Comment on Hyperbolicity of Wave Problem for Valanis’ Global Damage Theory
In a very interesting and stimulating recent paper, Valanis (199l) proposed a new type of nonlocal damage theory, called the global damage theory. Some conclusions of this paper, however, require further analysis, which is the purpose of this technical note. Offering as motivation some questionable and unfounded critical comments on the nonlocal damage theory originally proposed by Pijaudier-Cabot and Baiant (1987) and Baiant and Pijaudier-Cabot ( 1988), Valanis formulated a different theory and cltrimed it to be superior because, as he stated, it exhibits unconditional hyperbolicity of the wave problem. On closer scrutiny, though, Valanis' claim is found to be invalid, and for further development of nonlocal damage models it is important to understand why.
A Global Damage Theory and the Hyperbolicity of the Wave Problem
Here we develop a global damage theory by (a) introducing a damage coordinate which is a spatial functional of the strain field in the material domain and (b) stipulating that the rate of evolution of damage is with respect to the damage coordinate. We then derive the axial wave equation for a thin rod
Mathematical Simulation of Combustion of Boron Powder Gas Suspension
Based on a two-phase two-velocity model of a reacting gas-dispersed medium, a mathematical model of combustion of a boron powder gas suspension has been formulated. The results of numerical solution of the problem are presented. The influence of the composition of the gas suspension, its size, size distribution of particles, mass concentration of particles, as well as of the presence of aluminum powder in the suspension on the visible and normal velocities of flame propagation in the gas suspension, is shown. A comparison of the results of calculation with the well-known experimental and theoretical data is carried out. Satisfactory agreement of the predicted results with experimental data is shown.