Bounds on overall instantaneous properties of elastic-plastic composites

M inimum principles of plasticity are used to derive upper and lower bounds on ordered eigenvalues and on diagonal terms of instantaneous stiffness and compliance matrices of elastic-plastic composite aggregates subjected to uniform overall stress or strain increments. The method is implemented with the help of a periodic model of binary fibrous composites ; overall properties are derived from incremental solutions of an inclusion problem in a small unit cell. Actual results are found with displacement and equilibrium formulations of the finite element method. In this implementation the instantaneous properties of the inelastic phases of the composite are known only in terms of the approximate values calculated at each step, hence the bounds are valid for an aggregate in which the actual properties have been replaced by the approximate ones. Examples are presented for the fibrous B-A1 system. The technique can be used to evaluate instantaneous element properties in a finite element program for analysis of metal matrix composite structures.