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Tim Wynn (old ICE) schrieb: > I also suspect that the physics is too unfamiliar or advanced for many list > members. To that end, maybe the main protagonists (Rob Twiss, Dugald > Carmichael & Falk Koenemann) could recommend some good, basic text books > and/or papers on thermodynamics, tensors and elasticity for the rest of us > to chase down. Speaking for myself, I took many classes from intro Stress & Def to a graduate class in plasticity. Because I checked everything I learned if it helped me to get closer to the problems I wanted to solve, and since this was not the case, I looked for other means. I also took a full cycle in engineering math, and at some point I decided that I should use math as a the only guidance. It was several years before I understood that (a) engineering math is largely an application of potential theory, whereas (b) continuum mechanics has very little to do with potential theory (and violates several of its principles). I had filtered the relevant concepts of potential theory out of my math education without knowing it. Many of the concepts which I had developed for myself - and which often were rejected with scorn - I found neatly worked out in all desirable detail in O.D. Kellogg, Foundations of potential theory. Springer Verlag, 384pp (1929) It is a mathematial textbook, but I found it quite readable. One has to provide the physical context oneself; in a way, potential theory is not a physical theory, but it gives the mathematical structure to all physical theories. Of utmost importance is eg. the chapter on the properties and physical significance of divergence, or the discussion of the conditions when the Gauss divergence theorem is applicable (and when not). Once one has read the chapter on the Poisson equation, and compared this mathematical concept with the physical concept of the thermodynamic system and thd. work, everything falls into place. It is then easy to explain why the Cauchy theory is incompatible with potential theory. My intro class to Stress & Def used JF Nye, Physical Properties of Crystals, for the development of the Cauchy-stress theory. I found this book insufficient, it contains far too many implied assumptions which are not discussed, and the book was written in the early 1950s when textbooks did not give references yet. Today I would not recommend it. The conceptual differences cannot be bridged; the most profound reason is: The Euler-Cauchy-(EC) theory is not a field theory in the mathematical sense. I give two examples for illustration: 1. A field assigns a vector to any point X_i in space. If the vector of one particular point X_0 is subtracted from the vectors of all other points, it is like viewing the world from the viewpoint X_0, ie. at X_0 there is no vector, but flow towards or away from X_0 at the points X_i in the neighborhood of X_0 is then easily identified. The Cauchy stress instead considers force vectors f acting on all planes A containing the point X_0, with the average f per unit plane acting on X_0. That is, f may vary with the orientation of A, but this means that an infinite number of vectors f all acting on X_0 are considered. These two concepts are incompatible with one another. A textbook in wide use in the mechanics of solids community is M.E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, 265pp (1981). Gurtin calls stress "a system of forces". For good reason; he knows precisely that stress is not a field. 2. All the books on the EC-theory known to me start with an equation of motion, ie. Newton's f = ma. This particular f is a vector, but only one discrete vector, it is _not_ a member of a vector field. Mathematicians use different notations for discrete vectors and vector fields. Force fields are derived from a potential, eg. f = dU/dx, first explained by Lagrange in 1784. The historical context is very enlightening. Euler's stress theory is from 1740-1776; he died in 1783. Euler did not know vector fields yet, and this point shows up to today. The theory which I offer, is a proper field theory. For field theories there is a plethora of methods worked out. For example, the EC-theory needs the finite element method for the modelling of a deformation which offers as many solutions as there are points in a predetermined grid of points. I can do the same with the Fourier series method; it gives a general solution which can then be solved for any point desired. Falk Koenemann _____________________________________________________________________ | Dr. Falk H. Koenemann Aachen, Germany | | | | Email: [log in to unmask] Phone: *49-241-75885 | | | | URL: http://home.t-online.de/home/peregrine/hp-fkoe.htm | | stress elasticity deformation of solids plasticity strain | |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~| | The rain, it raineth on the Just | | And on the Unjust fella. | | But chiefly on the Just because | | The Unjust stole the Just's umbrella. | |_____________________________________________________________________|