Nonlinear Elastodynamics with Radial Symmetry (Elasticidade nao linear com simetria radial)
Abstract
This MSc thesis is an exploration into the qualitative and quantitative behaviour of wave propagation with radial symmetry in materials which are prestressed elastic, isotropic and homogeneous. This type of model approximates an explosion in a solid, such as a seismic source. Also, an understanding of the radial dynamics can bring insight and contribute to our comprehension of the general 3D case. This thesis focuses on modelling, shock conditions, the dynamics close to the centre of the body and examining the analytical solution of an linearised material
Summary
The image above shows the story of a wave propagating in a sphere, like a planet, travelling through both time t and space R (distance from origin).
The wave is an elastic wave with radial symmetry, so we can imagine this as a wave created from the centre of the earth. The colour indicates the amplitude of the wave, with yellow-ish corresponding to no wave. In this image the wave begins at 1km from the centre of the earth, R=1, at time t=0. As time progressing, we climb up through the vertical axis, and the wave splits into two: one heading to the centre of the earth of the other racing towards the surface. The wave that heads to the centre focuses its energy, as space becomes limited, and eventual “collides with the origin” and then reflects back towards the surface.