非线性弹性薄膜表面效应的尺寸相关性研究
1.中国科学技术大学力学和机械工程系中科院材料力学行为与设计重点实验室,合肥 230027
2.安徽理工大学化工系,安徽 淮南 232001
下一篇 上一篇
摘要
在Mindlin假设的前提下,考虑了几何非线性条件及表面效应的影响,建立了纳米尺度下尺寸相关的板状各向同性弹性薄膜模型;从哈密尔顿变分原理出发,导出了薄膜的控制方程,用公式明确阐述了由表面张力引起的符合经典板理论且与薄膜变形相关的残余膜力和弯矩;通过微小尺寸薄膜弯曲的算例,说明了表面效应与薄膜厚度的相关性,当薄膜厚度等于或者小于其内禀尺度时,表面效应对薄膜厚度表现出很强的敏感性。
参考文献
[ 1 ] Gleiter H.Nanostructured materials:basic concepts andmicrostructure[J].Acta Materialia, 2000, 48 (1) :1~29
[ 2 ] Ibach H.The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures[J].Surface Science Reports, 1997, 29 (5, 6) :195~263
[ 3 ] Lavrik N V, Sepaniak M J, Datskos P G.Cantilevertransducers as a platform for chemical and biologicalsensors[J].Review of Scientific Instruments, 2004, 75 (7) :2229~2253
[ 4 ] Chia C Y. Nonlinear Analysis of Plates [M]. New York: McGraw-Hill, 1980
[ 5 ] Reddy J N. Theory and Ananlysis of Elastic Plates [M]. Philadelphia: Taylor & Francis, 1999
[ 6 ] Timoshenko S, Woinowsky-Krieger S. Theory of Plates and Shells [M]. New York: McGraw-Hill, 1959
[ 7 ] Muller P, Saul A.Elastic effects on surface physics[J].Surface Science Reports, 2004, 54 (5—8) :157~258
[ 8 ] Andreussi F, Gurtin M E.On the wrinkling of a freesurface[J].Journal of Applied Physics, 1977, (48) :3798~3799
[ 9 ] Gurtin M E, Murdoch A I.Addenda to our paper:acontinuum theory of elastic material surfaces[J].ArchRat Mech Anal, 1975, (59) :389~390 链接1
[10] Gurtin M E, Murdoch A I.Surface stress in solids[J].International Journal of Solids And Structures, 1978, (14) :431~440
[11] Gurtin M E. Effect of surface stress on wave propagation in solids [J]. Journal of Applied Physics, 1976, (47) : 441
[12] Gurtin M E, Murdoch A I.A continuum theory of elasticmaterial surfaces[J].Archive for Rational Mechanics andAnalysis, 1975, (57) :291~323 链接1
[13] Miller R E, Shenoy V B.Size-dependent elastic propertiesof nanosized structural elements[J].Nanotechnology, 2000, 11 (3) :139~147
[14] He L H, Lim C W, Wu B S.Acontinuum model for size-dependent deformation of elastic films of nano-scalethickness[J].International Journal of Solids andStructures, 2004, 41 (3—4) :847~857
[15] Lim C W, He L H.Size-dependent nonlinear response ofthin elastic films with nano-scale thickness[J].International Journal of Mechanical Sciences, 2004, 46 (11) :1715~1726
[16] Sharma P, Ganti S.Size-dependent Eshelby’s tensor forembedded nano-inclusions incorporating surface/interfaceenergies[J].Journal of Applied Mechanics-Transactionsof the Asme, 2004, 71 (5) :663~671
[17] Sharma P, Ganti S, Bhate N.Effect of surfaces on thesize-dependent elastic state of nano-inhomogeneities[J].Applied Physics Letters, 2003, 82 (4) :535~537
[18] Shenoy V B.Size-dependent rigidities of nanosizedtorsional elements.[J].International Journal of Solids andStructures, 2002, 39 (15) :4039~4052
[19] Sun C T, Zhang H T.Size-dependent elastic moduli ofplatelike nanomaterials.[J].Journal of Applied Physics, 2003, 93 (2) :1212~1218
[20] Wong E W, Sheehan P E, Lieber C M.Nanobeammechanics:elasticity, strength, and toughness of nanorodsand nanotubes.[J].Science, 1997, 277 (5334) :1971~1975
[21] Jung S C, Kim S J, Imaishi N, et al.Effect of TiO2thinfilm thickness and specific surface area by low-pressuremetal-organic chemical vapor deposition on photocatalyticactivities[J].Applied Catalysis B-Environmental, 2005, 55 (4) :253~257
[22] Puri V, Salunkhe S M, Puranik M M.Size dependent leafoverlay effects on thin film microstrip patch antenna[J].Microelectronics International, 2005, 22 (1) :21~25
[23] Spaepen F.interfaces and stresses in thin films[J].ActaMaterialia, 2000, 48 (1) :31~42
[24] Zhang Z Y, Detch J, Metiu H.Surface-roughness in thin-film growth—the effect of mass-transport between layers[J].Physical Review B, 1993, 48 (7) :4972~4975
[25] Zheng D W, Jia Z Y, Liu C Y, et al.Size dependentdewetting and sideband reaction of eutectic SnPb on Au/Cu/Cr multilayered thin film[J].Journal of MaterialsResearch, 1998, 13 (5) :1103~1106
[26] Liang L H, Li J C, Jiang Q.Size-dependent elasticmodulus of Cu and Au thin films[J].Solid StateCommunications, 2002, 121 (8) :453~455