By N. Cristescu
This publication provides a self-contained and entire examine the sector of dynamic plasticity for researchers and graduates in mechanical engineering. Drawing at the author's lengthy occupation within the box, the publication drastically extends fabric from the 1967 unique variation with the addition of clean study chapters in addition to an entire creation to the hassle-free idea of plasticity.
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Additional resources for Dynamic Plasticity
7a) can also be written in terms of σ and p, as follows: v = - ( T- Jo Lcde lp(l+e*> de*. 7). 6) into the second eq. 5), we obtain j / l d& i _,Λ - + i? 9) is the velocity of displacement of the wave. 8) it follows that along the curves defined by ax] at = c + v (or ax/at = —c + v, if the propagation occurs in the opposite direction) the strain is constant, and therefore the stress and velocity are constant too. We therefore obtain the same results as when using Lagrangian coordinates. In most of the problems considered later in this work, Lagrangian coordinates will be used.
8). Furthermore the point M 2 in the loading/unloading boundary is located by the intersection of the character- ιι, §5] THE LOADING/UNLOADING 41 BOUNDARY istics M t M2 and BM 2 . In a similar way, we can locate the other points on the loading/unloading boundary, ending with the last one, S. Biderman also gives diagrams of the variation of the stress at different sections of the bar (fig. 10). It is clear that during propagation, the shape of the stress pulse changes from section to section, the amplitude decreasing as one moves away from the impacted end of the bar.
Equations of motion in Eulerian coordinates The propagation of elastic-plastic longitudinal waves in thin rods was also considered in terms of Eulerian coordinates by G. I. TAYLOR [1946, 1958a, 1958b]. We shall now describe the equations involved, following both Taylor's paper and the work by KOLSKY . As is known, in order to write the equations of motion in Eulerian coordinates, x is used to denote the coordinate, not of a material particle, but of a geometric point. We then study the motion of the material which passes through the geometrical locus possessing the coordinate x.
Dynamic Plasticity by N. Cristescu