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How engineering analyses the failure behaviour of brittle materials? 


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Engineering analyses the failure behavior of brittle materials by using various approaches and models. One approach is to improve existing failure theories, such as Rankine's and Mohr's, by addressing accuracy issues and offering improved models . Another approach involves developing versatile model-free methods for linking damage in highly heterogeneous materials at multiple scales, which can be applied even when statistical homogeneity ceases to exist . Additionally, supervised machine learning frameworks have been developed to predict failure in brittle materials by using time-series data and pattern recognition schemes . Unified failure criteria have also been proposed, consisting of conditions related to local stress and stress gradients, to determine failure in isotropic brittle materials regardless of the presence of cracks or notches . Furthermore, the brittle failure pattern of composite materials with interaction and energy feedback between different materials has been investigated through laboratory tests and numerical simulations .

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The provided paper discusses the use of a supervised machine learning framework to predict failure in brittle materials. It does not specifically mention how engineering analyses the failure behavior of brittle materials.
The paper presents a model-free approach that uses phase-field modeling and coarse-graining techniques to analyze the failure behavior of brittle materials.
The paper presents an improved mathematical model, based on Mohr's failure criterion, for predicting the failure of brittle materials under complex stresses.
The paper discusses the failure behavior of brittle materials and proposes a set of failure criteria to analyze the failure of structural components made of brittle materials.

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