By Gabi Ben-Dor

High-speed impression dynamics is of curiosity within the primary sciences, e.g., astrophysics and house sciences, and has a couple of vital purposes in army applied sciences, fatherland safety and engineering. compared to experiments or numerical simulations, analytical ways in effect mechanics simply seldom yield necessary effects. besides the fact that, whilst winning, analytical ways let us make sure basic legislation that aren't in basic terms vital in themselves but in addition function benchmarks for next numerical simulations and experiments. the most objective 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 homes and optimization of multi-layered shields, together with spaced and two-component ceramic shields. regardless of the big use of mathematical innovations, the acquired effects have a transparent engineering that means and are provided in an easy-to-use shape. one of many chapters is dedicated completely to a couple universal approximate versions, and this is often the 1st time entire description of the localized impactor/medium interplay procedure is given. within the monograph the authors current systematically their theoretical leads to the sphere of high-speed effect dynamics acquired over the last decade which simply partly seemed in clinical journals and meetings proceedings.

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**Example text**

1998) for the simplest degenerate model with Hˆ ( vimp ) , D = D( v ) , without considering the stage of incomplete immersion of the projectile into the target. 3 From aerodynamics to impact dynamics The conception and development of LIT (primarily for aerodynamic applications) have been discussed in monographs written by Bunimovich and Dubinsky (1995) and Miroshin and Khalidov (2002), as well as in the review of Bunimovich and Dubinsky (1996). Therefore, we will discuss here only briefly the principal points that are important for impact dynamics.

18) Using the same reasoning as in the case of the SIS, we arrive at the following formula that determines the model: Ω n (u ,v ) = −1 ⎡ ∂bˆ(sin −1 υ ,v ) ⎤ ⎢ ⎥ . 19) Note that the idea to restore a model using a known DOP function was used by Eisler et al. (1998) for the simplest degenerate model with Hˆ ( vimp ) , D = D( v ) , without considering the stage of incomplete immersion of the projectile into the target. 3 From aerodynamics to impact dynamics The conception and development of LIT (primarily for aerodynamic applications) have been discussed in monographs written by Bunimovich and Dubinsky (1995) and Miroshin and Khalidov (2002), as well as in the review of Bunimovich and Dubinsky (1996).

Actually, this procedure results in substitution of constant integration limits instead of variable integration limits in the expression for the drag force [ θ ( h ) is replaced by 0 for SFT and Θ ( h ) is replaced by L ] and in the appearance of the coefficient in the case of a SFT. 1 General localized interaction model for three-dimensional impactor We start from Eqs. 5) that determine the drag force of a 3-D impactor D as a function of its instantaneous coordinate h and velocity v . 1) Localized interaction approach 53 where u( x ,ϑ ) and U ( x ,ϑ ) are determined by Eqs.