Deformable solids

Monday, July 15, 2013 - 8:40am - 9:30am
Ricardo Nochetto (University of Maryland)
We present a comprehensive approach to the formulation and discretization of geometric PDE governing processes relevant in biophysics and materials science. We start with key elements of differential geometry and shape differential calculus which enable us to compute first variations of domain and boundary functionals. We propose geometric gradient flows as a relaxation towards equilibrium and derive the corresponding dynamic equations and their finite element approximation.
Thursday, July 18, 2013 - 3:30pm - 4:30pm
Shawn Walker (Louisiana State University)
We present a diffuse interface model for the phenomenon of electrowetting on dielectric and present an analysis of the arising system of equations. Moreover, we study discretization techniques for the problem. The model takes into account different material parameters in each phase and incorporates the most important physical processes, such as incompressibility,electrostatics and dynamic contact lines; all necessary to model the real phenomena.
Monday, May 16, 2011 - 4:30pm - 5:00pm
Efi Efrati (University of Chicago)
The language of Riemannian geometry arises naturally in the elastic description of amorphous solids, yet in the long history of elasticity it was put to very little practical use as a computational tool. In recent years the usage of Riemannian terminology has been revived, mostly in the context of incompatible irreversible deformations. In this talk I will compare different approaches to the description of growth and irreversible deformations focusing on the metric description of incompatible growth.
Tuesday, May 17, 2011 - 2:00pm - 3:00pm
Stuart Antman (University of Maryland)
The most accessible problems for the mechanics of deformable solid bodies
are those for thin bodies, namely, rods and shells, because their
equations respectively have but one and two independent spatial variables.
There is a voluminous literature devoted to the derivations of various models for such bodies
undergoing small deformations. On the other hand, geometrically exact theories
are derived directly from fundamental principles. They readily accommodate
general nonlinear material response. This lecture describes solutions of
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