For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.
| Title: | Mechanics of Active Materials with Long-Range Interactions |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Kaushik Dayal, Carnegie Mellon University |
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| Abstract: |
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| 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.
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Room Reservation Information
| Room Number: | MB106 |
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| Date: | 05 / 01 / 2009 |
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| Time: | 03:35pm - 04:25pm |
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