engleski

Modelling the elastoplastic behaviour of heterogeneous materials using neural networks

For centuries, constitutive material behaviour is described by long-established analytical expressions. Such constitutive material models, as well as material constants, have been obtained using many experimental trials conducted over many years throughout history. Traditionally, these expressions have been sufficient to describe classical engineering problems. However, due to increasing exploitation of known materials and usage of new materials with heterogeneous microstructure, there is need for more accurate and better description of the material constitutive behaviour. Several different approaches have been proposed to describe the constitutive behaviour of heterogeneous materials over past few decades, among which the most popular is the multiscale method. Although the results of multiscale numerical simulations are satisfactory accurate, the two-scale calculation is time-consuming and computationally expensive process. For this reason, many homogenization methods (reduced homogenization methods) have been developed that seek to find the optimum between the accuracy of the results and the complexity of the calculation. A robust and efficient method of homogenization with a reduced number of degrees of freedom, based on machine learning, has led to significant acceleration of multiscale modelling. The use of reduced order homogenization to solve multiscale problems has proven to be extremely useful for obtaining a large database that will be used to create neural network-based material models. The present work shows the use of the mentioned methods for numerical modelling of nodular cast iron. Calculations are performed on a nodular cast iron RVE using the clustering, and a large database is obtained for different cases of monotonic loading. This database is used to train the neural networks. The entire analysis is performed assuming small strains and plane strain. Deformations are used as input data for neural networks, while the goal is to accurately predict homogenized stress. Neural networks are made using open-source software TensorFlow and Keras API based on the Python programming language.

neural networks, heterogeneous materials, machine learning, elastoplastic behaviour, nodular cast iron

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