Radial basis function-based surrogate computational homogenization for elastoplastic composites at finite strain

A surrogate homogenization model (SHM) of finite strain elastoplastic composites is created by performing radial basis function (RBF)-based interpolation on a macroscopic constitutive dataset. The dataset is generated by numerical material tests on a unit cell under various loading conditions of macroscopic deformation histories and thus consists of data points and response points. The entities of the data points are feature variables consisting of the macroscopic deformation gradients and history-dependent variables (explanatory variable), and the response points are the macroscopic stress (objective variable). While following our previous study, this study has four new contributions as follows. First, the loss function is designed to ensure the generalization ability of the created SHM in the context of machine learning, allowing for a simplified optimization process without cross-validation. Second, we illustrate that the created SHM does not generate stresses for rigid body rotation, i.e., material flame-indifference. Third, thanks to the simple structure of RBFs, the first derivatives of the created SHM can be analytically obtained and are directly implemented to be used as the tangent moduli for the Newton–Raphson method. This allows more efficient solving of macroscopic boundary value problems than performing automatic differentiation to obtain the analytical tangent moduli. Fourth, the performance of the proposed model is also verified by comparing the solutions obtained by macroscopic and localization analyses using the created SHM with those obtained by FE².