Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid

Abstract

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible. Numerical results from both models showed the effect of compressibility.

Effect of the static strength of a metal on long-rod penetration at low velocities

“…The distribution of the pressure p along the radius in the cylindrical plastic region (accounting for o r = -t y [ Thus, the effect of compressibility on the radius of an elastoplastic interface is essential, which does not contradict earlier findings [13]. The results o f this analysis are close to the approximate solution for the dynamic expansion o f a cylindrical cavity, based on the similarity solution for plastic flow [11].…”

“…This component of resistance to penetration and its association with the characteristics of a material, determining its mechanical behavior, is examined in a number o f publications [8][9][10][11]. However, various models of penetration, models of an elastoplastic material used for its simulation, and methods o f solution of mathematical equations resulted in different values of resistance and dimensions o f a plastic region [3,5,8,[11][12][13][14]. It will suffice to mention that the pressure at the interface at penetration is assumed to be equal to the pressure necessary for the expansion o f a cylindrical or spherical cavity in the unlimited volume o f a material, or to some intermediate value [13,15,16].…”

Similarity Analysis of Projectile Penetration into Concrete

“…For penetration of non-deformable projectiles at sub ordnance or ordnance velocity into concrete targets, it is found experimentally that the influence of both modulus of elasticity and Poisson ratio of the projectile 19 as well as of the target 20,21 on the DOP can be neglected. In addition, most DOP models 10 appear independent on ρ t .…”

Modeling the Dynamic Penetration Processes of Dimensional Bodies in a Compressible Elastoplastic Medium

“…В соответствии с одной из реализаций МЛВ давление в каждой точке боковой поверхности ударника отождествляется с давлением на внутренней поверхности сферической или цилиндрической полости, расширяющейся в безграничной среде от ну-левого радиуса до радиуса ударника («Cavity Expansion Model» в зарубежной литературе). Таким образом, решения задач о расширении полости (см., например, [18][19][20][21][22][23]), имея са-мостоятельное значение, в то же время применяются для оценки параметров моделей ло-кального взаимодействия. Инженерные методики на базе МЛВ для исследования процес-сов удара и проникания продолжают совершенствоваться и в настоящее время на основе данных экспериментов и численного моделирования [23][24][25][26][27][28][29][30][31][32][33][34].…”