an interesting puzzle for fun:

Lame’s classical solution for an elastic 2D plate, with a hole of radius a and uniform tensile stress applied at the far field, gives a stress concentration factor (SCF) of two at the edge of the hole. This SCF=2 is independent of the hole radius.

Consider what happened to this concentration factor if the radius a approaches infinitely small. The SCF is independent of a, so it remains equal to two even when the hole disappears.

This is inconsistent with what one would expect physically, namely that the limit a->0 should be the same as when the plate is whole without a hole and has no stress concentration.

Henry.

Using the Griffith energy method for analysis of cavitation under hydrostatic tension we conclude that the critical tension tends to infinity when the cavity radius approaches zero (IJSS, 2006, doi: 10.1016/j.ijsolstr.2006.12.022). The conclusion is physically meaningless, of course. Moreover, if we assume that the failure process occurs at the edge of the cavity then the critical tension should be length-independent for small but finite cavities while the Griffith analysis always exhibits length-dependence. The main Griffith idea - introduction of the surface energy - is controversial because it sets up the characteristic length, say, surface energy over volume energy. By no means is this approach in peace with the length-independent classical continuum mechanics.

Several people have suggested that iMechanicians compile a set of classics in mechanics. Given the mission of iMechanica (to use the Internet to enhance communications among mechanicians, and to pave a way to evolve all knowledge of mechanics online), it seems fitting for us to facilitate the communication with mechanicians of all times, and to embrace publications of all times.

I'm adding "classics" as a tag featured at the top of iMechanica. You will have to interpret for yourself what you consider to be a classic. For me, a classic should have stood the test of time (say greater than 20 years) and have influenced me deeply and directly. I should have read it and used it in my own work.

A.A. Griffith (1893-1963) graduated from the University of Liverpool, England in 1921 with the degrees of B. Eng., M. Eng., and D. Eng. He entered the Royal Aircraft factory in 1915 and advanced through a workshop traineeship followed by other positions to become senior scientific officer in 1920. In 1917, together with G.I. Taylor, he published a pioneering paper on the use of soap films in solving torsion problems, and in 1920 he published his famous paper on the theory of brittle fracture. He then worked on the design theory of gas turbines. Griffith was Head of the Engine Department of the Royal Aircraft Establishment in 1938 and joined Rolls Royce as research engineer in 1939. He worked first on conceptual design of turbojet engines and later on vertical takeoff aircraft design. He retired in 1960 but continued working as a consultant for Rolls Royce.

His paper on fracture foreshadowed much of the later development of fracture mechanics. The paper should be read by every student in mechanics. A pdf file is available in JSTOR.