Impact force and moment problems on random mass density fields with fractal and Hurst effects

Abstract

This paper reports the application of cellular automata to study the dynamic responses of Lamb-type problems for a tangential point load and a concentrated moment applied on the free surface of a half-plane. The medium is homogeneous, isotropic and linear elastic while having a random mass density field with fractal and Hurst characteristics. Both Cauchy and Dagum random field models are used to capture these effects. First, the cellular automata approach is tested on progressively finer meshes to verify the code against the continuum elastodynamic solution in a homogeneous continuum. Then, the sensitivity of wave propagation on random fields is assessed for a wide range of fractal and Hurst parameters. Overall, the mean response amplitude is lowered by the mass density field’s randomness, while the Hurst parameter (especially, for β < 0.2) is found to have a stronger influence than the fractal dimension on the response. The resulting Rayleigh wave is modified more than the pressure wave for the same random field parameters. Additionally, comparisons with previously studied Lamb-type problems under normal in-plane and anti-plane loadings are given. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Modeling and Simulation of Head Trauma Utilizing White Matter Properties from Magnetic Resonance Elastography

“…It is clear that the attenuation is greater in the heterogeneous model as predicted. This is consistent with studies of transient wave propagation in elastodynamics of random media [45,46].…”

Simulation of mTBI Utilizing White Matter Properties from MRE

“…It is clear that the attenuation is greater in the heterogeneous model as predicted. This is consistent with studies of transient wave propagation in elastodynamics of random media [41,42].…”

Mach Fronts in Random Media with Fractal and Hurst Effects

“…From a general perspective, the present study continues our investigations of (i) structural mechanics problems, (ii) dynamical systems, (iii) waves and wavefronts and (iv) fracture on tensor-valued random fields (see, e.g., [14]). Only in the simplest cases of (i) and (ii) are explicit analytical solutions possible, whereby we note that even the explicit spectra of Cauchy and Dagum models are formidable mathematical challenges.…”