Engineering fields such as aerospace rely heavily on the Finite Element Method (FEM) as a modelling tool. In combination with the scale and complexity of the structures typically involved here, computational cost remains a traditional issue. To perform FEM analyses of such struct
...
Engineering fields such as aerospace rely heavily on the Finite Element Method (FEM) as a modelling tool. In combination with the scale and complexity of the structures typically involved here, computational cost remains a traditional issue. To perform FEM analyses of such structures efficiently nonetheless, engineers rely on techniques such as substructure homogenisation. Essentially, the advantages to using homogenised models are an easier division of labour, less model preparation time and a reduced computational time. Unfortunately, the classical approach to substructuring is either limited to linear elasticity as in the case of static condensation, or is still computationally expensive as non-linear FEA of detailed substructure models need to be performed each time a different loading is applied to the full structure. To improve the efficiency and/or accuracy of homogenised substructures, it would therefore be of interest to develop a methodology which allows to capture a complex structural response without constantly resorting to non-linear FEA. An emerging technology that may assist in improving the efficiency and accuracy of how homogenised substructures are modelled, is machine learning. While the fundamental principles of this field were developed in the 1940's, the ever-increasing accessibility and magnitude of computational power have resulted in a leap of popularity since the 1990's. Especially the (deep) Artificial Neural Network (ANN), a versatile machine learning framework, has proven to be a promising tool that can perform tasks ranging from image recognition to the failure analysis of composites. In the current master's thesis, a framework is developed that integrates ANN and FEM techniques as to establish a highly flexible approach to substructure homogenisation. More specifically, this framework allows to establish a homogenised representation of a substructure regardless of its structural complexity (e.g. inclusions or cut-outs) and material complexity (e.g. damage progression and failure). To achieve this, traditional techniques to approximate homogenised behaviour are replaced by a constitutive model that is captured in an ANN. The developed framework consists of three parts. Firstly, the data generator module creates, runs and post-processes a series of FEM simulations of a chosen substructure, based on a predetermined Design of Experiments. In this DoE, all independent parameters (e.g. applied loads) that influence the response to be modelled should be sufficiently varied. The second module trains an ANN based on the generated data. In doing so, it learns to predict the homogenised mechanical behaviour of the chosen substructure as a function of the independent parameters. The third module then integrates this trained ANN in the FEM software package Abaqus as a user material subroutine (UMAT). The substructure of choice is now homogenised and represented by a single element, which can be readily used together with traditional elements in a global model.
The described methodology was applied to two FEM models of increasing complexity. The first model was a biaxially loaded, 2D elasto-plastic high strength steel material without additional complexities. An initial ANN design was made based on this model and it turned out that a network with 2 Hidden Layers (HL) and 10 nodes per HL was ideal to capture the response. Furthermore, it was determined that the ANN converged after training for 1,500 epochs with the 'Nadam' scheme. The second model was a composite plate with an elliptical cut-out and Hashin damage, thus adding both structural and material complexities. This model was loaded in biaxial tension and in-plane shear. A 2-HL network was found to be the most suitable architecture with 60 and 40 nodes in each HL respectively. A training time of 10,000 epochs was required to reach convergence using the Nadam optimiser, which led to an excellent fit of the mechanical response. Moreover, several input and output vectors for the ANN were investigated. It was concluded that the best results are obtained if the input vector contains the previous and current stress and strain state as well as the strain increment, whereas the output is the predicted stress increment.
