An image-based numerical homogenization strategy for the characterization of viscoelastic composites

An image-based strategy to characterize viscoelastic composites is presented. The homogenized relaxation moduli are computed in the direct time domain at independent discrete instants by applying effective constant strain fields to a representative volume element of the heterogeneous material. The relaxation master curves are then adjusted via an optimization problem using the generalized Maxwell model represented by the Prony series. In the proposed strategy, we consider image-based modeling, in which every voxel can be interpreted as an element in the Finite Element Method (FEM) formulation, thus dramatically reducing the time-consuming task of meshing the domain. Here, a matrix-free solver is employed to handle the multiple simulations at each instant, which significantly lowers the memory requirements of the computations. Nevertheless, the procedure admits employment of other sorts of memory-efficient solvers. The proposed strategy enables the evaluation of viscoelastic properties of samples depicted by images with hundreds of millions of voxels using personal computers. In that sense, it can be an interesting option for those working with image acquisition devices. Two- and three-dimensional examples are analyzed to showcase effectiveness and to validate both the formulation and the implementation. The results captured well the anisotropic nature of the studied microstructures and the expected variation in the relaxation behavior given different ratios of elastic to viscoelastic constituents.