A differential homogenization method for estimating the macroscopic response and field statistics of particulate viscoelastic composites

Abstract

This work provides an analytical method for determining the time-dependent effective constitutive response of linear viscoelastic composites with particulate microstructures by means of a differential-algebraic system (DAS) of equations. By making use of differential equations instead of difference equations and utilizing, as primary variables, the variances of the field fluctuations instead of the properties of fictitious linear comparison composites, the new formulation is found to be more robust and to alleviate some of the issues associated with earlier incremental approaches. Remarkably, the new formulation can be shown to recover the exact results of the correspondence principle for isotropic incompressible composites subjected to proportional loading, as well as for isotropic compressible composites subjected to purely hydrostatic loading. More generally, the proposed formulation is not exact but still delivers reasonably accurate estimates in most cases. Lastly, a generalization of the DAS formulation is provided for nonlinear viscoelastic composites with incompressible phases and also found to be more robust than earlier approaches.