PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.

Title:Mechanics of Active Materials with Long-Range Interactions
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Kaushik Dayal, Carnegie Mellon University
Abstract:
This talk will deal with two aspects of the mechanics of symmetry-breaking defects such as phase boundaries, inclusions and free surfaces, and their role in the macroscopic response of active materials. We first examine the nucleation and kinetics using a nonlocal continuum model. Classical PDE continuum models of active materials are not closed. They require nucleation and kinetic information or regularization as additional constitutive input. We examine this problem in the peridynamic formulation. This is a nonlocal continuum model that uses integral equations to account for long-range forces that are important at small scales. This allows resolution of the structure of interfaces. Our analysis shows that kinetics is inherent to the theory. Viewing nucleation as a dynamic instability at small times, we obtain interesting scaling results, and insight into nucleation in regularized theories. Our analysis may also provide techniques applicable to MD-continuum connections. We exploit the computational ease of this theory to study an unusual mechanism that allows a phase boundary to bypass an inclusion. Shifting focus to a more applied problem, we consider issues in the design of ferroelectric optical/electronic circuit elements. Free surfaces and electrodes on these devices generate electrical fields that must be resolved over all space, and not just within the body as in the case of relatively well-characterized elastic fields. These fields greatly enhance the importance of geometry in understanding the electromechanical response of these materials, and give rise to strong size and shape dependence. I describe a computational method we have developed that transforms this problem into a local setting in an accurate and efficient manner. Problems of interest that are being studied using this method are presented. >

Room Reservation Information

Room Number:MB106
Date:05 / 01 / 2009
Time:03:35pm - 04:25pm