By Gabi Ben-Dor

High-speed impression dynamics is of curiosity within the basic sciences, e.g., astrophysics and area sciences, and has a few vital functions in army applied sciences, fatherland safety and engineering. compared to experiments or numerical simulations, analytical ways in effect mechanics basically seldom yield valuable effects. even if, whilst profitable, analytical techniques let us be sure normal legislation that aren't in simple terms very important in themselves but additionally function benchmarks for next numerical simulations and experiments. the most aim of this monograph is to illustrate the capability and effectiveness of analytical tools in utilized high-speed penetration mechanics for 2 sessions of challenge. the 1st type of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one category of challenge contains research of ballistic houses and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the large use of mathematical recommendations, the acquired effects have a transparent engineering which means and are provided in an easy-to-use shape. one of many chapters is dedicated exclusively to a couple universal approximate types, and this is often the 1st time finished description of the localized impactor/medium interplay technique is given. within the monograph the authors current systematically their theoretical ends up in the sector of high-speed impression dynamics got over the last decade which in simple terms in part seemed in clinical journals and meetings proceedings.

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**Additional info for Applied High-Speed Plate Penetration Dynamics**

**Sample text**

5) Let us now consider shield of finite thickness (SFT) and semi-infinite shield (SIS). In the case of a SFT, the equation for the BLV can be obtained by substituting v = 0 , vimp = vbl , h = b + L into Eq. 4): Fˆ ( vbl ) = b+ L Θ( h ) ∫ dhθ ∫ xdx . 6) (h) Using the identity Eq. 7), we can transform the right-hand side of Eq. 6) to bL2 2 , and this equation becomes Fˆ ( vbl ) = bL2 2 . Since Fˆ ′( z ) > 0 and, consequently, Fˆ ( z ) is an increasing function, the latter equation has only one solution: v bl = Fˆ −1 ( bL2 2 ) .

It later became apparent that this model is also applicable to dense media. Exactly the same situation is true for gasdynamics, for which a similar Newton’s model ( a0 – pressure in the undisturbed gas flow) and its modifications are widely used in calculations of the aerodynamic characteristics of supersonic projectiles (Hayes and Probstein, 1959; Chernyi, 1969). Interestingly, Nishiwaki did not refer to Newton’s model or to gasdynamics analogy. Localized interaction approach 29 Various semi-empirical models were collected and analyzed by Recht (1990).

Bunimovich (1973) was the first to note that the significance of the local interaction approach is beyond the scope of rarefied gasdynamics. At present this point of view is generally accepted, and the notions like localized interaction theory, localized interaction models, etc. are widely used (see Bunimovich and Dubinsky, 1995, 1996; Miroshin and Khalidov, 1991, 2002 and references therein). Studies in the framework of the LIT were continued in different directions, such as development of particular LIMs and effective methods for aerodynamic calculations, shape optimization, etc.