Falk H. KoenemannEmail: Peregrine@T-Online.de
Snailmail: Im Johannistal 19
The subject of this website is continuum mechanics. The groundwork in the understanding of stress and deformation was initiated in the 17th century, and was essentially finished ca. 1830. These foundations have been refined over time, but they have not been drastically revised.
Here, a thought experiment is suggested. Consider the hypothetical situation that we know about theoretical physics today what we actually do know, but for some reason nobody ever spent a minute of thought on stress and deformation. This is going to be done only now. The question is: What would be the very first thought as to how the topic is approached?
What is the quintessential aspect of deformation that characterizes it as a physical process, and assigns its proper place in the context of the rest of physics?
Would the answer to that question be the same as in 1700 or 1800?
I contend that this is not so. Whereas Hooke worked on the "power of springing bodies", Boyle worked on "the spring of the air". They co-authored a paper on Guericke's air pump. Thus they clearly knew they worked on the same problem. However, Hooke's law and elasticity of solids is today understood entirely in terms of Newtonian mechanics whereas Boyle's law is today a part of the thermodynamic equation of state.
Up to now, deformation is understood as a change of shape. Here I make the point that by nature, elastic deformation of solids is a change of state in the sense of the First Law of Thermodynamics.
But nothing in the theory of continuum mechanics suggests that it is so. This point is explained in detail on this homepage, and an alternative is offered.
One of the successes of the approach offered here is the identification of an instability at the transition from the elastic-reversible to irreversible material behavior. This instability is a strong candidate for the origin of turbulence, and its geometric properties permit the precise prediction of cracks in solids.
The new approach: the files can be downloaded in PDF-format.
A poster which I have shown recently on several conferences, contains the two cardinal points of my disagreement with the Euler-Cauchy theory, a condensed outline of the approach offered here, and some predictions based on the new approach on topics where the classical theory fails.
The approach which I worked out has very few precursors. In essence, it is an adaption and re-formulation of the thermodynamic theory. However, I have apparently duplicated the conceptual work by two founding fathers of thermodynamics, Rudolf Clausius and Eduard Grüneisen. Their papers are hard to find in libraries, and they are in German.
English translations of these papers can be downloaded here.
Last update: 18 November 2013