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PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM 总被引:1,自引:0,他引:1 下载免费PDF全文
The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase. 相似文献
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With the trends in miniaturization, and particularly the introduction of micro- and nano-electro-mechanical system,piezoelectric materials used in microelectronic devices are deposited usually in the form of thin film on elastic substrates.In this work, the bending of a bilayer comprising a piezoelectric film deposited on an elastic substrate, due to the mismatch,is investigated. An analytic formula relating the curvature of the bilayer to the mismatch, the electroelastic constants and the film thickness is obtained, and from this formula, a transverse piezoelectric constant d_31 can be estimated. Meanwhile the influence of electromechanical coupling coefficient on the curvature is discussed. 相似文献
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IntroductionQuasicrystalasanewstructureofsolidmatter[1,2 ]bringsprofoundnewideastothetraditionalcondensedmatterphysicsandencouragesconsiderabletheoreticalandexperimentalstudiesonthephysicalandmechanicalpropertiesofthematerial,includingtheelasticitytheoryofthequasicrystal,manyvaluableresultsweregiven[3~ 5 ].Defectsinthematerialwereobservedsoonafterthediscoveryofthequasicrystal[6 ,7].Cracksareonetypeofdefects,theirexistencegreatlyinfluencesthephysicalandmechanicalpropertiesofthequasicrystalinem… 相似文献
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Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments. 相似文献
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A method for analyzing the elasticity problem of cubic quasicrystal is developed. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the solutions of elastic field of cubic quasicrystal with a penny-shaped crack are obtained, and the stress intensity factor and strain energy release rate are determined. 相似文献
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IntroductionThediscoveryofquasicrystalaround 1 984 [1,2 ,3]issignificantbreakthroughforcondensedmatterphysicsinrecentyears.Thequasiperiodicsymmetryofsolidpresentsgreattheoreticalsignificance .Numerousquasicrystallinematerialswithstablepropertywereproduced ,thi… 相似文献