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RESEARCH PAPERS

# Fluid-Structure Interaction Analysis of Flow-Induced Deformation in a Two-Phase, Neo-Hookean Marine Egg

[+] Author and Article Information
T. Kim, C W. Wang

Department of Mechanical Engineering, University of Michigan, 2250 G.G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109-2125

F. I. Thomas

University of Hawaii, Hawaii Institute of Marine Biology, P. O. Box 1346, Kaneohe, HI 96744

A. M. Sastry1

Departments of Mechanical, Biomedical and Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2125amsastry@umich.edu

1

Corresponding author.

J. Eng. Mater. Technol 128(4), 519-526 (Jun 19, 2006) (8 pages) doi:10.1115/1.2345443 History: Received February 06, 2006; Revised June 19, 2006

## Abstract

Coupled computational fluid dynamics and finite element analyses were used to determine the material properties of the egg and jelly layer of the sea urchin Arbacia punctulata. Prior experimental shear flow results were used to provide material parameters for these simulations. A Neo-Hookean model was used to model the hyperelastic behaviors of the jelly layer and egg. A simple compressive simulation was then performed, to compare the maximum von Mises stresses within eggs, with and without jelly layers. Results of this study showed that (1) shear moduli range from $∼100to160Pa$, and $∼40to140Pa$ for an egg without a jelly layer, and jelly layer itself, respectively; and (2) the presence of the jelly layer significantly reduces maximum von Mises stress in an egg undergoing compression.

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## Figures

Figure 1

Egg and jelly layer of a sea urchin Arbacia punctulata(×200); Sumi ink was used for visualization

Figure 2

Detailed schematic of the flow channel; adapted from (41)

Figure 3

Sample images obtained from the shear flow experiments of (41), showing definitions of (a) diameter, de, of egg without jelly layer and without application of shear stress, (b) diameter of major axis length, de, of egg without jelly layer under a shear flow rate of 3.42×10−6m3∕s, (c) diameters of egg, de, and outer surface of jelly layer, ds, without application of shear stress, and (d) diameters of major axis length of egg, de, and outer surface of jelly layer, ds, under a shear flow rate of 3.4210−6m3∕s

Figure 4

Schematic of the CFD analysis; region 1 is divided into inlet and outlet, transient, and buffer zones. Region 2 was used for structural analysis.

Figure 5

Schematic comparing relative sizes of eggs and channel, and velocity profile between two parallel plates. Approximate velocity profile of the simulated region was obtained by linearization of the parabolic velocity profile, near the bottom (<300μm).

Figure 6

Definition of degree of contact, n, for description of contact area

Figure 7

Schematic representation of the strategy used to extract the shear moduli of neo-Hookean models for eggs and jelly layers

Figure 8

Schematic representations of the FSI model to simulate the egg, with or without a jelly layer, under shear stress due to fluid flow. The dimensions of the model are shown in (a); boundary conditions used in CFD and structural analyses are shown in (b) and (c), respectively.

Figure 9

Simulation results for group 1

Figure 10

Simulation results for group 2

Figure 11

Simulation results for group 3

Figure 12

Simulation results for group 4

Figure 13

Contour plots of von Mises stresses in an egg (a) without a jelly layer, and (b) with an intact jelly layer, each under an axisymmetric, compressive strain of 0.1

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