表面效应对SV波诱发的纳米孔洞周围弹性波散射的影响
|
摘要
基于表面弹性理论和经典弹性理论,用位移势函数法、波函数展开法和弹性波的多重散射理论,研究随机排列的多个纳米孔洞周围的弹性波散射和动应力集中问题,求得无限大空间中在一组纳米圆柱孔洞附近由平面剪切波(SV波)诱发的应力场.分析当任意两个相邻孔洞之间的距离都相等时,表面效应对孔洞周围动应力集中的影响.结果表明,纳米圆柱孔洞周围的动应力集中不仅和表面效应有关,而且和孔洞之间的距离有关.
Based on surface elasticity theory and classic elasticity theory and employing displacement potential function method,wave function developing method,and multiple scattering theory of elastic wave,multiple scattering of elastic wave at a set of randomly arranged nano-holes and dynamic stress concentration thereby are investigated,and the stress field at the set of cylindric nano-holes induced by planar shearing wave(SV wave)in infinite space is found.When the distance between arbitrary two adjacent holes is identical,the influence of surface effect on the dynamic stress concentration at the hole is analyzed.The results show that the dynamic stress concentration will depend not only on the surface effect but also on the interval of the holes.
Based on surface elasticity theory and classic elasticity theory and employing displacement potential function method,wave function developing method,and multiple scattering theory of elastic wave,multiple scattering of elastic wave at a set of randomly arranged nano-holes and dynamic stress concentration thereby are investigated,and the stress field at the set of cylindric nano-holes induced by planar shearing wave(SV wave)in infinite space is found.When the distance between arbitrary two adjacent holes is identical,the influence of surface effect on the dynamic stress concentration at the hole is analyzed.The results show that the dynamic stress concentration will depend not only on the surface effect but also on the interval of the holes.
引文
[1]MOW C C,PAO Y H.The diffraction of elastic waves and dynamic stress concentrations[M].New York:The Rand Corporation,1973.
[2]HASHEMINEJAD S M,BADSAR S A.Elastic wave scattering by two spherical inclusions in a poroelastic medium[J].Journal of Engineering Mechanics,2005,131(9):953-965.
[3]FANG X Q,HU C,HUANG W H.Scattering of elastic waves and dynamic stress in two-particle reinforced composite system[J].Mechanics of Materials,2007,39(6):538-547.
[4]LAKHTAKIA A,VARADAN V V,VARADAN V K.Reflection characteristics of an elastic slab containing aperiodic array of circular elastic cylinders:P and SV wave analysis[J].J Acoust Soc Am,1988,83(4):1267-1275.
[5]TWERSKY V.Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders[J].The Journal of the Acoustical Society of America,1952,24:42-46.
[6]WANG X,SUDAK L J.Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface[J].Waves in Random and Complex Media,2007,17(2):159-187.
[7]DAVIES J H.Elastic and piezoelectric fields around a buried quantum dot A simple picture[J].J Appl Phys,1998,84:1358-1365.
[8]WONG E W,SHEEHAN P E,LIEBER C M.Nanobeam mechanics:elasticity,strength,and toughness of nanorods and nanotubes[J].Science,1997,277(5334):1971-1975.
[9]GURTIN M E.A general theory of curved deformable interfaces in solids at equilibrium[J].Philosophical Magazine A,1998,78(5):1093-1109.
[10]GURTIN M E,MURDOCH A L.A continuum theory of elastic material surfaces[J].Arch Rat Mech Anal,1975,57:291-323.
[11]WANG G F,WANG T J.Deformation around a nanosized elliptical hole with surface effect[J].Appl Phys Lett,2006,89:1619011-1619013.
[12]OU Z Y,WANG G F,WANG T J.Elastic fields around a nanosized spheroidal cavity under arbitrary uniform remote loadings[J].Euro J Mech A,2009,28:110-120.
[13]HU Y F,LI Q,SHI J P.Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane[J].Journal of Applied Physics,2013,112:0343021-0343026.
[14]WANG G F.Multiple diffraction of plane compressional waves by two circular cylindrical holes with surface effects[J].J Appl Phys,2009,105:0135071-0135076.
[15]ZHANG Q F,WANG G F,SCHIAVONE P.Diffraction of plane compressional waves by an array of nanosized cylindrical holes[J].J Appl Mech,2011,78:0210031-0210036.
[2]HASHEMINEJAD S M,BADSAR S A.Elastic wave scattering by two spherical inclusions in a poroelastic medium[J].Journal of Engineering Mechanics,2005,131(9):953-965.
[3]FANG X Q,HU C,HUANG W H.Scattering of elastic waves and dynamic stress in two-particle reinforced composite system[J].Mechanics of Materials,2007,39(6):538-547.
[4]LAKHTAKIA A,VARADAN V V,VARADAN V K.Reflection characteristics of an elastic slab containing aperiodic array of circular elastic cylinders:P and SV wave analysis[J].J Acoust Soc Am,1988,83(4):1267-1275.
[5]TWERSKY V.Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders[J].The Journal of the Acoustical Society of America,1952,24:42-46.
[6]WANG X,SUDAK L J.Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface[J].Waves in Random and Complex Media,2007,17(2):159-187.
[7]DAVIES J H.Elastic and piezoelectric fields around a buried quantum dot A simple picture[J].J Appl Phys,1998,84:1358-1365.
[8]WONG E W,SHEEHAN P E,LIEBER C M.Nanobeam mechanics:elasticity,strength,and toughness of nanorods and nanotubes[J].Science,1997,277(5334):1971-1975.
[9]GURTIN M E.A general theory of curved deformable interfaces in solids at equilibrium[J].Philosophical Magazine A,1998,78(5):1093-1109.
[10]GURTIN M E,MURDOCH A L.A continuum theory of elastic material surfaces[J].Arch Rat Mech Anal,1975,57:291-323.
[11]WANG G F,WANG T J.Deformation around a nanosized elliptical hole with surface effect[J].Appl Phys Lett,2006,89:1619011-1619013.
[12]OU Z Y,WANG G F,WANG T J.Elastic fields around a nanosized spheroidal cavity under arbitrary uniform remote loadings[J].Euro J Mech A,2009,28:110-120.
[13]HU Y F,LI Q,SHI J P.Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane[J].Journal of Applied Physics,2013,112:0343021-0343026.
[14]WANG G F.Multiple diffraction of plane compressional waves by two circular cylindrical holes with surface effects[J].J Appl Phys,2009,105:0135071-0135076.
[15]ZHANG Q F,WANG G F,SCHIAVONE P.Diffraction of plane compressional waves by an array of nanosized cylindrical holes[J].J Appl Mech,2011,78:0210031-0210036.