References
- R.J. Asaro and D.M. Barnett, The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion, J. Mech. Phys. Solids 23 (1975), pp. 77–83. doi: 10.1016/0022-5096(75)90012-5
- C. Calvo-Jurado and W.J. Parnell, Hashin–Shtrikman bounds on the effective thermal conductivity of a transversely isotropic two-phase composite material, J. Math. Chem. 53 (2014), pp. 828–843. doi: 10.1007/s10910-014-0452-8
- C. Calvo-Jurado and W.J. Parnell, The influence of two-point statistics on the Hashin–Shtrikman bounds for three-phase composites, J. Comput. Appl. Math. 318 (2017), pp. 354–365. doi: 10.1016/j.cam.2016.08.046
- L.H. Donnel, Stress concentration due to elliptical discontinuities in plates under edge forces, Theodore von Karman Anniversary Volume., Cal. Inst. Tech. (1941), pp. 293–309.
- J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. A 241 (1957), pp. 376–396. doi: 10.1098/rspa.1957.0133
- J.D. Eshelby, The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. A 252 (1959), pp. 561–569. doi: 10.1098/rspa.1959.0173
- J.D. Eshelby, Elastic inclusions and inhomogeneities, in Progress in Solid Mechanics, Vol. 2, I.N. Sneddon and R. Hill, eds., North-Holland, Amsterdam, 1960, pp. 89–140.
- S.X. Gong, A unified treatment of the elastic elliptical inclusion under antiplane shear, Arch. Appl. Mech. 65 (1995), pp. 56–64.
- N.J. Hardiman, Elliptic elastic inclusion in an infinite elastic plate, Q. J. Mech. Appl. Math. 7 (1954), pp. 226–230. doi: 10.1093/qjmam/7.2.226
- Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids 11 (1963), pp. 127–140. doi: 10.1016/0022-5096(63)90060-7
- D. Joyce and W.J. Parnell, The Newtonian potential inhomogeneity problem: Non-uniform eigenstrains in cylinders of non-elliptical cross section, J. Eng. Math. 107 (2017), pp. 283–303. doi: 10.1007/s10665-017-9923-9
- D. Joyce, W.J. Parnell, I.D. Abrahams, and R.C. Assier, An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems, Proc. Roy. Soc. A 473 (2017), p. 20170080. doi: 10.1098/rspa.2017.0080
- H. Kang and G.W. Milton, Solutions to the Polya–Szego conjecture and the weak Eshelby conjecture, Arch. Ration. Mech. Anal. 188 (2008), pp. 93–116. doi: 10.1007/s00205-007-0087-z
- L.P. Liu, Solutions to the Eshelby conjectures, Proc. R. Soc. A 464 (2008), pp. 573–594. doi: 10.1098/rspa.2007.0219
- J.C. Maxwell, A Treatise on Electricity and Magnetism, Vols 1 and 2, Oxford University Press, Oxford, 1998.
- L.M. Milne-Thomson, Theoretical Hydrodynamics, Macmillan, London, 1960.
- T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, Dordrecht, 1982.
- N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen, the Netherlands, 1943.
- W.J. Parnell, The Eshelby, hill, moment and concentration tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostatics, J. Elast. 125 (2016), pp. 231–294. doi: 10.1007/s10659-016-9573-6
- W.J. Parnell and I.D. Abrahams, A new integral equation approach to elastodynamic homogenization, Proc. R. Soc. A 464 (2008), pp. 1461–1482. doi: 10.1098/rspa.2007.0254
- W.J. Parnell and C. Calvo-Jurado, On the computation of the Hashin–Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites, J. Eng. Math. 95 (2015), pp. 295–323. doi: 10.1007/s10665-014-9777-3
- S.D. Poisson, Second mémoire sur la théorie de magnetisme, Mém. Acad. R. Sci. Inst. Fr. 5 (1826), pp. 488–533.
- C.Q. Ru and P. Schiavone, On the elliptic inclusion in anti-plane shear, Math. Mech. Solids 1 (1996), pp. 327–333. doi: 10.1177/108128659600100304
- G.P. Sendeckyj, Longitudinal shear modulus of filamentary composite containing curvilinear fibers, Fibre Sci. Technol. 2(3) (1970), pp. 211–222. doi: 10.1016/0015-0568(70)90003-5
- G.P. Sendeckyj, Elastic inclusion problems in plane elastostatics, Int. J. Solids Structures 6 (1970), pp. 1535–1543. doi: 10.1016/0020-7683(70)90062-4
- E. Smith, The interaction between dislocations and inhomogeneities, Int. J. Eng. Sci. 6(3) (1968), pp. 129–143. doi: 10.1016/0020-7225(68)90012-8