By N. Cristescu
This booklet offers a self-contained and accomplished examine the sphere of dynamic plasticity for researchers and graduates in mechanical engineering. Drawing at the author's lengthy occupation within the box, the e-book vastly extends fabric from the 1967 unique variation with the addition of unpolluted learn chapters in addition to a whole advent to the common thought of plasticity.
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Additional resources for Dynamic Plasticity
The small steps which can be observed on the graphs of figs. 18 correspond to the small steps in fig. 15. These are due to the method used and certainly do not correspond to any physical phenomenon. The advantage of the numerical method indicated in the present subsection is that the calculations can be performed very easily with an electronic computer and the loading/unloading boundary is obtained using a large number of points. This number can be increased indefinitely by choosing an appropriate small interval Ax.
In Lagrangian coordinates the velocity of a material particle depends only on its initial position and the time, while the acceleration is simply the partial ιι, §6] 51 EQUATIONS OF MOTION derivative of the velocity with respect to time. In Eulerian coordinates, the velocity of a material particle varies with respect to time (local) but it is also a contribution of the motion of the particle in the instantaneous velocity field (convective part). If, at time t, the velocity of a certain section of the rod is equal to v, then during an interval ôt this section will move through a distance νδΐ; the velocity at time t + ôt will then be v+(dvldx)vôt+(dvldt)ôt, and the acceleration will be (dvldt) + v(dvldx).
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. In Lagrangian coordinates the velocity of a material particle depends only on its initial position and the time, while the acceleration is simply the partial ιι, §6] 51 EQUATIONS OF MOTION derivative of the velocity with respect to time.