On the reduction of constants in plane elasticity with eigenstrains

In this paper the reduced parameter dependence in linear plane elasticity with eigenstrains (transformation strains) is studied. The focus is on simply connected inhomogeneous materials and two-phase materials with perfectly bonded interfaces. In the analysis we rely on the result of Cherkaev, Lurie and Milton (Proc. Roy. Soc. Lond. A 438, 519-529, 1992), and we show that the stress field is invariant under a shift in area bulk and shear compliances, if the eigenstrains obey certain conditions. The analysis can be extended to multiply connected inhomogeneous materials and materials with slipping interfaces.