Trajectory instability and convergence of the curvilinear motion of a hard projectile in deep penetration

Penetration trajectory of rigid projectile in the heterogeneous meso-scale concrete target

“…For a given concrete target, only the projectile parameters, that is, M , v , D , L , and N *, which are the mass, initial impact velocity, diameter, length and the nose factor of the projectile, respectively, as well as L c which is the distance between the center of mass and the nose tip of the projectile, need to be considered. A dimensional analysis leads towhere f c is the unconfined uniaxial strength of aggregate; the first term in equation (1) is a dimensionless “impact factor” (Li et al, 2005) defined byL/D is the length-to-diameter ratio of projectile and Lc/L is the relative location of mass center of projectile, which has significant influence on the projectile stability (Gao and Li, 2017).…”

“…Experimental results show that, in comparison with the symmetric projectile structure (with the straight groove or no groove), the asymmetrical projectile with spiral groove structure is disadvantageous in terms of trajectory stability. Li and Flores-Johnson (2011) and Gao and Li (2017) proposed a model to predict the projectile trajectory under various oblique and yaw angles based on the rigid body dynamics, Differential Area Force Law (DAFL) method and semi-empirical resistance function. It was shown that the relative location of mass center of the projectile has significant influence on the control of the rotation of the projectile, the projectile stability and the change of trajectory direction.…”

Advances in Projectile Penetration Mechanism in Soil Media

“…The analysis of general penetration dynamics problem including the non-normal penetration is carried out by Ben-Dor et al [64] considering the impact penetration as an inverse problem using semi-empirical relations that employ the dependencies between the initial velocity and the depth of penetration. The deep penetration study of hard projectile in soil target by Gao and Li [65] concluded that the trajectory instability occurs at critical impact velocity, and the projectile trajectory returns to a straight line (linear motion) from the curvilinear motion near the characteristic convergent velocity. The trajectory instability and convergence of the curvilinear motion of projectile is driven by increase in impact velocity, projectile geometry, uniformity of grain size distribution within the soil mass, increase in grain size and porosity, and other striking parameters [66].…”

“…Analytical model for rigid projectile dynamics is proposed by Simonov and Osipenko [67] to analyze the trajectory and stability of the projectile during deep penetration in an elasto-plastic medium. A "differential area force law (DAFL)"-based analytical method, proposed by the AVCO Corporation [16] in which the projectile surface resistance is written as a quadratic function of velocity, is most effective in studying the projectile's curvilinear motion and stability during non-deformable projectile deep penetration into hard soil media [65].…”

“…dρ dt + ρ (v r,r + v z,z ) = − ρur r dρ * dt = dρ dt h (ρ − ρ * )h dρ dtSpherical Cavity Expansion (SCE)[168] ∂σr ∂t + 2 σr−σθ r = −ρ ∂v ∂t + v∂v ∂r Cylindrical Cavity Expansion (CCE) or Disc or Orthogonal layers model [42]F d (t) = F z + A .R t) + B R(t)..R(t)F z = − 1 2 τ 0 (t) ln(ε L ) A = − 1 2 ρ 0 1 − ρL ρ0 ln(ε L ) , B = − 1 2 ρ L ln(ε L )] Modified Archimedes' law [46] F d = k ∅ ρ s g V div (hẑ)dV = k ∅ ρ s g VNon-linear differential area force law (DAFL)[65] …”