Celebrating the 100th Anniversary of Inglis Result: From a Single Notch to Random Surface Stress Concentration Solutions

We celebrate the first quantitative evidence for the stress concentration effect of flaws analyzed by Inglis. Stress concentration factor (SCF) studies have evolved ever since Inglis' 1913 result related to the problem of the elliptical hole in a plate, which also approximately applies to the half-elliptical notch case. We summarize a hundred years of development of the SCF with the exclusive focus on analytical solutions, with a very specific route: the series of works reviewed and presented herein include a parade of solutions beginning with (and those that followed) Inglis famous result, continue with periodic discrete discontinuities, sinusoidal periodic surfaces, and end with more complex continuous configurations such as random surfaces. Furthermore, we show that the form of Inglis' result is powerful enough to serve as first-order approximation for some cases of multiple discontinuities and even continuous rough topologies. Thus, we proposed the Modified Inglis formula (MIF), to estimate the SCF for a variety of configurations, in honor to Inglis' historical result. The impetus of this review stems from the fact that for many engineering problems involving multiphysical solid-fluid interactions, there is a broad interest to couple stress concentration relationships with thermodynamics, fluid dynamics, or even diffusion equations in order to expand understanding on stress-driven interactions at the solid-fluid interface. Additionally, a handy first-order estimate of the SCF can serve in the initial stage of designs of structures and parts containing discontinuities.