Abstract
By incorporating the periodic Green function, which is obtained from the instantaneous nominal moduli of the matrix, in the method of periodic structures (MPS), and utilizing the extremum principles of Hashin and Shtrikman (1962), the overall moduli of a rate-independent elastic-plastic matrix reiforced with periodic distribution of cylindrical inclusions are obtained. The MPS, itself, is re-examined by homogenizing the quasi-static rate equilibrium equations and utilizing a periodic stress-free velocity gradient. It is shown that by evaluating the instantaneous nominal moduli of the matrix based on the velocity gradient in the matrix adjacent to the inclusion, instead of the average velocity gradient in the matrix, a lower bound to the overall moduli can be obtained. The numerical example involves analysis of the growth of circular cylindrical cavities in an isotropically hardening matrix.
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