UPPER AND LOWER BOUNDS FOR NONLINEAR COMPOSITE BEHAVIOR

Existing theory for bounding the non-linear behaviour of composites is reviewed and extended. In particular, some new bounds for the overall creep behaviour of textured polycrystals are presented, for illustration. A deficiency of the established machinery for bounding non-linear properties is that it usually generates only one bound, either a lower or an upper bound, that improves on the corresponding ''classical'' bound, and for some composites it may produce no new bound at all. Theory is at present being developed to rectify this situation: improved bounds are now in prospect for all composites to which the ''classical'' bounds may be applied. It involves some relatively sophisticated analysis more appropriate for presentation elsewhere. The essential ideas are described, however, and a formula which encapsulates the new reasoning and reproduces automatically the already-established non-linear results is displayed.