Transient wave propagation on random fields with fractal and Hurst effects

Due to its significance in natural sciences and engineering fields, wave propagation through random heterogeneous media is a significant area of fundamental and applied research. Recently two models have been developed, Cauchy and Dagum models, that can simulate random fields with fractal and Hurst characteristics. Not only can fractal and Hurst characteristics be captured with these models, but they are decoupled. We evaluate the impact of these random fields on linear and nonlinear wave propagation using cellular automata, a local computational method, and propagation of acceleration waves. In this study, we evaluate cellular automata's response to a normal, impulse line load on a half-space. We first evaluate the surface response for homogeneous material properties by comparing cellular automata to the theoretical, analytical solution from classical elasticity and experimental results. We also include the response of peridynamics, a non-local continuum mechanics theory which is based on an integro-differential governing equation. We then introduce disorder to the mass-density. We first evaluate the surface response of cellular automata to uncorrelated mass-density fields, known as white noise. The random fields vary in coarseness as compared to cellular automata's node density. Then, we evaluate the response of cellular automata to Dagum and Cauchy random fields using the Monte Carlo method. For the propagation of acceleration waves, we apply Dagum and Cauchy random fields to dissipation and elastic non-linearity. We study how the fractal and Hurst characteristics alter the probability of shock formation as well as the distance to form a shock. Lastly, in our studies of peridynamics, we found that peridynamic problems are typically solved via numerical simulations. Some analytical solutions exist for one-dimensional systems. Here, we propose an alternative method to find analytical solutions by assuming a form for displacement and determine the loading function required to achieve that deformation. Our analytical peridynamic solutions are presented