69:3203

    Article  CAS  Google Scholar 

  148. Sigmund O (2001) Comput Methods Appl Mech Eng 190:6605

    Article  Google Scholar 

  149. Jung T, Torquato S (2005) Phys Rev E 72:056319

    Article  CAS  Google Scholar 

  150. Torquato S (1990) Phys Rev Lett 64:2644

    Article  Google Scholar 

  151. Gevertz J, Torquato S (2009) Phys Rev E 80:011102

    Article  CAS  Google Scholar 

  152. Jung Y, Chu KT, Torquato S (2007) J Comput Phys 223:711

    Article  Google Scholar 

  153. Guest JK, Prevost JH (2007) Comput Methods Appl Mech Eng 196:1006

    Article  Google Scholar 

  154. Evgrafov A (2005) Appl Math Optim 52:263

    Article  Google Scholar 

  155. Chen Y, Zhou S, Cadman J, Li Q (2010) Biotechnol Bioeng 107:737

    Article  CAS  Google Scholar 

  156. Kapellos GE, Alexiou TS, Payatakes AC (2010) Math Biosci 225:83

    Article  Google Scholar 

  157. Chen Y, Zhou S, Li Q (2011) Biomaterials 32:5003

    Article  CAS  Google Scholar 

  158. Chen Y, Zhou S, Li Q (2011) Acta Biomater 7:1140

    Article  CAS  Google Scholar 

  159. Zhou S, Li W, Chen Y, Sun G, Li Q (2011) Acta Mater 59:2624

    Article  CAS  Google Scholar 

  160. Sakai K, Mohtai M, Iwamoto Y (1998) Calcif Tissue Int 63:515

    Article  CAS  Google Scholar 

  161. Cioffi M, Boschetti F, Raimondi MT, Dubini G (2006) Biotechnol Bioeng 93:500

    Article  CAS  Google Scholar 

  162. Chen HB, Sundararaj U, Nandakumar K (2004) Polym Eng Sci 44:1258

    Article  CAS  Google Scholar 

  163. Chen YH, Schellekens M, Zhou SW, Cadman J, Li W, Appleyard R, Li Q (2011) J Biomech Eng 133:081008-1

    Google Scholar 

  164. Amada S, Untao S (2001) Compos B Eng 32:451

    Article  Google Scholar 

  165. Silva ECN, Walters MC, Paulino GH (2006) J Mater Sci 41:6991. doi:10.1007/s10853-006-0232-3

    Article  CAS  Google Scholar 

  166. Nogata F, Takahashi H (1995) Compos Eng 5:743

    Article  Google Scholar 

  167. Coelho PG, Fernandes PR, Rodrigues HC (2011) J Biomech 44:321

    Article  Google Scholar 

  168. Coelho PG, Fernandes PR, Rodrigues HC, Cardoso JB, Guedes JM (2009) J Biomech 42:830

    Article  CAS  Google Scholar 

  169. Mori T, Tanaka K (1973) Acta Metall 21:571

    Article  Google Scholar 

  170. Hill R (1965) J MechPhys Solids 13:213

    Article  Google Scholar 

  171. Reiter T, Dvorak GJ, Tvergaard V (1997) J Mech Phys Solids 45:1281

    Article  CAS  Google Scholar 

  172. Almeida SRM, Paulino GH, Silva ECN (2010) Struct Multidiscip Optim 42:855

    Article  Google Scholar 

  173. Guest JK, Prevost JH (2006) Int J Solids Struct 43:7028

    Article  Google Scholar 

  174. Yang XY, Huang X, Xie YM, Li Q, Rong JH (2011) Iran Univ Sci Technol 1(3):397

    Google Scholar 

  175. Hollister SJ (2005) Nat Mater 4:518

    Article  CAS  Google Scholar 

  176. Challis VJ, Roberts AP, Grotowski JF, Zhang LC, Sercombe TB (2010) Adv Eng Mater 12:1106

    Article  CAS  Google Scholar 

  177. Hollister SJ (2011) JOM 63:56

    Article  Google Scholar 

  178. Hollister SJ, Maddox RD, Taboas JM (2002) Biomaterials 23:4095

    Article  CAS  Google Scholar 

  179. Lee M, Dunn JCY, Wu BM (2005) Biomaterials 26:4281

    Article  CAS  Google Scholar 

  180. Cadman J, Chen Y, Zhou S, Li Q (2010) Mater Sci Forum 654–656:2229

    Article  CAS  Google Scholar 

  181. Darwin CG (1914) Philos Mag 27:675

    Article  CAS  Google Scholar 

  182. Cox SJ, Dobson DC (1999) SIAM J Appl Math 59:2108

    Article  Google Scholar 

  183. Sigmud O, Jensen JS (2003) Philos Trans R Soci A 361:1001

    Article  Google Scholar 

  184. Halkjær S, Sigmund O, Jensen JS (2006) Struct Multidiscip Optim 32:263

    Article  Google Scholar 

  185. Sigmund O, Hougaard K (2008) Phys Rev Lett 100:153904

    Article  CAS  Google Scholar 

  186. Veselago VG (1968) Sov Phys USPEKI 10:509

    Article  Google Scholar 

  187. Jamaian SS, Mackay TG (2010) J Nanophoton 4:041535

    Article  Google Scholar 

  188. Liu YH, Chang CC (2010) J Phys Soc Jpn 79:014401

    Article  CAS  Google Scholar 

  189. Zhou SW, Li W, Li Q (2010) IEEE Trans Microw Theory Tech 58:910

    Article  Google Scholar 

  190. Diaz AR, Sigmund O (2010) Struct Multidiscip Optim 41:163

    Article  Google Scholar 

  191. Zhou SW, Li W, Sun GY, Li Q (2010) Opt Express 18:6693

    Article  CAS  Google Scholar 

  192. Zhou SW, Li W, Li Q (2010) J Comput Phys 229:6915

    Article  CAS  Google Scholar 

  193. Yamasaki S, Nomura T, Sato K, Michishita N, Yamada Y, Kawamoto A (2012) Int J Numer Meth Eng 89:1272

    Article  Google Scholar 

  194. Xu WK, Liu ST, Dong YZ (2010) J Wuhan Univ Technol 25:282

    Article  Google Scholar 

  195. Wang W, Xu WK, Hai H (2011) Eur Phys J 53

  196. Zhao YX, Chen F, Shen Q, Liu QW, Zhang LM (2011) Opt Express 19:11605

    Article  CAS  Google Scholar 

  197. Chen PY, Chen CH, Wang H, Tsai JH, Ni WX (2008) Opt Express 16:12806

    Article  CAS  Google Scholar 

  198. Otomori M, Yamada T, Izui K, Nishiwaki S, Andkjær J (2012) Comput Methods Appl Mech Eng 237–240:192

  199. Liu N, Guo HC, Fu LW, Kaiser S, Schweizer H, Giessen H (2008) Nat Mater 7:31

    Article  CAS  Google Scholar 

  200. Huang XD, Xie YM, Jia B, Li Q, Zhou S (2012) Struct Multidiscip Optim. doi:10.1007/s00158-012-0766-8

  201. Forestiere C, Donelli M, Walsh GF, Zeni E, Miano G, Negro LD (2010) Opt Lett 35:133

    Article  Google Scholar 

  202. Soh H, Yoo J (2011) J Electromagn Waves Appl 25:629

    Article  Google Scholar 

  203. Andkjær J, Nishiwaki S, Nomura T, Sigmund O (2010) J Opt Soc Am B 27:1828

    Article  CAS  Google Scholar 

  204. Jensen JS, Sigmund O (2011) Laser Photonics Rev 5:308

    Article  CAS  Google Scholar 

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Acknowledgements

The financial support was from Australian Research Council (ARC) is acknowledged. The first author is also a grateful recipient of a University Postgraduate Award (UPA) at The University of Sydney.

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Authors and Affiliations

  1. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    Joseph E. Cadman & Qing Li

  2. Innovative Structures Group, School of Civil, Environmental and Chemical Engineering, RMIT University, GPO Box 2476, Melbourne, 3001, Australia

    Shiwei Zhou

  3. Institute of Mechanical, Process and Energy Engineering (IMPEE), School of Engineering and Physical Sciences, Heriot-watt University, Edinburgh, UK

    Yuhang Chen

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  1. Joseph E. Cadman
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Correspondence to Qing Li.

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Cadman, J.E., Zhou, S., Chen, Y. et al. On design of multi-functional microstructural materials. J Mater Sci 48, 51–66 (2013). https://doi.org/10.1007/s10853-012-6643-4

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