Macroscopic behavior and field fluctuations in viscoplastic composites: second-order estimates vs. full-field simulations

M. I. IDIART; H. MOULINEC; P. PONTE CASTAÑEDA; P. SUQUET

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

Elsevier

Año: 2006 vol. 54 p. 1029 - 1063

0022-5096

This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm (Moulinec & Suquet, C.R. Acad. Sci. Paris II 318 (1994) 1417), while the theoretical estimates follow from the so-called ``second-order´´ procedure (Ponte Casta~neda, J. Mech. Phys. Solids 50 (2002) 737). Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding ``second-order´´ estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general,  the ``second-order´´ estimates  are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates.  Thus, it is demonstrated that the ``second-order´´ method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites.