A new derivative on the shift property of effective elastic compliances for planar and three-dimensional composites

Based on Hill's condition and a field-fluctuation approach, a new derivation is given for the shift property of effective compliances for both planar and three-dimensional composites. The derived relations are exact, and hold for any kind of microstructures and anisotropy. To provide a link to the well-known shift property of Cherkaev, Lurie Milton in plane elasticity, special reference is given to two-dimensional composites and voided materials with isotropic constituents, but covering both overall inplane isotropy and orthotropy. This method is substantially simpler than the stress-invariance approach commonly adopted in the literature and it provides a new means of addressing the shift characteristics of the effective compliances. By this approach, several universal relations governing the effective compliances of three-dimensional and two-dimensional composites are also found, to our knowledge, for the first time.