Statistics of maximum stress for elastic wave propagation in a random porous solid

The stochastic characteristics of elastic wave scattering in random porous solids lead to the complexity and uncertainty for the determination of local maximum stress. There are limited studies to predict and estimate the maximum stress in such medium mainly due to the lack of efficient and accurate modeling tools. In order to address this issue, this work presents a new approach to quantify the statistics of maximum stress induced by multiple wave scattering effects in such medium. By combining the high-fidelity finite element method with Monte Carlo simulation, this work provides a comprehensive framework for evaluating the mean, standard deviation and probability distribution of maximum stress in random porous solids. It is demonstrated that the mean and standard deviation of maximum stress depend highly on the wave frequency and the correlations among cavities. The probability density function of maximum stress is analytically formulated by Burr Ⅻ distribution where the wave frequency and the correlation among cavities are taken into account jointly. The related parameters involved in the statistical distribution are estimated by maximum likelihood method and the Kolmogorov-Smirnov test is adopted to examine the goodness of fitting distribution. The heavy-tailed behavior observed in the statistical distribution is elaborated by linking to the interaction effects of waves with random microstructures, which is crucial for the dynamic failure assessment of porous solids. Finally, the dynamic stress concentration associated with maximum stress in random porous solid is investigated, which potentially relates to the scatterer resonance effects. This work facilitates the understanding of wave-induced dynamic stress in heterogeneous media, providing a statistical approach for dynamic failure assessment in random porous solids.