Two-scale Analysis of Elastoplastic Material by Means of RBF-Based Surrogate Model
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In recent years, several surrogate models and data-driven methods have been developed to replace the classical constitutive model for history-dependent materials, such as elastoplastic materials, with mechanistic machine learning techniques (MMLT) [1]. Also, the application of MMLT to multi-scale problems has been studied with a view to reducing computational costs [2]. However, to the best of our knowledge, most of those studies employ neural networks, in which the processes for regression are black box-like in terms of mechanism. Against this issue, we develop a surrogate model to replace the macroscopic elastoplastic constitutive models by means of radial basis function (RBF) interpolation. Thanks to the simplicity of RBF interpolation, we can easily understand how the macro-stress is regressed. At first, by conducting numerical material tests on a representative volume element (RVE) consisting of multiple elastoplastic materials, we obtain a data set that represents the macroscopic constitutive relationship associated with the RVE. Using the data set, we construct a surrogate model utilizing RBF interpolation after determining appropriate values for hyperparameters through optimization. To verify the applicability of the proposed model for two-scale analysis, we carry out macroscopic analysis of a structure by using the constructed surrogate model.
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