Influence of elastic material compressibility on parameters of an expanding spherical stress wave |
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Authors: | Edward Włodarczyk Mariusz Zielenkiewicz |
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Institution: | (1) Faculty of Mechatronics, Military University of Technology, S. Kaliskiego str. 2, 00-908 Warszawa, Poland;(2) Military Institute of Armament Technology, Prymasa Stefana Wyszyńskiego str. 7, 05-220 Zielonka, Poland |
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Abstract: | We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The
material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic
elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement,
particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained
for surge pressure p(t) = p
0 = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences
the course of material parameters in space and time. All parameters intensively decrease in space together with an increase
of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course
of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about
0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when
ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static
values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration
amplitude and decrease of vibration “damping”.
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Keywords: | Expansion of spherical stress wave Isotropic elastic material Dynamic load |
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