Spherical Cavity Expansion Approach for the Study of Rigid-Penetrator’s Impact Problems

Abstract

In recent years, Spherical Cavity Expansion (SCE) theory has been extensively utilized to model dynamic deformation processes related to indentation and penetration problems in many fields. In this review, the SCE theory is introduced by explaining the different mathematical features of this theory, its solution, and a potential application to model the penetration of a rigid penetrator into a deformable target. First, a chronologically literature review of the most common models used to study this kind of penetration problems is introduced, focusing on the SCE theory. Then, the engineering model of penetration is presented using the SCE approach. The model is then compared and validated with some FE numerical simulations and with previous penetration results. It is concluded that this engineering model based on the SCE theory can be utilized to predict the projectile deceleration and penetration depth into the semi-infinite and finite targets impacted by rigid penetrators.

Behavior of oil-based modeling clay at medium strain rates

“…Cavity pressure is given by p c = − σ r ( r = a ) , where σ r is the radial stress component, which is related to the oil-based modeling clay material response through the effective stress calculated as σ e = σ θ − σ r , 31 where σ θ is the circumferential stress component. Given the fact that oil-based modeling clay is a nearly incompressible material, its response in terms of stresses, density and radial velocity can be determined by the following set of equations: 30,35–37…”

“…In the scientific literature, 31,37,39 it have been shown that p c can be expressed as a power-law relation of the non-dimensional cavity expansion velocity:…”

“…Notice that in Equation ( 10), selfsimilarity transformation was used for the rate-dependant term due to the fact that the process is developed under low penetration velocities, where the assumption of steady state of stresses above the nose of the sphere is valid, according to preliminary results. 38 In the scientific literature, 31,37,39 it have been shown that p c can be expressed as a power-law relation of the non-dimensional cavity expansion velocity:…”

Force in Cable of Pretensioner Tube—A Possibility of Car Accident Reconstruction

“…In [20,21], studies on the dynamic deformations produced by spherical projectiles at high speeds are presented. We consider that the level of energies produced during the interaction between the target and the projectile is too high to make comparisons with the present situation, and subsequently these studies are not suitable for determining indentations with much smaller dimensions, as found in the case of pretensioning systems.…”

Advances in Projectile Penetration Mechanism in Soil Media

“…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] …”