Generalized plane deformation of electromagnetic thermoelastic solids II. Further results on invariance shifts and reduced dependences

The validity of the invariance shifts on electromagnetic thermoelastic modu li is rigorously proven to be true for a multiply connected domain with pie cewise continuously varying moduli and/or with various spring-layer and con strained spring-layer interfaces. These results are further applied to esta blish the reduced dependence relations of the effective moduli upon the mat erial parameters. Particularly, for a homogeneous matrix with parallel infi nitely long cylindrical surfaces (including parallel tunnels of holes of va rious shapes and microcracks) in generalized plane strain deformation, all the stress, electric displacement and magnetic induction fields under presc ribed stress, electric displacement and magnetic induction boundary conditi ons, and all the normalized differences between the effective compliance an d the matrix compliance depend upon only the completely symmetric parts of the moduli tensors. For example, the in-plane minor symmetric elastic compl iance S-ijkl = S-jikl = S-ijlk and the piezoelectric tensor p(kij) = p(kji) may at most contain nine and six independent components, respectively: whi le the completely symmetric parts of S-ijkl and p(kij) contain at most five and four completely symmetric parts.