The second-order procedure: Exact vs approximate results for isotropic, two-phase composites (Q1975228)

The authors investigate the effect of relaxing the proportional strain hypothesis used by the second author [ibid. 44, No. 6, 827-862 (1966; Zbl 1054.74708)] in the context of second-order estimates for effective behaviour of three-dimensional statistically isotropic two-phase nonlinearly or viscous composites. It is found that this hypothesis does not hold in general, but it leads to fairly small errors. Finally, it is emphasized that the improvement given in this paper affects only three-dimensional statistically isotropic two-phase systems.