Abstract
Accuracy and computational simplicity are both sine qua non for micro-mechanical models which would be candidates for incorporation in structural analysis treating combined nonlinearities. To date there are a number of micro-models and most of these employ either a square cell or a circular cell as the representative volume element. The present paper discusses the accuracy of typical micro-models belonging to either category. A simplified square cell model (SSCM) derived from elementary mechanics is presented and this model is shown to give results almost identical to those of Aboudi's method of cells (AMC). A finite element-based 3-phase cylindrical fiber model (FECM) is developed with the primary object of determining the stress variation at the micro-level and thus the initiation of local failure. This model is apparently the most accurate in the set of models considered in the paper.
It is confirmed that the closed form expressions of Hashin and Rosen in conjunction with the expressions to determine the transverse shear modulus given by Christensen and Lo offer a viable approach to the determination of elastic constants. The AMC and SSCM too provide sufficiently accurate prediction of plastic constants. However for the determination of initial yielding under combined loading, a micro-model which gives the variation of stresses across the model is required. The problem of the prediction of first yield of a metal matrix composite is considered and the results of the FECM are compared with those of the simpler square cell models and the hexagonal array model of Dvorak. The square cell models fail in the prediction of the first yield in the context of stress states which are nearly hydrostatic. The present FECM model is seen to be very effective because of the uncoupling of harmonics in the solution process and promises to be an effective tool for the inelastic analysis of the composites.
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