A data-driven micro-macro coupled multiscale analysis for hyperelastic composite materials

A data-driven approach is developed for micro-macro coupled multiscale analysis of hypere-lastic composite materials. The offline process in this approach is to make a database that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients. This can be done by carrying out an adequate number of numerical material tests on a periodic microstructures, or equivalently, a unit cell and followed by the proper orthogonal decomposition (POD) to extract the principal components of the data along with the corre-sponding basis vectors. In order to realize FE²-type two-scale analysis in the online process, we interpolate each of the coefficients with the radial basis functions as a function of a macroscopic deformation gradient and make the resulting continuous function gently varying by means of the L2-regularization followed by the cross-validation and Bayesian optimization techniques. Each of the functions thus obtained is referred to as “data-driven function” of the microscopic stress distribution and can be used to obtain the macroscopic stress by the averaging process in the homogenization method. A representative numerical example is presented to validate the proposed data-driven FE² analyses in comparison with high-fidelity direct FE² .