### Monday, 11 October 2004 - 1:00 PM

### This presentation is part of : Torquato Symposium

### Bounds on the creep of composites under hydrostatic loading

**Vladimir Vinogradov** and Graeme W. Milton. University of Utah, Department of Mathematics, 155 S 1400 E, Rm 233, Salt Lake City, UT 84112
Most materials exhibit some viscoelastic response: polymers, wood, bone tissue, metals at high temperature and many others demonstrate such behavior. Once mixed together, viscoelastic materials form a composite with effective viscoelastic properties, which are of interest for practical applications.

We consider the problem of bounding the total creep (or total stress relaxation) of a composite made of two linear viscoelastic materials and subjected to a constant hydrostatic stress/strain. For a linear viscoelastic material subjected to a monotonic loading, the response can be evaluated as a superposition of cyclic loadings of the complete spectrum of frequencies. However, the immediate and the relaxed responses of the phases as well as the composite are purely elastic and correspond to the responses at infinite and zero frequency loadings, respectively.

We apply the translation method to correlate the effective bulk moduli of a viscoelastic composite at zero and infinite time. A number of microgeometries are found to attain the coupled bounds. It is shown that Hashin's composite sphere assemblage does not necessarily have the maximum or minimum overall creep. For instance, there are cases when doubly coated sphere microstructures or more complicated microstructures have the maximum or minimum possible creep.

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