The Breadth and Depth of Continuum Mechanics: A Collection - download pdf or read online
By Professor Dr. Constantine M. Dafermos, Professor Dr. Daniel D. Joseph, Professor Dr. Frank M. Leslie (auth.)
This quantity collects papers devoted to Jerry Ericksen on his 60th birthday, December 20, 1984. They first seemed in Volumes 82-90 (1983-1985) of the Archive for Rational Mechanics and research. on the request of the Editors the checklist of authors to be invited was once drawn up via C. M. Dafermos, D. D. Joseph, and F. M. Leslie. The breadth and intensity of the works right here reprinted mirror the corresponding features in Jerry Ericksen's examine, educating, scholarship, and notion. His pursuits and expertness heart upon the mechanics of fabrics and expand to every thing which may give a contribution to it: natural research, algebra, geometry, via all facets of theoretical mechanics to basic scan, all of those illumi nated by way of an intimate and deep familiarity with the resources, even very outdated ones. he's self reliant of faculty and contemptuous of occasion spirit; his generosity in freely giving his principles is popular, yet no longer everyone seems to be able to accepting what's provided. His writings are for free of huge claims and attributions past his personal learn. a few are decisive, a few are prophetic, and all are forthright. His paintings has served as a beacon of perception and straightforward honesty in an age of ever extra trivial and corrupt technology. The authors of the memoirs during this quantity are his scholars, colleagues, admirers, and (above all) his friends.
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Extra resources for The Breadth and Depth of Continuum Mechanics: A Collection of Papers Dedicated to J.L. Ericksen on His Sixtieth Birthday
12) yield a one-parameter family of necks and bulges. *, there is a unique bulge (b). Z' z" z _ Fig. 6. 2). 16)1 can be solved to yield a value of A" with T(A") < r. 2) in which the fiber would appear striated with A' and A" the extremal values of A. Fig. 7. 2). Two such pairs, (A', A") and (ii, ;h, are shown here. General Remark. 17a) = T*. 17b) A. 18) A. , that A (J() ) yeA) c + exp ( 2 / y(;) tis = O. 19) 32 B. D. ) is differ- = f3(A) 1 ="2 d dA y(A). 2) is obtained from a variational principle requiring the vanishing of the first variation bG of the mean Gibbs free energy G of a fiber in equilibrium under a tensile load ro.
D. 10) where T* stands for the uniform tension TO. Such a solution may be called a fully developed draw, and (for A* > A*) the ratio A*/A* may be called the draw ratio. As the second sketch in Figure 2 can be generated from the first by reflection of the z-axis through the point where Azz = 0, we may confine attention to cases where A* > A*. 10) uniquely determine the triplet (T*, A*, A*), and hence only one fully developed draw is possible. 10) is shown in Figure 3. 7) with A(a) = A* and ro = T* (and with chosen so that A(Z) is any preassigned value of A in the range A* < A < A*).
22). , the reciprocal of the expansion of the scale of z. 4), accounts for those departures from homogeneity of the deformation field that are of order two or less in the scaling of distance, and the remaining terms are of order four. 18) will be derived below. In this section I have sought to explain why the relation may serve as a good, but approximate, model of an extendable long fiber in tension. xFig. 1. Graph of the function T relating the tension in a homogeneous extension to the stretch ratio J..
The Breadth and Depth of Continuum Mechanics: A Collection of Papers Dedicated to J.L. Ericksen on His Sixtieth Birthday by Professor Dr. Constantine M. Dafermos, Professor Dr. Daniel D. Joseph, Professor Dr. Frank M. Leslie (auth.)