Abstract
The problem of nanocomposite materials under far-field antiplane mechanical load and inplane electric load is investigated. Based on the theory of Gurtin–Murdoch surface/interface model, an exact solution is obtained for the inhomogeneity/matrix/equivalent medium model, in terms of which a generalized self-consistent approach is proposed for predicting the effective electroelastic moduli of nanocomposites. A closed-form solution of the effective electroelastic moduli is presented. The numerical results reveal that the effective electroelastic moduli are size dependent when the size of the inhomogeneity is on the order of nanometer. With the increase in the size of the inhomogeneity, the present solution approaches to the classical results obtained in the classical theory.
Similar content being viewed by others
References
Luo J., Wang X.: On the anti-plane shear of an elliptic nano inhomogeneity. Eur. J. Mech. A/Solids 28, 926–934 (2009)
Mogilevskaya S.G., Crouch S.L., Stolarski H.K.: Multiple interacting circular nano-inhomogeneities with surface/interface effects. J. Mech. Phys. Solids 56, 2298–2327 (2008)
Wong E.W., Sheehan P.E., Lieber C.M.: Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes. Science 277, 1971–1975 (1997)
Sharma P., Ganti S., Bhate N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82, 535–537 (2003)
He L.H., Li Z.R.: Impact of surface stress on stress concentration. Int. J. Solids. Struct. 43, 6208–6219 (2006)
Xun F., Hu G.K., Huang Z.P.: Effective in plane moduli of composites with a micropolar matrix and coated fibers. Int. J. Solids. Struct. 41, 247–265 (2004)
Sharma P., Ganti S.: Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies. J. Appl. Mech. 71, 663–671 (2004)
Yang F.Q.: Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations. J. Appl. Phys. 95, 3516–3520 (2004)
Duan H.L., Wang J., Huang Z.P., Karihaloo B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574–1596 (2005)
Lim C.W., Li Z.R., He L.H.: Size dependent, non-uniform elastic field inside a nano-scale spherical inclusion due to interface stress. Int. J. Solids. Struct. 43, 5055–5065 (2006)
Chen T., Dvorak G.J., Yu C.C.: Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech. 188, 39–54 (2007)
Tian L., Rajapakse R.K.N.D.: Finite element modelling of nanoscale inhomogeneities in an elastic matrix. Comput. Mater. Sci. 41, 44–53 (2007)
Chen T.: Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta Mech. 196, 205–217 (2008)
Mogilevskaya S.G., Crouch S.L., Stolarski H.K., Benusiglio A.: Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects. Int. J. Solids. Struct. 47, 407–418 (2010)
Mogilevskaya S.G., Crouch S.L., Grotta A.L., Stolarski H.K.: The effects of surface elasticity and surface tension on the transverse overall elastic behavior of unidirectional nano-composites. Compos. Sci. Technol. 70, 427–434 (2010)
Gurtin M.E., Murdoch A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)
Gurtin M.E., Murdoch A.I.: Surface stress in solids. Int. J. Solids. Struct. 14, 431–440 (1978)
Gurtin M.E., Weissmuller J., Larche F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A: Phys. Condens. Matter. Struct. Defects. Mech. Prop. 78, 1093–1109 (1998)
Tiersten H.F.: Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969)
Chen T., Chiu M.S., Weng C.N.: Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. J. Appl. Phys. 100, 074308 (2006)
Miller R.E., Shenoy V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139–147 (2000)
Muskhelishvili N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)
Benveniste Y., Miloh T.: Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech. Mater. 33, 309–323 (2001)
Jiang C.P., Cheung Y.K.: An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites. Int. J. Solids. Struct. 38, 4777–4796 (2001)
Huang G.Y., Yu S.W.: Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring. Phys. Stat. Sol. (b) 243, R22–R24 (2006)
Friesen C., Dimitrov N., Cammarata R.C., Sieradzki K.: Surface stress and electrocapillarity of solid electrodes. Langmuir 17, 807–815 (2001)
Michalski P.J., Sai N., Mele E.J.: Continuum theory for nanotube piezoelectricity. Phys. Rev. Lett. 95, 116803 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xiao, J.H., Xu, Y.L. & Zhang, F.C. Size-dependent effective electroelastic moduli of piezoelectric nanocomposites with interface effect. Acta Mech 222, 59 (2011). https://doi.org/10.1007/s00707-011-0523-x
Received:
Published:
DOI: https://doi.org/10.1007/s00707-011-0523-x