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Graduate Student-Faculty Seminars
Monday, February 13,
Cullimore Hall Room 611
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Multi-Scale and Multi-Physics
Modeling of Flexible Biological Shell-Like Structures in Aqueous Environment
X. Sheldon Wang
Department
of Mathematical Sciences
New
Jersey Institute of Technology
Abstract
Deformable shell-like structures immersed in aqueous
environment are ubiquitous in various biosystems. In
addition to large structural deformations and nonlinear material behaviors,
complex chemical and physical conditions at micro-scale also play important
roles. The objective of this paper is to develop novel multi-scale and
multi-physics based computational models for such structures in aqueous
environment. The results will be used to obtain better understanding of sickle
cell diseases and its treatments. As an added benefit, the developed models and
methods will assist in motivating a new generation of research ideas for
computational biomechanics, in particular the formulation of new synthetic
materials mimicing nature as well as further
development of various micromanipulation techniques such as microneedle,
micropipet, poker, and optical tweezer.
An overview of the newly proposed immersed continuum method will be presented
in this paper in conjunction with the traditional treatment of fluid-structure
interaction problems, the immersed boundary method, the extended immersed
boundary method, the immersed finite element method, and the fictitious domain
method. In particular, the key aspects of the immersed continuum method in
comparison with the immersed boundary method are discussed. The immersed
continuum method retains the same strategies employed in the extended immersed
boundary method and the immersed finite element method, namely, the independent
solid mesh moves on top of a fixed or prescribed background fluid mesh, and
employs fully implicit time integration with a combination of Newton-Raphson iteration and GMRES iterative linear solver.
Therefore, the immersed continuum method is capable of handling compressible
fluid interacting with compressible solid. In shell models, the immersed
structures occupy no physical volume, therefore, both
compressibility and incompressibility assumptions can be incorporated.