Multi-scale Modelling of Natural Composites Using Thermodynamics-Based Artificial Neural Networks and Dimensionality Reduction Techniques

Abstract

Modelling natural composites, as the majority of real geomaterials, requires facing their intrinsic multiscale nature. This allows to consider multiphysics coupling occurring at the microscale, then reflected onto the macroscopic behavior. Geotechnics is constantly requiring reliable constitutive models of natural composites to solve large-scale engineering problems accurately and efficiently. This need motivates the contribution. To capture in detail the macroscopic effects of microscopic processes, many authors have developed multi-scale numerical schemes. A common drawback of such methods is the prohibitive computational cost. Recently, Machine Learning based approaches have raised as promising alternatives to traditional methods. Artificial Neural Networks -ANNs -have been used to predict the constitutive behaviour of complex, heterogeneous materials, with reduced calculation costs. However, a major weakness of ANN is the lack of a rigorous framework based on principles of physics. This often implies a limited capability to extrapolate values ranging outside the training set and the need of large, high-quality datasets, on which performing the training. This work focuses on the use of Thermodynamics-based Artificial Neural Networks -TANN -to predict the constitutive behaviour of natural composites. Dimensionality reduction techniques -DRTs -are used to embed information of microscopic processes into a lower dimensional manifold. The obtained set of variables is used to characterize the state of the material at the macroscopic scale. Entanglement of DRTs with TANN allows to reproduce the complex nonlinear material response with reduced computational costs and guarantying thermodynamic admissibility. To demonstrate the method capabilities an application to a heterogeneous material model is presented.