Abstract:Self-healing, obtained by the oxidation of a glass-forming phase, is a crucial phenomenon to ensure the lifetime of new-generation refractory ceramic-matrix composites. The dynamics of oxygen diffusion, glass formation and flow are the basic ingredients of a self-healing model that has been developed here in 2D in a transverse crack of a mini-composite. The presented model can work on a realistic image of the material section and is able to simulate the healing process and to quantify the exposure of the material to oxygen: a prerequisite for its lifetime prediction. Crack reopening events are handled satisfactorily, and healing under cyclic loading can be simulated. This paper describes and discusses a typical case in order to show the model capabilities.Keywords: self-healing; ceramic-matrix composites; image-based modelling
e-Xstream engineering develops and commercializes the Digimat suite of software, a state-of-the-art multi-scale material modeling technology that speeds up the development process for composite materials and structures. Digimat is a core technology of 10xICME Solution and is used to perform detailed analyses of materials on the microscopic level and to derive micromechanical material models suited for multi-scale coupling of the micro- and macroscopic level. Digimat material models provide the means to combine processing simulation with structural FEA. This means to move towards more predictive simulation by taking into account the influence of processing conditions on the performance of the finally produced part.
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The weight matrices of a neural network are initialized randomly or obtained from a pre-trained model. These weight matrices are multiplied with the input matrix (or output from a previous layer) and subjected to a nonlinear activation function to yield updated representations, which are often referred to as activations or feature maps. The loss function (also known as an objective function or empirical risk) is calculated by comparing the output of the neural network and the known target value data. Typically, network weights are iteratively updated via stochastic gradient descent algorithms to minimize the loss function until the desired accuracy is achieved. Most modern deep learning frameworks facilitate this by using reverse-mode automatic differentiation58 to obtain the partial derivatives of the loss function with respect to each network parameter through recursive application of the chain rule. Colloquially, this is also known as back-propagation.
At present, GNNs are probably the most popular AI method for predicting various materials properties based on structural information33,65,66,67,68,69. Graph neural networks (GNNs) are DL methods that operate on graph domain and can capture the dependence of graphs via message passing between the nodes and edges of graphs. There are two key steps in GNN training: (a) we first aggregate information from neighbors and (b) update the nodes and/or edges. Importantly, aggregation is permutation invariant. Similar to the fully connected NNs, the input node features, X (with embedding matrix) are multiplied with the adjacency matrix and the weight matrices and then multiplied with the nonlinear activation function to provide outputs for the next layer. This method is called the propagation rule.
Kusche et al. applied DL to localize defects in panoramic SEM images of dual-phase steel230. Manual thresholding was applied to identify dark defects against the brighter matrix. Regions containing defects were classified via two neural networks. The first neural network distinguished between inclusions and ductile damage in the material. The second classified the type of ductile damage (i.e., notching, martensite cracking, etc.) Each defect was also segmented via a watershed algorithm to obtain detailed information on its size, position, and morphology.
One of the major uses of NLP methods is to extract datasets from the text in published studies. Conventionally, such datasets required manual entry of datasets by researchers combing the literature, a laborious and time-consuming process. Recently, software tools such as ChemDataExtractor262 and other methods263 based on more conventional machine learning and rule-based approaches have enabled automated or semi-automated extraction of datasets such as Curie and Néel magnetic phase transition temperatures264, battery properties265, UV-vis spectra266, and surface and pore characteristics of metal-organic frameworks267. In the past few years, DL approaches such as LSTMs and transformer-based models have been employed to extract various categories of information268, and in particular materials synthesis information269,270,271 from text sources. Such data have been used to predict synthesis maps for titania nanotubes272, various binary and ternary oxides273, and perovskites274. 2ff7e9595c