Thoughts on the Concept of Stress

The concept of contact stress was introduced by Cauchy in 1823. It is a special case of what, in Sect. 4, I call a contactor for a surface interaction. Another special case is heat flux, introduced by Fourier in the beginning of the 19th century. In the past 60 years or so, a lot of work has been done to investigate the conditions needed to prove the existence of contactors, but there are still open questions. More recently, a concept of stress has been considered that describes interactions at a distance. For force-interactions, I call this kind of stress a reaching stress and give a precise mathematical definition in Sects. 5 and 6. Perhaps contact stresses can be derived as limit cases of reaching stresses.