Computational Mechanics and Design Group

Department of Civil & Structural Engineering

Theory of critical distance and gradient mechanics


This project aims to develop novel finite element software based on the combined use of the Theory of Critical Distance (TCD) and Gradient Mechanics suitable for performing the static and high-cycle fatigue assessment of notched/cracked components subjected to in-service complex systems of forces. Even though they are designed to address two different problems, the most interesting feature of the above two theories is that both make use of a length scale that is intrinsic to the material: the TCD uses a critical distance, which is treated as a material property, to perform the strength analysis, whereas Gradient Mechanics employs a scale length to perform the stress analysis. In spite of the evident analogies, so far such theories have never been attempted to be coupled consistently. However, a unification has many potentials for scientific breakthroughs: it would take full advantage, on one hand, of the TCD’s accuracy in estimating static and high-cycle fatigue strength of notched/cracked components and, on the other hand, of the computational efficiency of Gradient Mechanics in determining equivalent stress fields whose distribution fully depends on the actual value of the adopted length scale.

In this scenario, aim of the present joint project is then to reformulate the Gradient Mechanics concepts to develop the governing equations of specific bi- and tri-dimensional finite elements which can be used to determine the stress fields in the vicinity of the crack initiation sites, the strength analysis being directly, but implicitly, performed according to the TCD.


The University of Sheffield & Safe Technology

Project dates

Start date: 
February 2012