Formalisation of a novel finite element design method based on the combined use of Gradient Elasticity and the Theory of Critical Distances

The present research work is dedicated to the development, implementation and validation of a unified finite element methodology based on the combination of gradient elasticity and the Theory of Critical Distances, for the static and high-cycle fatigue assessment of notched engineering components. The proposed methodology, developed for plane, axisymmetric and three-dimensional problems, takes full advantage of both the TCD's accuracy in estimating static and high-cycle fatigue strength of notched components and of the computational efficiency of gradient elasticity in determining non-local stress fields whose distribution fully depends on the value of the adopted length scale parameter. In particular, the developed methodology, due to the ability of gradient elasticity to smooth stress fields in the vicinity of notch tips, has the great advantage of allowing accurate and reliable static and fatigue assessments of notched components by directly considering the relevant gradient-enriched stresses at the hot-spot on the surface of the component, in contrast to existing conventional approaches that require the knowledge of the failure location into the material a priori. This advantage, together with the fact that the proposed methodology can be easily implemented in commercial finite element software, makes the developed methodology a powerful and easy-to-use tool for the static and fatigue design/assessment of notched components. The developed methodology is accompanied by an accurate investigation of the best integration rules to be used as well as a comprehensive convergence study both in absence and presence of cracks, leading to a practical guideline on optimum element size. The proposed gradient-enriched methodology has been validated against a large number of problems involving notched components subject to both static and fatigue loading, covering a wide range of materials, geometries and loading conditions, clearly showing its accuracy and versatility. The developed gradient-enriched methodology has also been extended to the study of the dynamic behaviour of visco-elastic materials subject to vibration.