The present paper discusses the evolution of a critical plane‐based multiaxial high‐cycle fatigue criterion, known as Carpinteri–Spagnoli criterion. By proposing appropriate changes to the original formulation, the extended versions of the aforementioned criterion are able to assess smooth and notched metallic structural components subjected to different fatigue loading conditions, such as multiaxial in‐phase and out‐of‐phase synchronous cyclic loading, asynchronous cyclic loading and random loading. The results obtained through this criterion are compared with some experimental results related to relevant data reported in the literature.

In this paper a unified finite element methodology based on gradient-elasticity is proposed for both two-and three-dimensional problems, along with some considerations about the best integration rules to be used and a comprehensive convergence study. From the convergence study it has emerged that for both two and three-dimensional problems, the implemented elements show a convergence rate virtually equal to the corresponding theoretical values.Recommendations on optimal element size are also provided. Furthermore, the ability of the proposed methodology to remove singularities in statics has been demonstrated through a couple of examples, in both two and three dimensions.

The present paper investigates the importance and relevance of using microstructural length scale parameters in estimating the high-cycle fatigue strength of notched plain concrete. In particular, the accuracy and reliability of the Theory of Critical Distances and Gradient Elasticity are checked against a number of experimental results generated by testing, under cyclic bending, square section beams of plain concrete containing stress concentrators of different sharpness. The common feature of these two modelling approaches is that the required effective stress is calculated by using a length scale which depends on the microstructural material morphology. The performed validation exercise demonstrates that microstructural length scale parameters are successful in modelling the behaviour of notched plain concrete in the high-cycle fatigue regime.

ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.Please This comprehensive validation exercise demonstrates that the systematic usage of this transformative design approach leads to the same level of accuracy as the one which is obtained by applying the classic Theory of Critical Distances. This result is certainly remarkable since the proposed approach is not only very efficient from a computational point of view, but it also allows high-cycle fatigue damage to be assessed by directly postprocessing gradient-enriched stress states determined on the surface of the component being assessed., cite this paper as: Bagni, C., Askes, H., Susmel, L. Gradient elasticity: a transformative stress analysis tool to design notched components against uniaxial/multiaxial high-cycle fatigue. Fatigue Fract Engng Mater Struct. 39 8, pp. 1012-1029

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