Mathematics Graduate Students Organization

Seminar:

Date: November 20

In this talk we will present a numerical study of an anti-plane shear wave propagation and it's interaction with a re-entrant notch in a recently introduced nonlinear elastic models. The governing equation for the out-of-plane displacement component is a quasilinear hyperbolic partial differential equation. An energy conserving finite element algorithm is utilized for the present study. The numerical results indicate that even very close to the tip of the notch both stress and strain remain much smaller in magnitude compared to the corresponding predictions from the linearized theory, which supports the previous asymptotic study of the static anti-plane fracture. Further, the displacement and stress wave observed within the present study is quite different from what one can observe from the classical models near the notch tip while it is nearly identical to the classical linear wave away from the strain concentrating notch-tip. Finally if time permits, I will describe some open problems within the recently developed modeling frameworks. If this is not convincing enough, I promise you that I will show some movies of the displacement and stress wave propagation from the numerical simulations. All the computations are done using deal.II library.