By Gabi Ben-Dor
High-speed impression dynamics is of curiosity within the primary sciences, e.g., astrophysics and house sciences, and has a few very important purposes in army applied sciences, place of origin safeguard and engineering. compared to experiments or numerical simulations, analytical ways in impression mechanics simply seldom yield invaluable effects. despite the fact that, while winning, analytical techniques let us confirm basic legislation that aren't purely vital in themselves but additionally function benchmarks for next numerical simulations and experiments. the most target 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 classification of challenge is form optimization of impactors penetrating into ductile, concrete and a few composite media. the second one category of challenge includes 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 innovations, the acquired effects have a transparent engineering that means and are offered in an easy-to-use shape. one of many chapters is dedicated completely to a few universal approximate versions, and this is often the 1st time accomplished description of the localized impactor/medium interplay strategy is given. within the monograph the authors current systematically their theoretical ends up in the sphere of high-speed effect dynamics got over the past decade which in basic terms partly seemed in clinical journals and meetings proceedings.
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Additional info for Applied High-Speed Plate Penetration Dynamics
Differentiating, after this substitution, both sides of this equation with respect to vimp , we obtain: mvimp 1 ∂Hˆ ( = Θ 2 Hˆ ( υ , vimp ) . 14) ( Substitution of D from Eq. 11) yields: Ω n (sinυ ,vimp ) −1 ⎡ 2 ∂Hˆ ⎤ = ⎥ . 15) After the change of variables, υ = sin −1 u , vimp = v , we obtain an expression for function Ω n (u ,v ) that determines the LIM: Ω n (u ,v ) = −1 ⎡ 2 ˆ ∂Hˆ ⎤ −1 ⎢Θ H (sin υ ,v ) ⎥ . 16) A similar approach can be used for a SFT, provided that the function vˆbl ( υ ,b ) , which determines the dependence of the BLV of a straight circular conical impactor vs.
1) as follows: D = Ω n (sin υ , v )∆σ ( h ) . , FD = FD ( υ ,v ) . Then, for each penetrator, function FD will assume the same values for the same penetration velocity, although this velocity in different experiments can be attained at different penetration depths. Then, equating functions FD ( υ ,v ) and D ∆σ ( h ) and using Eq. 7), we arrive at the following LIM: Ω n (u ,v ) = FD (sin −1 u ,v ), Ωτ = 0 . 8) Note, that the mere fact that the function FD depends solely on the penetrator’s velocity and does not depend explicitly on the location of the penetrator inside the shield, can be used as a criterion of the “locality” of the model of interaction between the impactor and the shield.
Classic” DLIMs postulate a polynomial dependence D( v ) , and solving the equation of motion in this case reduces to calculating the integral M ( 1,1,c0 ,c1 ,c2 ;W ) in Eq. 01). A brief analysis of these models and references to the early studies can be found in Goldsmith (1960) and Backman and Goldsmith (1978). Heimdahl and Schulz (1986) studied the motion of an impactor for an arbitrary function D( v ) . , 1986). Various approaches to determine the drag force acting on the body as a function of its velocity and penetration depth were considered by Stone (1994), Zook (1977), Beth (1946), Allen et al.