Fully optimized variational estimates for the macroscopic response of nonlinear composites (INVITED)

Abstract eng:
A variational method is proposed to estimate the macroscopic constitutive response of composite materials with nonlinear properties. The method derives from a stationary variational principle for the macroscopic potential in terms of the corresponding potential of a linear comparison composite (LCC) whose properties are the trial fields in the variational principle. The resulting estimates for the macroscopic response are guaranteed to be exact to second-order in the heterogeneity contrast, and to satisfy known bounds. In addition, the new method allows full optimization with respect to the properties of the LCC, leading to estimates that are fully stationary and exhibit no duality gaps. Consequently, the macroscopic response and field statistics of the nonlinear composite can be estimated directly from the suitably optimized linear comparison composite, without the need for difficult-to-compute correction terms. The method is applied to a porous viscoplastic material, and the results are compared with earlier estimates.

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