Field fluctuations and macroscopic properties for nonlinear composites (Q1434662)

The authors study a new version of the second-order method of \textit{P. Ponte Castañeda} [J. Mech. Phys. Solids 50, No.~4, 737--757 (2002; Zbl 1116.74412)] to estimate the effective behaviour of power-law fibrous composites with arbitrary heterogeneity contrasts subject to plane- and anti-plane strain loading conditions. Estimates of Hashin-Shtrikman type for macroscopic behaviour, along with the corresponding estimates for strain and stress fluctuations, are presented and discussed. Simple expressions for strongly nonlinear rigid-perfectly plastic limit are derived and studied in detail. The resulting predictions seem to be consistent with deformation mechanisms involving shear bands. In the fiber-reinforced case, this translates into non-reinforcement effect, and infinite strain fluctuations are predicted in the matrix.