We explore the possibility to cloak a region in curvilinearly anisotropic background materials in the context of conductivity. Materials with curvilinear anisotropy possess constant properties in specific curvilinear coordinate. For cylindrically and spherically anisotropic solids, the cloak center and the origin of material coordinate are generally not collocated. We show that in combination with a rigid-body translation from the cloak center to the material origin, the previous coordinate transformation procedure remains applicable. But now the transformed material specifications depend on the position of cloak center. The validity of the cloak parameters is verified by finite element simulations.
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