Abstract
This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements, including nanoparticles, nanowires, nanobeams, and nanofilms, and heterogeneous materials containing nanoscale inhomogeneities. It begins with the fundamental formulations of surface mechanics of solids, including the definition of surface stress as a surface excess quantity, the surface constitutive relations, and the surface equilibrium equations. Then, it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements, as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption. Afterwards, the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing. The effect of surface elasticity on the diffraction of elastic waves is elucidated. Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations, finite element approaches have been developed for heterogeneous materials with the surface stress. Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips. The solutions of crack problems taking into account surface stress effects are also included. Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention. The advances in this topic are inevitably delineated. Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications. Some most recent work is reviewed. Finally, some challenges are pointed out. They include the characterization of surfaces and interfaces of real nanomaterials, experimental measurements and verification of mechanical parameters of complex surfaces, and the effects of the physical and chemical processes on the surface properties, etc.
Similar content being viewed by others
References
Gibbs, J.W., The Scientific Papers of J. Willard Gibbs, Vol.1. London: Longmans-Green, 1906.
Cammarata, R.C., Surface and interface stress effects on interfacial and nanostructured materials. Materials Science and Engineering, 1997, A237: 180–184.
Shuttleworth, R., The surface tension of solids. Proceedings of the Physical Society A, 1950, 63: 444–457.
Herring, C., The use of classical macroscopic concepts in surface energy problems. In: Structure and Properties of Solid Surfaces (Gomer, R. and Smith, C.S. eds.), pp. 5–81. Chicago: The University of Chicago Press, 1953.
Orowan, E., Surface energy and surface tension in solids and liquids. Proceedings of the Royal Society, 1970, A316: 473–491.
Murr, L.E., Interfacial Phenomena in Metals and Alloys. London: Addison- Wesley, 1975.
Cahn, J.W., Thermodynamics of solid and fluid surfaces. In: Interfacial Segregation (Johnson, W.C. and Blakely, J.M. eds.), pp. 3–23. Ohio: Americal Society for Metals, Metals Park, 1978.
Cammarata, R.C., Surface and interface stresses effects in thin films. Progress in Surface Science, 1994, 46: 1–38.
Ibach, H., The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures. Surface Science Reports, 1997, 29: 195–263.
Haiss, W., Surface stress of clean and adsorbate-covered solids. Reports on Progress in Physics, 2001, 64: 591–648.
Muller, P. and Saul, A., Elastic effects on surface physics. Surface Science Reports, 2004, 54: 157–258.
Rusanov, A.I., Surface thermodynamics revisited. Surface Science Reports, 2005, 58: 111–239.
Kramer, D. and Weissmuller, J., A note on surface stress and surface tension and their interrelation via Shuttleworths equation and the Lippmann equation. Surface Science, 2007, 601: 3042–3051.
Sun, C.Q., Thermo-mechanical behavior of low-dimensional systems: The local bond average approach. Progress in Materials Science, 2009, 54: 179–307.
Pomeau, Y. and Villermaux, E., Two hundred years of capillarity research. Physics Today, 2006, March: 39-44.
Laplace, P.S., Mecanique Celeste, Vol.4. Courcier, Paris, 1805.
Young, T., An essay on the cohesion of fluids. Proceedings of the Royal Society, 1805, A95: 65–87.
Lennard-Jones, J.E. and Dent, B.M., The change in lattice spacing at a crystal boundary. Proceedings of the Royal Society, 1928, A121: 247–259.
Nicolson, M.M., Surface tension in ionic crystals. Proceedings of the Royal Society, 1955, A228: 490–510.
Vermaak, J.S., Mays, C.W. and Kuhlmann-Wilsdorf, D., On surface stress and surface tension. I. Theoretical considerations. Surface Science, 1968, 12: 128–133.
Gurtin, M.E. and Murdoch, A.I., A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 1975, 57: 291–323.
Gurtin, M.E. and Murdoch, A.I., Surface stress in solids. International Journal of Solids and Structures, 1978, 14: 431–440.
Steigmann, D.J. and Ogden, R.W., Elastic surface-substrate interactions. Proceedings of the Royal Society, 1999, A455: 437–474.
Weissmuller, J. and Cahn, J.W., Mean stresses in microstructure due to interface stresses: a generalization of a capillary equation for solids. Acta Materialia, 1997, 45: 1899–1906.
Gurtin, M.E., Weissmuller, J. and Larche, F., A general theory of curved deformable interfaces in solids at equilibrium. Philisophical Magazine A, 1998, A78: 1093–1109.
Rottman, C., Landau theory of coherent interphase interface. Physical Review B, 1988, 38: 12031–12034.
Stoney, G.C., The tension of metallic films deposited by electrolysis. Proceedings of the Royal Society, 1909, A82: 172–175.
Cammarata, R.C. and Sieradzki, K., Effect of surface stress on the elastic moduli of thin films and super-lattices. Physical Review Letters, 1989, 62: 2005–2008.
Fartash, A., Fullerton, E.E., Schuller, I.K., Bobbin, S. E., Wagner, J.W., Cammarata, R.C., Kumar, S. and Grimsditch, M., Evidence for the supermodulus effect and enhanced hardness in lettalic superlattices. Physical Review B, 1991, 44: 13760–13763.
Streitz, F.H., Cammarata, R.C. and Sieradzki, K., Surface-stress effects on elastic properties. I. Thin metal films. Physical Review B, 1994, 49:10699–10706.
Streitz, F.H., Cammarata, R.C. and Sieradzki, K., Surface-stress effects on elastic properties. II. Metallic multilayers. Physical Review B, 1994, 49: 10707–10716.
Dingreville, R. and Qu, J., Interfacial excess energy, excess stress and excess strain in elastic solids: Planar interfaces. Journal of the Mechanics and Physics of Solids, 2008, 56: 1944–1954.
Duan, H.L., Wang, J. and Karihaloo, B.L., Theory of elasticity at the nano-scale. Advances in Applied Mechanics, 2009, 42: 1–68.
Theocaris, P.S., The Mesophase Concept in Composites. Berlin: Springer Verlag, 1987.
Zhang, T.-Y. and Hack, J.E., On the elastic stiffness of grain boundaries. Physica Status Solidi A, 1992, 131: 437–443.
Schiotz, J., Di Tolla, F.D. and Jacobsen, K.W., Softening of nanocrystalline metals at very small grain sizes. Nature, 1998, 391: 561–563.
Wei, Y.J. and Anand, L., Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals. Journal of the Mechanics and Physics of Solids, 2004, 52: 2587–2616.
Weng, G.J. A composite model of nanocrystalline materials. In: Mechanical Properties of Nanocrystalline Materials(Li, J.C.M. ed.). Hackensack, NJ: Pan Stanford Publishing, C/o World Scientific Publishing Co., Inc., 2010.
Benveniste, Y., The effective mechanical behaviour of composite materials with imperfect contact between the constituents. Mechanics of Materials, 1985, 4: 197–208.
Hashin, Z., Thermoelastic properties of particulate composites with imperfect interface. Journal of the Mechanics and Physics of Solids, 1991, 39: 745–762.
Qu, J., The effect of slightly weakened interfaces on the overall elastic properties of composites. Mechanics of Materials, 1993, 14: 269–281.
Zhong, Z. and Meguid, S.A., On the elastic field of a spherical inhomogeneity with an imperfectly bonded interface. Journal of Elasticity, 1997, 46: 91–113.
Wang, G.F., Feng, X.Q., Yu, S.W. and Nan, C.W., Interface effects on effective elastic moduli of nanocrystalline materials. Materials Science and Engineering A, 2003, 363: 1–8.
Jiang, B. and Weng, G.J., A composite model for the grain-size dependence of yield stress of nanograined materials. Metallurgical and Materials Transactions, 2003, A34: 765–772.
Jiang, B. and Weng, G.J., A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials. Journal of the Mechanics and Physics of Solids, 2004, 52: 1125–1149.
Wu, Y.M., Huang, Z.P., Zhong, Y. and Wang, J., Effective moduli of particle-filled composite with inhomogeneous interphase — Part I: bounds. Composites Science and Technology, 2004, 64: 1345–1351.
Zhong, Y., Wang, J., Wu, Y.M. and Huang, Z.P., Effective moduli of particle-filled composite with inhomogeneous interphase — Part II: mapping method and evaluation. Composites Science and Technology, 2004, 64: 1353–1362.
Shen, L.X. and Li, J., Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites. Proceedings of the Royal Society, 2005, A461: 1475–1504.
Duan, H.L., Wang, J., Huang, Z.P. and Zhong, Y., Stress fields of a spheroidal inhomogeneity with an interphase in an infinite medium under remote loadings. Proceedings of the Royal Society, 2005, A461: 1055–1080.
Tan, H., Huang, Y., Liu, C. and Geubelle, P.H., The Moric Tanaka method for composite materials with nonlinear interface debonding. International Journal of Plasticity, 2005, 21: 1890–1918.
Zhang, W.X., Li, L.X. and Wang, T.J., Interphase effect on the strengthening behavior of particle-reinforced metal matrix composites. Computational Materials Science, 2007, 41: 145–155.
Zhu, L.L. and Zheng, X.J., Influence of interface energy and grain boundary on the elastic modulus of nanocrystalline materials. Acta Mechanica, 2010, 213: 223–234.
Rubin, M.B. and Benveniste, Y., A Cosserat shell model for interphases in elastic media. Journal of the Mechanics and Physics of Solids, 2004, 52: 1023–1052.
Benveniste, Y. and Miloh, T., Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials, 2001, 33: 309–323.
Hashin, Z., The interphase/imperfect interface in elasticity with application to coated fiber composites. Journal of the Mechanics and Physics of Solids, 2002, 50: 2509–2537.
Wang, J., Duan, H.L., Zhang, Z. and Huang, Z.P., An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites. International Journal of Mechanical Sciences, 2005, 47: 701–718.
Benveniste, Y., A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. Journal of the Mechanics and Physics of Solids, 2006, 54: 708–734.
Bovik, P., On the modelling of thin interface layers in elastic and acoustic scattering problems. Quarterly Journal of Mechanics and Applied Mathematics, 1994, 47: 17–42.
Nix, W.D. and Gao, H.J., An atomistic interpretation of interface stress. Scripta Materialia, 1998, 39: 1653–1661.
Pan, X.H., Yu, S.W. and Feng, X.Q., Oriented thermomechanics of isothermal planar elastic surfaces under small deformation. Presented at, and to appear in the Proceedings of, the IUTAM Symposium on Surface Effects in the Mechanics of Nanomaterials and Heterostructures. Beijing, August, 2010.
Huang, Z.P. and Wang, J., A theory of hyperelasticity of multi-phase media with surface/interface energy effect. Acta Mechanica, 2006, 182: 195–210.
Huang, Z.P. and Sun, L., Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis. Acta Mechanica, 2007, 190: 151–163.
Wang, J., Duan, H.L., Huang, Z.P. and Karihaloo, B.L., A scaling law for properties of nano-structured materials. Proceedings of the Royal Society, 2006, A462: 1355–1363.
Duan, H.L., Yi, X., Huang, Z.P. and Wang, J., A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part II — application and scaling laws. Mechanics of Materials, 2007, 39: 94–103.
Palla, P.L., Giordano, S. and Colombo, L., Lattice model describing scale effects in nonlinear elasticity of nanoinhomogeneities. Physical Review B, 2010, 81: Art. 214113.
Zhang, T.-Y., Wang, Z.J. and Chan, W.K., Eigenstress model for surface stress of solids. Physical Review B, 2010, 81: Art. 195427.
Green, A.E. and Zerna, W., Theoretical Elasticity. London: Oxford University Press, 1954.
Chu, H.J., Mechanics of semiconductor quantum dot structures. PhD Thesis, Department of Mechanics and Engineering Science, Peking University, 2006.
Povstenko, Y.Z., Theoretical investigation of phenomena caused by heterogeneous surface-tension in solids. Journal of the Mechanics and Physics of Solids, 1993, 41: 1499–1514.
Duan, H.L., Interface effect in mechanics of heterogeneous materials. PhD Thesis, Department of Mechanics and Engineering Science, Peking University, 2005.
Chen, T., Chiu, M.-S. and Weng, C.N., Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. Journal of Applied Physics, 2006, 100: Art. 074308.
Chen, H., Hu, G.K. and Huang, Z.P., Effective moduli for micropolar composite with interface effect. International Journal of Solids and Structures, 2007, 44: 8106–8118.
Sun, L., Wu, Y.M., Huang, Z.P. and Wang, J., Interface effect on the effective bulk modulus of a particle-reinforced composite. Acta Mechanica Sinica (English series), 2004, 20: 676–679.
Huang, Z.P., Wang, Z.Q., Zhao, Y.P. and Wang, J, Influence of particle-size distribution on effective properties of nanocomposites. In: Advances in Heterogeneous Material Mechanics (ICHMM-2008) (Fan, J.H. and Chen, H.B. eds.), pp. 925–932. Pennsylvania: Destech Publications, 2008.
Ru, C.Q., Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions. Science China Physics, Mechanics & Astonomy, 2010, 53: 536–544.
Altenbach, H., Eremeyev, V.A. and Lebedev, L.P., On the existence of solution in the linear elasticity with surface stresses. ZAMM (Journal of Applied Mathematics and Mechanics), 2010, 90: 231–240.
Fisher, F.D., Waitz, T., Vollath, D. and Simha, N.K., On the role of surface energy and surface stress in phase-transforming nanoparticles. Progress in Materials Science, 2008, 53: 481–527.
Dunham, R.S. and Gurtin, M.E., Surface stress and the equilibrium shape of an ealstic crystal. Journal of Applied Physics, 1977, 30: 255–256.
Huang, Z.X., and Zheng, Q.-S., Effects of the surface energy on the lattice contraction and eigen-frequency of a nano-grain. Acta Mechanica Sinica, 1998, 30: 247–251 (in Chinese).
Liang, L.H., Ma, H.S. and Wei, Y.G., Size-dependent elastic modulus and vibration frequency of nanocrystals. Journal of Nanomaterial, 2010, 2011: Art. 670857.
Cammarata, R.C. and Eby, R.K., Effects and measurement of internal surface stresses in materials with ultrafine microstructures. Journal of Materials Research, 1991, 6: 888–890.
Gumbsch, P. and Daw, M.S., Interface stresses and their effects on the elastic moduli of metallic multilayers. Physical Review B, 1991, 44: 3934–3938.
Ruud, J.A., Witvrouw, A. and Spaepen, F., Bulk and interface stresses in silver-nickel multilayered thin films. Journal of Applied Physics, 1993, 74: 2517–2523.
Berger, S. and Spaepen, F., The Ag/Cu interface stress. NanoStructured Materials, 1995, 6: 201–204.
Josell, D., Bonevich, J.E., Shao, I. and Cammarata, R.C., Measuring the interface stress: Silver/nickel interfaces. Journal of Materials Research, 1999, 14: 4358–4365.
Gilbert, B., Huang, F., Zhang, H., Waychunas, G.A. and Banfield, J.F., Nanoparticles: Strained and stiff. Science, 2004, 305: 651–654.
Ouyang, G., Li, X.L., Tang, X. and Yang, G.W., Size-induced strain and stiffness of nanocrystals. Applied Physics Letters, 2006, 89: Art. 031904.
Dingreville, R., Qu, J. and Cherkaoui, M., Surface free energy and its effect on the elastic behavior of nanosized particles, wires and films. Journal of the Mechanics and Physics of Solids, 2005, 53: 1827–1854.
Huang, Z.X., Thomson, P. and Di, S.L., Lattic contraction of a nanoparticle due to the surface tension: A model of elasticity. Journal of Physics and Chemistry of Solids, 2007, 68: 530–535.
Tolman, R.C., The effect of droplet size on surface tension. Journal of Chemical Physics, 1949, 17: 333–337.
Wong, E.W., Sheehan, P.E. and Lieber, C.M., Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes. Science, 1997, 277: 1971–1975.
Miller, R.E. and Shenoy, V.B., Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 2000, 11: 139–147.
Daw, M.S. and Baskes, M.I., Embedded-atom methof: derivation and application to impurities, surfaces, and other defects in metals. Physical Review B, 1984, 29: 6443–6453.
Stillinger, F.H. and Weber, T.A., Computer-simulation of local order in condensed phases of silicon. Physical Review B, 1985, 31: 5262–5271.
Shenoy, V.B., Size-dependent rigidities of nanosized torsional elements. International Journal of Solids and Structures, 2002, 39: 4039–4052.
Cuenot, S., Fretigny, C., Demoustier-Champagne, S. and Nysten, B., Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Physical Review B, 2004, 69: 165410–165413.
Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J. and Yu, D.P., Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Physical Review B, 2006, 73: Art. 235409.
Chen, C.Q., Shi, Y., Zhang, Y.S., Zhu, J. and Yan, Y.J., Size dependence of Youngs modulus in ZnO nanowires. Physical Review Letters, 2006, 96: Art. 075505.
Pirota, K.R., Silva, E.L., Zanchet, D., Navas, D., Vazquez, M., Hernandez-Velez, M. and Knobel, M., Size effect and surface tension measurements in Ni and Co nanowires. Physical Review B, 2007, 76: Art. 233410.
Tan, E.P.S., Zhu, Y., Yu, T., Dai, L., Sow, C.H., Tan, V.B.C. and Lim, C.T., Crystallinity and surface effects on Young’s modulus of CuO nanowires. Applied Physics Letters, 2007, 90: Art. 163112.
Gavan, K.B., Westra, H.J.R., van der Drift, E.W.J.M., Venstra, W.J. and van der Zant, H.S.J., Size-dependent effective Young’s modulus of silicon nitride cantilevers. Applied Physics Letters, 2009, 94: Art. 233108.
Dingreville, R. and Qu, J., A semi-analytical method to compute surface elastic properties. Acta Materialia, 2007, 55: 141–147.
Lee, B. and Rudd, R.E., First-principles study of the Youngs modulus of Si⟨001⟩ nanowires. Physical Review B, 2007, 75: Art. 041305(R).
Wang, G.F. and Li, X.D., Size dependency of the elastic modulus of ZnO nanowires: Surface stress effect. Applied Physics Letters, 2007, 91: Art. 231912.
Wang, G.F. and Li, X.D., Predicting Young’s modulus of nanowires from first-principles calculations on their surface and bulk materials. Journal of Applied Physics, 2008, 104: Art. 113517.
Guo, J.G. and Zhao, Y.P., The size-dependent elastic properties of nanofilms with surface effects. Journal of Applied Physics, 2005, 98: Art. 074306.
Guo, J.G. and Zhao, Y.P., The surface- and size-dependent elastic moduli of nanostructures. Surface Review and Letters, 2007, 14: 667–670.
Guo, J.G. and Zhao, Y.P., The size-dependent bending elastic properties of nanobeams with surface effects. Nanotechnology, 2007, 18: Art. 295701.
Wang, G.F., Feng, X.Q. and Yu, S.W., Surface buckling of a bending microbeam due to surface elasticity. Europhysics Letters, 2007, 77: Art. 44002.
Cao, G.X. and Chen, X., Energy analysis of size-dependent elastic properties of ZnO nanofilms using atomistic simulations. Physical Review B, 2007, 76: Art. 165407.
Cao, G.X. and Chen, X., Size dependence and orientation dependence of elastic properties of ZnO nanofilms. International Journal of Solids and Structures, 2008, 45: 1730–1753.
He, J. and Lilley, C.M., Surface effect on the elastic behavior of static bending nanowires. Nano Letters, 2008, 8: 1798–1802.
Zhu, H.X., The effects of surface and initial stresses on the bending stiffness of nanowires. Nanotechnology, 2008, 19: Art. 405703.
Wang, J.S., Feng, X.Q., Wang, G.F. and Yu, S.W., Twisting of nanowries induced by anisotropic surface stresses. Applied Physics Letters, 2008, 92: 191901.
Ye, H.M. Wang, J.S., Tang, S., Xu, J., Feng, X.Q., Guo, B.H., Xie, X.M., Zhou, J.J., Li, L., Wu, Q. and Chen, G.Q., Surface stress effects on the bending direction and twisting chirality of lamellar crystals of chiral polymer. Macromolecules, 2010, 43: 5762–5770.
Zhang, J.-H., Huang, Q.-A., Yu, H. and Wang, J., The influence of surface effects on size-dependent mechanical properties of silicon nanobeams at finite temperature. Journal of Physics D: Applied Physics, 2009, 42: Art. 045409.
Zheng, X.P., Cao, Y.P., Li, B., Feng, X.Q. and Wang, G.F., Surface effects in various bending-based test methods for measuring the elastic property of nanowires. Nanotechnology, 2010, 21: Art. 205702.
Wang, Z.Q., Zhao, Y.P. and Huang, Z.P., The effects of surface tension on the elastic properties of nano structures. International Journal of Engineering Science, 2010, 48: 140–150.
Huang, G.Y. and Yu, S.W., Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Physica Status Solidi (b), 2006, 243: R22–R24.
Pan, X.H., Yu, L., Yu, S.W. and Feng, X.Q., A continuum theory for nanosized piezoelectric and piezomagnetic solids with surface effects. In: Proceedings of the 14th International Symposium on Applied Electromagnetics and Mechanics, September 20–24, 2009, Xi’an, China. Eds. by Z. Chen et al., 2009, 533-534.
Wang, G.F. and Feng, X.Q., Effect of surface stresses on the vibration and buckling of piezoelectric nanowires. Europhysics Letters, 2010, 91: Art. 56007.
Zhu, L.L., Qiao, L. and Zheng, X.J., Molecular dynamics simulation of the elastic properties of metal nanowires in a transverse electric field. Nanotechnology, 2007, 18: Art. 385703.
Zheng, X.J., and Zhu, L.L., Theoretical analysis of electric field effect on Young’s modulus of nanowires. Applied Physics Letters, 2006, 89: Art. 153110.
Zhu, L.L. and Zheng, X.J., Transverse surface mechanical behavior and modified elastic modulus for charged nanostructures. Europhysics Letters, 2008, 83: Art. 66007.
Zhu, L.L. and Zheng, X.J., Modification of the elastic properties of nanostructures with surface charges in applied electric fields. European Journal of Mechanics A/Solids, 2010, 29: 337–347.
McDowell, M.T., Leach, A.M. and Gall, K., Bending and tensile deformation of metallic nanowires. Modelling and Simulation in Materials Science and Engineering, 2008, 16: Art. 045003.
McDowell, M.T., Leach, A.M. and Gall, K., On the elastic modulus of metallic nanowires. Nano Letters, 2008, 8: 3613–3618.
Zhang, T.-Y., Luo, M. and Chan, W.K., Size-dependent surface stress, surface stiffness and Young’s modulus of hexagonal prism [111] β-SiC nanowires. Journal of Applied Physics, 2008, 103: Art. 104308.
Wang, G.F. and Feng, X.Q., Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Applied Physics Letters, 2007, 90: Art. 231904.
Wang, G.F. and Feng, X.Q., Surface effects on buckling of nanowires under uniaxial compression. Applied Physics Letters, 2009, 94: Art. 141913.
Wang, G.F., and Feng, X.Q., Timoshenko beam model for buckling and vibration of nanowires with surface effects. Journal of Physics D: Applied Physics, 2009b, 42: Art. 155411.
Wang, J.S., Cui, Y.H., Feng, X.Q., Wang, G.F. and Qin, Q.H., Surface effects on the elasticity of nanosprings. Europhysics Letters, 2010, 92: 16002–1-6.
Wang, J.S., Feng, X.Q., Xu, J., Qin, Q.H. and Yu, S.W., Chirality transfer from molecular to morphlogical scales in quasi-one-dimensional nanomaterials: A continuum model. International Journal of Mechanical Sciences, 2010 (In press).
Zhou, L.G. and Huang, H.C., Are surfaces elastically softer or stiffer? Applied Physics Letters, 2004, 84: 1940–1942.
Tang, Y.Z., Zheng, Z.J., Xia, M.F. and Bai, Y.L., Mechanisms underlying two kinds of surface effects on elastic constants. Acta Mechanica Solida Sinica, 2009, 22: 605–622.
Tang, Y.Z., Zheng, Z.J., Xia, M.F. and Bai, Y.L., A unified guide to two opposite size effects in nano elastic materials. Chinese Physics Letters, 2009, 26: Art. 126201.
Zheng, X.J. and Qiao, L., Electric field effects on Young’s modulus of nanowires. Acta Mechanica Sinica, 2009, 22: 511–523.
He, L.H., Lim, C.W. and Wu, B.S., A continuum model for size-dependent deformation of elastic films of nano-scale thickness. International Journal of Solids and Structures, 2004, 41: 847–857.
Lim, C.W. and He, L.H., Size-dependent nonlinear response of thin elastic films with nano-scale thickness. International Journal of Mechanical Sciences, 2004, 46: 1715–1726.
Lu, P., He, L.H., Lee, H.P. and Lu, C., Thin plate theory including surface effects. International Journal of Solids and Structures, 2006, 43: 4631–4647.
Huang, D.W., Size-dependent response of ultra-thin films with surface effects. International Journal of Solids and Structures, 2008, 45: 568–579.
Wang, Z.Q. and Zhao, Y.P., Self-instability and bending behaviours of nanoplates. Acta Mechanica Solida Sinica, 2009, 22: 630–643.
Zhu, H.X., Wang, J.X. and Karihaloo, B.L., Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms. Journal of Mechanics of Materials and Structures, 2009, 4: 589–604.
Eremeyev, V.A., Altenbach, H. and Morozov, N.F., The influence of surface tension on the effective stiffness of nanosize plates. Doklady Physics, 2009, 54: 98–100.
Altenbach, H., Eremeyev, V.A. and Morozov, N.F., Linear theory of shells taking into account surface stresses. Doklady Physics, 2009, 54: 531–535.
Altenbach, H., Eremeyev, V.A. and Morozov, N.F., On equations of the linear theory of shells with surface stresses taken into account. Mechanics of Solids, 2010, 45: 331–342.
Yang, Z.Y. and Zhao, Y.P., Size-dependent elastic properties of Ni nanofilms by molecular dynamic simulations. Surface Review and Letters, 2007, 14: 661–665.
Guo, J.G., Zhou, L.J. and Zhao, Y.-P., Size-dependent elastic modulus and fracture toughness of the thin film with surface effects. Surface Review and Letters, 2008, 15: 599–603.
Zhu, H.X., and Karihaloo, B.L., Size-dependent bending of thin metallic films. International Journal of Plasticity, 2008, 24: 991–1007.
Lu, C.F., Chen, W.Q., and Lim, C.W., Elastic mechanical behavior of nano-scaled FGM films incorporating surface energies. Composites Science and Technology, 2009, 69: 1124–1130.
Pan, X.H., Huang, S.Q., Yu, S.W. and Feng, X.Q., Interfacial slippage effect on the surface instability of a thin elastic film under van der Waals force. Journal of Physics D: Applied Physics, 2009, 42: Art. 055302.
Gurtin, M.E., Markenscoff, X. and Thurston, R.N., Effect of surface stress on the natural frequency of thin crystals. Applied Physics Letters, 1976, 29: 529–530.
Ren, Q. and Zhao, Y.-P., Influence of surface stress on frequency of microcantilever-based biosensors. Microsystem Technologies, 2004, 10: 307–314.
Lu, P., Lee, H.P., Lu, C.Lu. and O’Shea, S.J., Surface stress effects on the resonance properties of cantilever sensors. Physical Review B, 2005, 72: Art. 085405.
Zhang, Y., Ren, Q. and Zhao, Y.-P., Modelling analysis of surface stress on a rectangular cantilever beam. Journal of Physics D: Applied Physics, 2004, 37: 2140–2145.
Sadeghian, H., Goosen, J.F.L., Bossche, A. and van Keulen, F., Surface stress-induced change of overall elastic behaviour and self-bending of ultrathin cantilever plates. Applied Physics Letters, 2009, 94: Art. 231908.
Huang, G.Y., Gao, W. and Yu, S.W., Model for the adsorption-induced change in resonance frequency of a cantilever. Applied Physics Letters, 2006, 89: Art. 043506.
Zhang, J.Q., Yu, S.W. and Feng, X.Q., Theoretical analysis of resonance frequency change induced by adsorption. Journal of Physics D: Applied Physics, 2008, 41: Art. 125306.
Zhang, J.Q., Yu, S.W., Feng, X.Q. and Wang, G.F., Theoretical analysis of adsorption-induced microcantilever bending. Journal of Applied Physics, 2008, 103: Art. 093506.
Zhang, J.Q., Pan, X.H., Yu, S.W. and Feng, X.Q., Elastic analysis of physisorption-induced substrate deformation. Chinese Physics Letters, 2008, 26: 205–208.
He, J. and Lilley, C.M., Surface stress effect on bending resonance of nanowires with different boundary conditions. Applied Physics Letters, 2008, 93: Art. 263108.
He, J. and Lilley, C.M., The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation. Computional Mechanics, 2009, 44: 395–403.
Yi, X. and Duan, H.L., Surface stress induced by interactions of adsorbates and its effect on deformation and frequency of microcantilever sensors. Journal of the Mechanics and Physics of Solids, 2009, 57: 1254–1266.
Park, H.S. and Klein, P.A., Surface Cauchy-Born analysis of surface stress effects on metallic nanowires. Physical Review B, 2007, 75: Art. 085408.
Park, H.S., Surface stress effects on the resonant properties of silicon nanowires. Journal of Applied Physics, 2008, 103: Art. 123504.
Park, H.S. and Klein, P.A., Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kine- matics and the impact of the residual surface stress. Journal of the Mechanics and Physics of Solids, 2008, 56: 3144–3166.
Park, H.S., Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered. Nanotechnology, 2009, 20: Art. 115701.
Yun, G. and Park, H.S., Surface stress effects on the bending properties of fcc metal nanowires. Physical Review B, 2009, 79: Art. 195421.
Wang, Y., Weissmuller, J. and Duan, H.L., Tuning and monitoring of quantum dot growth by an in situ cantilever. Physical Review B, 2009, 79: Art. 045401.
Chen, G.Y., Thundat, T., Wachter, E.A. and Warmack, R.J., Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers. Journal of Applied Physics, 1995, 77: 3618–3622.
Berger, R., Delamarche, E., Lang, H.P., Gerber, C., Gimzewski, J.K., Meyer, E. and Guntherodt, H.J., Surface stress in the self-assembly of alkanethiols on gold. Science, 1997, 276: 2021–2024.
Wu, G.H., Datar, R.H., Hansen, K.M., Thundat, T., Cote, R.J. and Majumdar, A., Bioassay of prostate-specific antigen (PSA) using microcantilevers. Nature Biotechnology, 2001, 19: 856–860.
McFarland, A.W., Poggi, M.A., Doyle, M.J., Bottomley, L.A. and Colton, J.S., Influence of surface stress on the resonance behavior of microcantilevers. Applied Physics Letters, 2005, 87: Art. 053505.
Hwang, K.S., Eom, K., Lee, J.H., Chun, D.W., Cha, B.H., Yoon, D.S., Kim, T.S. and Park, J.H., Dominant surface stress driven by biomolecular interactions in the dynamical response of nanomechanical micro-cantilevers. Applied Physics Letters, 2006, 89: Art. 173905.
Cahn, J.W. and Larche, F., Surface stress and the chemical equillibrium of small crystals II. Solid particles embedded in a solid matrix. Acta Metallurgica, 1982, 30: 51–56.
Huo, B., Zheng, Q.S. and Huang, Y., A note on the effect of surface energy and void size to void growth. European Journal of Mechanics A/Solids, 1999, 18: 987–994.
Suo, Z., Evolving material structures of small feature sizes. International Journal of Solids and Structures, 2000, 37: 367–378.
Eshelby, J.D., The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society, 1957, A241: 376–396.
Eshelby, J.D., The elastic field outside an ellipsoidal inclusion. Proceedings of the Royal Society, 1959, A252: 561–569.
Sharma, P., Ganti, S. and Bhate, N., Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Applied Physics Letters, 2003, 82: 535–537.
Sharma, P. and Ganti, S., Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface. Journal of Applied Mechanics, 2004, 71: 663–671.
Duan, H.L., Wang, J., Huang, Z.P. and Luo, Z.Y., Stress concentration tensors of inhomogeneities with interface effects. Mechanics of Materials, 2005, 37: 723–736.
Duan, H.L., Wang, J., Huang, Z.P. and Karihaloo, B.L., Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society, 2005, A461: 3335–3353.
Eshelby, J.D., The continuum theory of lattice defects. Solid State Physics, 1956, 3: 79–144.
Lim, C.W., Li, Z.R. and He, L.H., Size dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress. International Journal of Solids and Structures, 2006, 43: 5055–5065.
Li, Z.R., Lim, C.W. and He, L.H., Stress concentration around a nano-scale spherical cavity in elastic media: effect of surface stress. European Journal of Mechanics A/Solids, 2006, 25: 260–270.
Duan, H.L., Jiao, Y., Yi, X., Huang, Z.P. and Wang, J., Solutions of inhomogeneity problems with graded shells and application to core-shell nanoparticles and composites. Journal of the Mechanics and Physics of Solids, 2006, 54: 1401–1425.
Sharma, P. and Wheeler, L.T., Size-dependent elastic state of ellipsoidal nano-inclusions incorporating surface/interface tension. Journal of Applied Mechanics, 2007, 74: 447–454
Benveniste, Y. and Miloh, T., Soft neutral elastic inhomogeneities with membrane-type interface conditions. Journal of Elasticity, 2007, 88: 87–111.
Hatami-Marbini, H. and Shodja, H.M., Effects of interface conditions on thermo-mechanical field of multiphase nano-fibers/particles. Journal of Thermal Stresses, 2009, 32: 1166–1180.
Fisher, F.D. and Svoboda, J., Stresses in hollow nanoparticles. International Journal of Solids and Structures, 2010, 47: 2799–2805.
He, L.H., Self-strain of solids with spherical nanovoids. Applied Physics Letters, 2006, 88: Art. 151909.
He, L.H. and Li, Z.R., Impact of surface stress on stress concentration. International Journal of Solids and Structures, 2006, 43: 6208–6219.
Mi, C.W. and Kouris, D.A., Nanoparticles under the influence of surface/interface elasticity. Journal of Mechanics of Materials and Structures, 2006, 1: 763–791.
Wang, G.F. and Wang, T.J., Deformation around a nanosized elliptical hole with surface effect. Applied Physics Letters, 2006, 89: Art. 161901.
Ou, Z.Y., Wang, G.F. and Wang, T.J., Effect of residual surface tension on the stress concentration around a nanosized spheroidal cavity. International Journal of Engineering Science, 2008, 46: 475–485.
Ou, Z.Y., Wang, G.F. and Wang, T.J., Elastic fields around a nanosized spheroidal cavity under arbitrary uniform remote loadings. European Journal of Mechanics A/Solids, 2009, 28:110–120.
Ou, Z.Y., Wang, G.F. and Wang, T.J., An analytical solution for the elastic fields near spheroidal nano-inclusions. Acta Mechanica Sinica, 2009, 25: 821–830.
Tian, L. and Rajapakse, R.K.N.D., Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity. Journal of Applied Mechanics, 2007, 74: 568–574.
Tian, L. and Rajapakse, R.K.N.D., Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity. International Journal of Solids and Structures, 2007, 44: 7988–8005.
Luo, J. and Wang, X., On the anti-plane shear of an elliptic nano inhomogeneity. European Journal of Mechanics A/Solids, 2009, 28: 926–934.
Avazmohammadi, R., Yang, F.Q. and Abbasion, S., Effect of interface stresses on the elastic deformation of an elastic half-plane containing an elastic inclusion. International Journal of Solids and Structures, 2009, 46: 2897–2906.
Li, Q. and Chen, Y.H., Surface effect and size dependence on the energy release due to a nanosized hole expansion in plane elastic materials. Journal of Applied Mechanics, 2008, 75: Art. 061008.
Hui, T. and Chen, Y.H., The M-integral analysis for a nano-inclusion in plane elastic materials under uniaxial or bi-axial loadings. Journal of Applied Mechanics, 2010, 77: Art. 021019.
Hui, T. and Chen, Y.H., Two state M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Journal of Applied Mechanics, 2010, 77: Art. 024505.
Gao, W., Yu, S.W. and Huang, G.Y., Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology, 2006, 17: 1118–1122.
Gao, W. and Yu, S.W., Finite element characterization of the size-dependent mechanical behaviour of nanosystem — Formulation for plane strain and axisymmetric problem. In: Proc. of ECCM14, Budapest, June 6–8, 2010.
Tian, L. and Rajapakse, R.K.N.D., Finite element modelling of nanoscale inhomogeneities in an elastic matrix. Computational Materials Science, 2007, 41: 44–53.
Chen, X.L., Ma, H.S., Liang, L.H. and Wei, Y.G., A surface energy model and application to mechanical behavior analysis of single crystals at sub-micron scale. Computational Materials Science, 2009, 46: 723–727.
Mogilevskaya, S.G., Crouch, S.L. and Stolarski, H.K., Multiple interacting circular nano-inhomogeneities with surface/interface effects. Journal of the Mechanics and Physics of Solids, 2008, 56: 2298–2327.
Jammes, M., Mogilevskaya, S.G. and Crouch, S.L., Multiple circular nano-inhomogeneities and/or nano-pores in one of two joined isotropic elastic half-planes. Engineering Analysis with Boundary Elements, 2009, 33: 233–248.
Mogilevskaya, S.G., Crouch, S.L., Ballarini, R., and Stolarski, H., Interaction between a crack and a circular inhomogeneity with interface stiffness and tension. International Journal of Fractures, 2009, 159: 191–207.
Fang, Q.H. and Liu, Y.W., Size-dependent elastic interaction of a screw dislocation with a circular nano-inhomogeneity incorporating interface stress. Scripta Materialia, 2006, 55: 99–102.
Fang, Q.H. and Liu, Y.W., Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects. Acta Materialia, 2006, 54: 4213–4220.
Fang, Q.H., Li, B. and Liu, Y.W., Interaction between edge dislocations and a circular hole with surface stress. Physica Status Solidi B — Basic Solid State Physics, 2007, 244: 2576–2588.
Fang, Q.H., Liu, Y.W. and Wen, P.H., Screw dislocations in a three-phase composite cylinder model with interface stress. Journal of Applied Mechanics, 2008, 75: 041019.
Luo, J. and Xiao, Z.M., Analysis of a screw dislocation interacting with an elliptical nano inhomogeneity. International Journal of Engineering Science, 2009, 47: 883–893.
Wang, G.F., Feng, X.Q. and Yu, S.W., Interface effects on the diffraction of plane compressional waves by a nanosized spherical inclusion. Journal of Applied Physics, 2007, 102: Art. 043533.
Wang, G.F., Wang, T.J. and Feng, X.Q., Surface effects on the diffraction of plane compressional waves by a nanosized circular hole. Applied Physics Letters, 2006, 89: 231923-1-3.
Wang, G.F., Diffraction of shear waves by nanosized spherical cavity. Journal of Applied Physics, 2008, 103: Art. 053519.
Wang, G.F., Multiple diffractions of plane compressional waves by two circular cylindrical holes with surface effects. Journal of Applied Physics, 2009, 105: Art. 013507.
Ru, Y., Wang, G.F. and Wang, T.J., Diffractions of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect. Journal of Vibration and Acoustics, 2009, 131: Art. 061011.
Hasheminejad, S.M. and Avazmohammadi, R., Size-dependent effective dynamic properties of unidirectional nanocomposites with interface energy effects. Composites Science and Technology, 2009, 69: 2538–2546.
Wu, X.-F. and Dzenis, Y.A., Wave propagation in nanofibers. Journal of Applied Physics, 2006, 100: Art. 124318.
Griffith, A.A., The phenomena of rupture and flow in solids. Philosophical Transaction of the Royal Society A, 1920, 221: 163–198.
Wu, C.H., The effect of surface stress on the configurational equilibrium of voids and cracks. Journal of the Mechanics and Physics of Solids, 1999, 47: 2469–2492.
Wang, G.F., Feng, X.Q., Wang, T.J. and Gao, W., Surface effects on the near-tip stresses for mode-I and mode-III cracks. Journal of Applied Mechanics, 2008, 75: Art. 011001.
Fu, X.L., Wang, G.F. and Feng, X.Q., Surface effects on mode-I crack tip fields: A numerical study. Engineering Fracture Mechanics, 2010, 77:1048–1057.
Fu, X.L., Wang, G.F. and Feng, X.Q., Surface effects on the near-tip stress fields of a mode-II crack. International Journal of Fracture, 2008, 151: 95–106.
Kim, C.I., Schiavone, P. and Ru, C.Q., The effects of surface elasticity on an elastic solid with mode-III crack: complete solution. Journal of Applied Mechanics, 2010, 77: Art. 021011.
Weissmuller, J., Viswanath, R.N., Kramer, D., Zimmer, P., Wurschum, R. and Gleiter, H., Charge-induced reversible strain in a metal. Science, 2003, 300: 312–315.
Kramer, D., Viswanath, R.N. and Weissmu1ller, J., Surface-stress induced macroscopic bending of nanoporous gold cantilevers. Nano Letters, 2004, 4: 793–796.
Yang, F.Q., Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations. Journal of Applied Physics, 2004, 95: 3516–3520.
Yang, F.Q., Effect of interfacial stresses on the elastic behavior of nanocomposite materials. Journal of Applied Physics, 2006, 99: 054306.
Hashin, Z., The elastic moduli of heterogeneous materials. Journal of Applied Mechanics, 1962, 29: 143–150.
Duan, H.L., Wang, J., Huang, Z.P. and Karihaloo, B.L., Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. Journal of the Mechanics and Physics of Solids, 2005, 53: 1574–1596.
Mori, T. and Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 1973, 21: 571–574.
Christensen, R.M. and Lo, K.H., Solutions for effective shear properties in three phase sphere and cylinder models. Journal of the Mechanics and Physics of Solids, 1979, 27: 315–330.
Masuda, H. and Fukuda, K., Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina. Science, 1995, 268: 1466–1468.
Martin, C.R. and Siwy, Z., Molecular filters-pores within pores. Nature Materials, 2004, 3: 284–285.
Duan, H.L., Wang, J., Karihaloo, B.L. and Huang, Z.P., Nanoporous materials can be made stiffer than non-porous counterparts by surface modification. Acta Materialia, 2006, 54: 2983–2990.
Eremeyev, V.A. and Morozov, N.F., The effective stiffness of a nanoporous rod. Doklady Physics, 2010, 55: 279–282.
Duan, H.L., Yi, X., Huang, Z.P. and Wang, J., A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part I — theoretical framework. Mechanics of Materials, 2007, 39: 81–93.
Huang, Y., Hu, K.X., Wei, X. and Chandra, A., A generalized self-consistent mechanics method for composite materials with multiphase inclusions. Journal of the Mechanics and Physics of Solids, 1994, 42: 491–504.
Chen, T. and Dvorak, G.J., Fiberous nanocomposites with interface stress: Hill’s and Levin’s connections for effective moduli. Applied Physics Letters, 2006, 88: Art. 211912.
Levin, V.M., On the coefficients of thermal expansion of heterogeneous materials. Mechanics of Solids, 1967, 2: 58–61.
Hill, R., Theory of mechanical properties of fibre-strengthened materials — I. Elastic behavior. Journal of the Mechanics and Physics of Solids, 1964, 12: 199–212.
Chen, T., Dvorak, G.J. and Yu, C.C., Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal-mechanical connections. International Journal of Solids and Structures, 2007, 44: 941–955.
Chen, T., Dvorak, G.J. and Yu, C.C., Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mechanica, 2007, 188: 39–54.
Mogilevskaya, S.G., Crouch, S.L., La Grotta, A. and Stolarski, H.K., The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nanocomposites. Composites Science and Technology, 2010, 70: 427–434.
Mogilevskaya, S.G., Crouch, S.L., Stolarski, H.K. and Benusiglio, A., Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects. International Journal of Solids and Structures, 2010b, 47: 407–418.
Murdoch, A.I., Thermodynamical theory of elastic-material interfaces. The Quarterly Journal of Mechanics and Applied Mathematics, 1976, 29: 245–275.
Murdoch, A.I., Some fundamental aspects of surface modelling. Journal of Elasticity, 2005, 80: 33–52.
Duan, H.L. and Karihaloo, B.L., Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized Levin’s formula and Hill’s connections. Journal of the Mechanics and Physics of Solids, 2007, 55: 1036–1052.
Le Quang, H. and He, Q.C., Size-dependent effective thermoelastic properties of nanocomposites with spherically anisotropic phases. Journal of the Mechanics and Physics of Solids, 2007, 55: 1889–1921.
He, Q.C. and Benveniste, Y., Exactly solvable spherically anisotropic thermoelastic microstructures. Journal of the Mechanics and Physics of Solids, 2004, 52: 2661–2682.
Le Quang, H. and He, Q.C., Estimation of the effective thermoelastic moduli of firous nanocomposites with cylindrically anisotropic phases. Archive of Applied Mechanics, 2009, 79: 225–248.
Le Quang, H. and He, Q.C., Variational principles and bounds for elastic inhomogeneous materials with coherent imperfect interfaces. Mechanics of Materials, 2008, 40: 865–884.
Brisard, S., Dormieux, L. and Kondo, D., Hashin-Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects. Computational Materials Science, 2010, 48: 589–596.
Yvonnet, J., Le Quang, H. and He, Q.C., An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites. Computational Mechanics, 2008, 42: 119–131.
Feng, X.Q., Xia, R., Li, X. and Li, B., Surface effects on the elastic modulus of nanoporous materials. Applied Physics Letters, 2009, 94: Art. 011916.
Pan, E., Wang, X. and Wang, R., Enhancement of magnetoelectric effect in multiferroic nanocomposites via size-dependent material properties. Applied Physics Letters, 2009, 95: Art. 181904.
Yang, F.Q., Size effect on the effective bulk modulus of nanocomposites with core-shell nanospherical inclusions. Materials Science and Engineering A, 2010, 527: 3913–3917.
Zhu, H.X., Size-dependent elastic properties of micro- and nano-honeycombs. Journal of the Mechanics and Physics of Solids, 2010, 58: 696–709.
Zhang, W.X. and Wang, T.J., Effect of surface energy on the yield strength of nanoporous materials. Applied Physics Letters, 2007, 90: Art. 063104.
Zhang, W.X., Wang, T.J. and Chen, X., Effect of surfface stress on the asymmetric yield strength of nanowires. Journal of Applied Physics, 2008, 103: Art. 123527.
Zhang, W.X., Wang, T.J. and Chen, X., Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites. International Journal of Plasticity, 2010, 26: 957–975.
Chen, H., Liu, X.N. and Hu, G.K., Overall plasticity of micropolar composites with interface effect. Mechanics of Materials, 2008, 40: 721–728.
Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: Part I, yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, 1977, 99: 2–15.
Dormieux, L. and Kondo, D., An extension of Gurson model incorporating interface stresses effects. International Journal of Engineering Science, 2010, 48: 575–581.
Volkert, C.A., Lilleodden, E.T., Kramer, D. and Weissmueller, J., Approaching the theoretical strength in nanoporous Au. Applied Physics Letters, 2006, 89: Art. 061920.
Jin, H.J., Kramer, D., Ivanisenko, Y. and Weissmuller, J., Macroscopically strong nanoporous Pt prepared by dealloying. Advanced Engineering Materials, 2007, 9: 849–854.
Biener, J., Hodge, A.M. Hayes, J.R., Volkert, C.A., Zepeda-Ruiz, L.A., Hamza, A.V. and Abraham, F.F., Size effects on the mechanical behavior of nanoporous Au. Nano Letters, 2006, 6: 2379–2382.
Hakamada, M. and Mabuchi, M., Mechanical strength of nanoporous gold fabricated by dealloying. Scripta Materialia, 2007, 56: 1003–1006.
Smetanin, M., Viswanath, R.N., Kramer, D., Beckmann, D., Koch, T., Kibler, L.A., Kolb, D.M. and Weissmuller, J., Surface stress-charge response of a (111)-textured gold electrode under conditions of weak ion adsorption. Langmuir, 2008, 24: 8561–8567.
Duan, H.L., Weissmuller, J. and Wang, Y., Instabilities of core shell heterostructured cylinders due to diffusions and epitaxy: Spheroidization and blossom of nanowires. Journal of the Mechanics and Physics of Solids, 2008, 56: 1831–1851.
Weissmuller, J. and Duan, H.L., Cantilever bending with rough surfaces. Physical Review Letters, 2008, 101: Art. 146102.
Blanco-Rey, M., Pratt, S.J. and Jenkins, S.J., Surface stress of stepped chiral metal surfaces. Physical Review Letters, 2009, 102: Art. 026102.
Huang, G.Y. and Yu, S.W., Effect of surface elasticity on the interaction between steps. Journal of Applied Mechanics, 2007, 74: 821–823.
Qiao, L. and Zheng, X.J., Elastic property of fcc metal nanowires via an atomic-scale analysis. Applied Physics Letters, 2008, 92: Art. 231908.
Duan, H.L., Xue, Y.H. and Yi, X., Vibration of cantilevers with rough surfaces. Acta Mechanica Solida Sinica, 2009, 22: 550–554.
Wang, Y., Weissmuller, J. and Duan, H.L., Mechanics of corrugated surfaces. Journal of the Mechanics and Physics of Solids, 2010, 58: 1552–1566.
Duan, H.L., Surface-enhanced cantilever sensors with nano-porous films. Acta Mechanica Solida Sinica, 2010, 23: 1–12.
Guo, W.L., Xie, H.M. and Zheng, Q.S., Current trends of micro- and nanomechanics. Acta Mechanica Solida Sinica, 2009, 22: I–III.
Shao, L.-H., Jin, H.-J., Viswanath, R.N. and Weissmuller, J., Different measures for the capillarity-driven deformation of a nanoporous metal. Europhysics Letters, 2010, 89: Art. 66001.
Jiang, Q., Zhao, D.S. and Zhao, M., Size-dependent interface energy and related interface stress. Acta Materialia, 2001, 49: 3143–3147.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, J., Huang, Z., Duan, H. et al. Surface stress effect in mechanics of nanostructured materials. Acta Mech. Solida Sin. 24, 52–82 (2011). https://doi.org/10.1016/S0894-9166(11)60009-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(11)60009-8