Neuber’s rules and other solutions: Theoretical differences, formal analogies and energy interpretations

•A brief overview of the solutions for nonlinear notch stress–strain concentration is provided.•Particular focus is dedicated to their theoretical differences and formal analogies.•Energy interpretations of different solutions are discussed as well.

The aim of this paper is to present a brief overview of the solutions provided in the literature on the analysis of nonlinear stress–strain concentration at pointed and radiused notches, with particular focus on their theoretical differences and formal analogies. In addition, energy interpretations of different solutions are discussed, with the aim to shed some additional light on their theoretical differences.