Extension of Maxwell homogenization scheme for piezoelectric composites containing spheroidal inhomogeneities

[1]  J. Maxwell.  A Treatise on Electricity and Magnetism , 1873, Nature.

[2]  L. Rayleigh,et al.  LVI. On the influence of obstacles arranged in rectangular order upon the properties of a medium , 1892 .

[3]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[4]  D. Jeffrey,et al.  Conduction through a random suspension of spheres , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  M. Nafi Toksöz,et al.  Velocity and attenuation of seismic waves in two-phase media; Part I, Theoretical formulations , 1974 .

[6]  D. M. Barnett,et al.  Dislocations and line charges in anisotropic piezoelectric insulators , 1975 .

[7]  E. Fukada,et al.  Electromechanical Properties in the Composites of Epoxy Resin and PZT Ceramics , 1976 .

[8]  J. Unsworth,et al.  Simple model for piezoelectric ceramic/polymer 1-3 composites used in ultrasonic transducer applications , 1989 .

[9]  V. Varadan,et al.  Scattering and attenuation of elastic waves in random media , 1989 .

[10]  Y. Benveniste.  Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior , 1993 .

[11]  Martin L. Dunn,et al.  Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites , 1993 .

[12]  M. Taya,et al.  An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  Mark Kachanov,et al.  Elastic Solids with Many Cracks and Related Problems , 1993 .

[14]  Martin L. Dunn,et al.  Electroelastic Green's functions for transversely isotropic piezoelectric media and their application to the solution of inclusion and inhomogeneity problems , 1994 .

[15]  Salvatore Torquato,et al.  Optimal design of 1-3 composite piezoelectrics , 1997 .

[16]  Marco Avellaneda,et al.  Calculating the performance of 1–3 piezoelectric composites for hydrophone applications: An effective medium approach , 1998 .

[17]  Ching-Ping Wong,et al.  Thermal conductivity, elastic modulus, and coefficient of thermal expansion of polymer composites filled with ceramic particles for electronic packaging , 1999 .

[18]  Valery M. Levin,et al.  Spheroidal inhomogeneity in a transversely isotropic piezoelectric medium , 2000 .

[19]  K. Markov,et al.  Elementary Micromechanics of Heterogeneous Media , 2000 .

[20]  S. Yi,et al.  An effective inclusion model for effective moduli of heterogeneous materials with ellipsoidal inhomogeneities , 2001 .

[21]  Julián Bravo-Castillero,et al.  Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents. I: Elastic and hexagonal symmetry , 2001 .

[22]  Graeme W. Milton,et al.  The Theory of Composites: Frontmatter , 2002 .

[23]  Jacqueline J. Li,et al.  A numerical simulation for effective elastic moduli of plates with various distributions and sizes of cracks , 2004 .

[24]  R. Kar-Gupta,et al.  Electromechanical response of 1-3 piezoelectric composites: Effect of poling characteristics , 2005 .

[25]  A. Kelly,et al.  Maxwell's far-field methodology applied to the prediction of properties of multi-phase isotropic particulate composites , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  R. Kar-Gupta,et al.  Electromechanical response of porous piezoelectric materials: Effects of porosity distribution , 2007 .

[27]  C. Della,et al.  The performance of 1-3 piezoelectric composites with a porous non-piezoelectric matrix , 2008 .

[28]  Julián Bravo-Castillero,et al.  Analysis of effective properties of electroelastic composites using the self-consistent and asymptotic homogenization methods , 2008 .

[29]  S. L. Crouch,et al.  Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects , 2010 .

[30]  G. Weng.  A dynamical theory for the Mori–Tanaka and Ponte Castañeda–Willis estimates , 2010 .

[31]  L. McCartney,et al.  Maxwell's far-field methodology predicting elastic properties of multiphase composites reinforced with aligned transversely isotropic spheroids , 2010 .

[32]  V. Levin,et al.  Propagation of electroacoustic axial shear waves in a piezoelectric medium reinforced by continuous fibers , 2011 .

[33]  I. Sevostianov,et al.  Effective properties of heterogeneous materials: Proper application of the non-interaction and the “dilute limit” approximations , 2012 .

[34]  V. Levin,et al.  Generalized Maxwell’s scheme for homogenization of poroelastic composites , 2012 .

[35]  S. L. Crouch,et al.  On Maxwell's concept of equivalent inhomogeneity: When do the interactions matter? , 2012 .

[36]  S. L. Crouch,et al.  Evaluation of the effective elastic moduli of particulate composites based on Maxwell’s concept of equivalent inhomogeneity: microstructure-induced anisotropy , 2013 .

[37]  Albert Giraud,et al.  Generalization of Maxwell homogenization scheme for elastic material containing inhomogeneities of diverse shape , 2013 .

[38]  I. Sevostianov.  On the shape of effective inclusion in the Maxwell homogenization scheme for anisotropic elastic composites , 2014 .

[39]  I. Sevostianov,et al.  Effective elastic properties of a particulate composite with transversely-isotropic matrix , 2015 .

[40]  R. Rodríguez-Ramos,et al.  Static effective characteristics in piezoelectric composite materials , 2017 .