Welcome to the home page of the Mathematics Graduate Student Organization (MGSO) at Texas A&M University in College Station. The purpose of this organization is to encourage communication among students, faculty, and staff, and contribute to a rich social life in the department through cultural and scientific dialogue. We would also like to provide an environment where students in the mathematics department can practice their presentation skills as well as view the techniques of others. It is our goal to be a source of support and information for all graduate students.
The main activity of the MGSO is the Graduate Student Seminar. This seminar is for grad students, (largely) by grad students: Volunteer to give a talk!
Seminar: Fall 2014, Thursdays, Blocker 506A, 4:00-4:50 PM
Speaker: Mallikarjuna Muddamallappa
Title: Wave propagation in nonlinear materials: (little) theory and numerical simulations.
Time / Date: 4:00 - 5:00 , 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.