Morphological characterization of shocked porous material

Morphological measures are introduced to probe the complex procedure of shock wave reaction on porous material. They characterize the geometry and the topology of the pixelized map of a state variable like temperature. The relevance to thermodynamical properties of a material is revealed and various experimental conditions are simulated. Numerical results indicate that the shock wave reaction results in a complicated sequence of compressions and rarefactions in porous material. The increasing rate of the total fractional white area A roughly gives the velocity D of a compressive-wave series. When a velocity D is mentioned, the corresponding threshold contour level of the state variable, such as temperature, should also be stated. When the threshold contour level increases, D becomes smaller. The area A increases parabolically with time t during the initial period. The A(t) curve goes back to being linear in the following three cases: (i) when the porosity δ approaches 1, (ii) when the initial shock becomes stronger and (iii) when the contour level approaches the minimum value of the state variable. The area with high temperature may continue to increase even after the early compressive waves have arrived at the downstream free surface and some rarefactive waves have come back into the target body. In the case of energetic material needing a higher temperature for initiation, a higher porosity is preferred and the material may be initiated after the precursory compressive waves have scanned the entire target body. In some cases we need scattered hot spots, but in others we need connected ones. One may desire the fabrication of a porous body and choose the appropriate shock strength according to what is needed. With the Minkowski measures, the dependence on experimental conditions is reflected simply by a few coefficients. They may be used as order parameters to classify the maps of physical variables in a similar way to thermodynamic phase transitions.