Development of an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface

A comprehensive investigation on the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces is performed in this study. First, the mathematical models commonly used for predicting the static displacement of a sphere located at an elastic medium interface are presented and their performances are compared. After that, based on the finite element analyses, an accurate mathematical model to predict the static displacement of a sphere located at an elastic medium interface valid for different Poisson’s ratios of the medium and small and large sphere displacements is proposed. Then, an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface is developed. In addition to the Young’s modulus of the medium and the radius of the sphere, the model takes into account the density, Poisson’s ratio and viscosity of the medium, the mass of the sphere and the radiation damping. The effects of the radiation damping, the Young’s modulus, density and viscosity of the medium and the density of the sphere on the dynamic response of the sphere located at a viscoelastic medium interface are explored. The developed model can be used to understand the dynamic responses of spherical objects located at viscoelastic medium interfaces in practical applications. Furthermore, the proposed model is a significant tool for graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres located at viscoelastic medium interfaces.

Magmatic sill formation during dike opening

The origin of horizontal magma-filled sills is disputed, particularly for extensional settings where the opening of vertical dikes is the predicted mode of magma intrusion. We simulate long-term extension followed by short-term dike opening in a two-dimensional viscoelastic medium representing a plate spreading center. We show that dike opening in extensionally stressed lithosphere can reduce sublithospheric vertical stresses enough for sill opening given three conditions: (1) the Maxwell time of the asthenosphere is <5× the time interval between dike episodes; (2) the average density of the lithosphere is not much greater than the magma density; and (3) the depth of an axial valley is smaller than a few hundred meters. This mechanism explains the presence of sills along much of the axis of faster-spreading ridges and their absence along slower-spreading centers where thick dense lithosphere and/or sizeable axial valleys exist.