PhD Thesis Defense: Shicheng Huang

Tuesday, September 10, 2019, 9:00–11:00am

Rm 201 (Rett's Rm), MacLean ESC

“Theoretical and computational modeling of buckled rods, multi-stable strips, and deformable cells”

Abstract

Spontaneous deformation of thin structures can be observed in many natural systems, e.g. the buckling of cytoskeletal microtubules bearing compressive loads. A better characterization of those shape changes, especially in large deformation regime where geometrical non-linearity plays a role, can benefit the understanding of morphology generation and facilitate more engineering designs. For this purpose, this study aims to model the large deformation and instability of thin structures through both elasticity theory and computational techniques, namely, pseudo-spectral algorithm, finite element method (FEM), and Java graphics.

First, we present a computational framework for simulating large deformations of thin beams embedded in elastic media. The Beam-Equivalent Hooke’s Model (BEHM) defines a simple set of first-order three-dimensional ordinary differential equations that captures minimum physics needed to simulate beam-medium interaction. We employ pseudo-spectral methods with Chebyshev differentiation matrix in the framework to apply the loading iteratively and discretize the rod structure for high numerical performance and computational efficiency. This framework complements traditional techniques for thin beams in that it is applicable at large deformations and can model 3D restoring forces from media.

Second, we develop a method for fabricating dual-handedness helical ribbons with varying intrinsic curvatures and negative helix angle, where the helix rotates backwards and interacts with itself. Elastic strips are bonded to a layer of non-uniformly stretched rubber sheet to form these bi-layer ribbons. We develop theories and computational algorithms on strain distributions and curvature patterns to predict the ribbon configuration. In addition, we further design a partially bonded bilayer structure composed of a shape memory polymer layer and a rubber strip. When subjected to changes in temperature, this structure exhibits tri-stability and transits between hemihelical, left-handed and right handed-helical shapes. We conduct FEM simulations and add different perturbations to demonstrate tri-stability and predict the deformed configuration given geometric and material parameters. These proposed fabrication methods and computational frameworks can serve as a tool for developing functional structures and devices featuring tunable, morphing geometries.

Third, we study the multi-stable behavior of an edge-effect driven Si/Cr micro-claw. We develop geometrical relationships and bending and stretching energy expressions. By minimizing the energy, we obtain the curvatures of the micro-claw in the stable configuration under different edge effects. Micro-claws demonstrate either mono-stability or bi-stability as the magnitude of the edge effect is varied.

Finally, we use FEM and Java graphics to simulate the apical constriction of ventral mesodermal cells during early gastrulation of drosophila embryos. With FEM, we model each cell as a 4-node plate unit and construct a global stiffness matrix. We observe differences in configurations of invagination under different material properties among different units. In simulations using Java graphics, we model each cell as linked blobs and introduce four mechanism of interaction between the blobs, which drives the shape change of the tissue. We inherit from the built-in JFrame class in Java, and override functions with respect to the moving mechanism. Results of these simulations help answer the question on how the apical constriction in mesodermal cells is transmitted through the bulk tissue of cells to generate the global shape change.

Thesis Committee

For more information, contact Daryl Laware at daryl.a.laware@dartmouth.edu.