Chapter 22
Simulation and Similarity of Destructions Caused by Shock Waves
Destruction occurs when the stress in a material reaches limit values. Similarity will therefore be achieved if we use the same material in the model as in the actual case, and, of course, if the model is geometrically similar to the actual object.
By using the same material we will be sure to have a similarity in the propagation of the shock wave, in its transition from one medium to the other, and so on. We have seen that the characteristic pressure amplitude is constant. In similar explosions the pressures are identical at similar points.
The regions in which the stresses caused by the explosion exceed the permissible values and bring about the destruction of the material will also be similar.
Destruction requires that a specific deformation be reached, i.e., that certain particles of the body be shifted with respect to other particles. Inertial forces and elasticity prevent deformation and destruction from occurring instantly. Could it be that the existence of a specific deformation time will lead to a violation of similarity?
But we can easily see that similarity will be maintained. It is precisely the inertia of the substance, which depends on density, and its elasticity that determine the speed of sound in the substance. It can be formally shown by means of analysis that from density and elasticity we can plot deformation time only on the basis of the dimensions of the body, and this will be the time required by the wave to pass through the body. The time will turn out to be proportional to the size of the body. If we change the scale, deformation time changes following the same law as the one governing the shock wave action time, and the relationship between the times will remain constant. This ensures similarity of the phenomena.
Similarity is also applicable to the more complex type of destruction, in which the shock wave momentum is decisive (see Chapter 20) rather than peak pressure.
Let us take an elastic beam, the oscillation period of which exceeds shock wave action time.
