Surrogate Computational Homogenization of Viscoelastic Composites

Abstract

We establish a surrogate model for computational homogenization of composite materials consisting of multiple viscoelastic constituents. A surrogate macroscopic material is identified by performing interpolation using radial basis functions (RBFs) and cubic spline functions on a constitutive database generated by a series of microscopic analyses or, equivalently, numerical material tests (NMTs) on a unit cell to represent anisotropic stress relaxation behavior as well as its dependence on strain rate and temperature. After briefly reviewing the two-scale boundary value problem derived based on homogenization theory, an RBF interpolation with a normalized kernel is formulated for a discrete dataset, and an optimization algorithm is applied to determine the three hyperparameters so as to achieve proper interpolation. Then, we formulate the surrogate homogenization model (SHM) using the interpolants to substitute for the macroscopic viscoelastic response. To show the specific procedure of the proposed surrogate modeling and demonstrate the performance of the created SHM, a representative numerical example is presented in the offline and online stages. In the offline stage, NMTs are carried out in the space of training data, including the temperature, to generate a dataset as long as the macroscopic stresses can be learned exhaustively, and then optimization is performed to determine the set of hyperparameters. Then, to validate the created SHM, its responses to unseen loading and temperature histories are compared with the corresponding NMT results. In the online stage, the created SHM is used to carry out a macroscopic analysis of a simple structure under specific loading and temperature conditions, and subsequently, the obtained macroscopic stresses are compared with those obtained from the localization analysis results. The results are also compared with those obtained from the single-scale direct numerical analyses.