We examine the neutrality of an elliptical inhomogeneity embedded in a particular class of compressible hyperelastic materials of harmonic type when a uniform Piola stress field is prescribed in the surrounding matrix. The present method is based on a spring-type imperfect interface model and on the proper choice of imperfect interface function, which realizes the same degree of imperfection in both normal and tangential directions. The analysis indicates that, in general, the neutral shape and the single imperfect interface function are both dependent on the magnitude of the prescribed stress field.
Van VlietDSchiavonePMioduchowskiA. On the design of neutral elastic inhomogeneities in the case of nonuniform loading. Math Mech Solids2003; 8: 161–169.
5.
SchiavoneP.Neutrality of an elliptic inhomogeneity in the case of non-uniform loading. Int J Eng Sci2003; 41: 2081–2090.
6.
VasudevanMSchiavoneP.New results concerning the identification of neutral inhomogeneities in plane elasticity. Arch Mech2006; 58: 45–58.
7.
MiltonGWSerkovSK.Neutral inclusions for conductivity and anti-plane elasticity. Proc Roy Soc London A2001; 457: 1973–1997.
8.
ChenTBenvenisteYChuangPC.Exact solution in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages. Proc Roy Soc London A2002; 458: 1719–1959.
9.
WangXSchiavoneP.Neutral coated circular inclusions in finite plane elasticity of harmonic materials. Euro J Mech A/Solids2012; 33: 75–81.
10.
WangXSchiavoneP.Neutrality in the case of N-phase elliptical inclusions with internal uniform hydrostatic stresses. Int J Solids Struct2012; 49: 800–807.
11.
RuCQ.On complex-variable formulation for finite plane elastostatics of harmonic materials. Acta Mech2002; 156: 219–234.
12.
SudakLJRuCQSchiavoneP. A circular inclusion with inhomogeneously imperfect interface in plane elasticity. J Elast1999; 55: 19–41.
13.
WangXPanESudakLJ.Uniform stresses inside an elliptical inhomogeneity with an imperfect interface in plane elasticity. ASME J Appl Mech2008; 75: 054501.
14.
WangX.A circular inclusion with imperfect interface in finite plane elastostatics. Acta Mech2012; 223: 481–491.
15.
McArthurDRSudakLJ. A circular inclusion with circumferentially inhomogeneous imperfect interface in harmonic materials. Continuum Mech Thermodyn. 2016; 28: 317–329.
16.
JohnF.Plane strain problems for a perfectly elastic material of harmonic type. Commun Pure Appl Math1960; XIII: 239–290.
17.
KnowlesJKSternbergE.On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics. Int J Solids Struct1975; 11: 1173–1201.
18.
AbeyaratneRHorganCO.The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials. Int J Solids Struct1984; 20: 715–723.
LiXSteigmannDJ.Finite plane twist of an annular membrane. Q J Mech Appl Math1993; 46: 601–625.
21.
AbeyaratneR.Some finite elasticity problems involving crack tips. In: PinderaJT (ed.) Modelling problems in crack tip mechanics. Waterloo, Canada: University of Waterloo, 19833–24.
22.
HorganCO. Equilibrium solutions for compressible nonlinearly elastic materials. In: FuYBOgdenRW (ed.) Nonlinear elasticity: theory and applications (London Mathematical Society Lecture Notes No. 283). Cambridge: Cambridge University Press, 2001, 135–159.
23.
HorganCOMurphyJG.A Lie group analysis of the axisymmetric equations of finite elastostatics for compressible materials. Math Mech Solids2005; 10: 311–333.
