Research Papers

On the Role of the Plaque Porous Structure in Mussel Adhesion: Implications for Adhesion Control Using Bulk Patterning

[+] Author and Article Information
Ahmed Ghareeb

Civil and Environmental Engineering,
University of Illinois at Urbana-Champaign,
2119 Newmark Civil Engineering Lab,
205 N. Mathews Ave,
Urbana, IL 61801
e-mail: ghareeb2@illinois.edu

Ahmed Elbanna

Civil and Environmental Engineering,
University of Illinois at Urbana-Champaign,
2219 Newmark Civil Engineering Lab,
205 N. Mathews Ave,
Urbana, IL 61801
e-mail: elbanna2@illinois.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 21, 2018; final manuscript received August 19, 2018; published online September 7, 2018. Assoc. Editor: Yong Zhu.

J. Appl. Mech 85(12), 121003 (Sep 07, 2018) (11 pages) Paper No: JAM-18-1357; doi: 10.1115/1.4041223 History: Received June 21, 2018; Revised August 19, 2018

Mussel adhesion is a problem of great interest to scientists and engineers. Recent microscopic imaging suggests that the mussel material is porous with patterned void distributions. In this paper, we study the effect of the pore distribution on the interfacial-to-the overall response of an elastic porous plate, inspired from mussel plaque, glued to a rigid substrate by a cohesive interface. We show using a semi-analytical approach that the existence of pores in the vicinity of the crack reduces the driving force for crack growth and increases the effective ductility and fracture toughness of the system. We also demonstrate how the failure mode may switch between edge crack propagation and inner crack nucleation depending on the geometric characteristics of the bulk in the vicinity of the interface. Numerically, we investigate using the finite element method two different void patterns; uniform and graded. Each case is analyzed under displacement-controlled loading. We show that by changing the void size, gradation, or volume fraction, we may control the peak pulling force, maximum elongation at failure, as well as the total energy dissipated at complete separation. We discuss the implications of our results on design of bulk heterogeneities for enhanced interfacial behavior.

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Fig. 1

The adhesive system in mussels: (a) a mussel attached to substrate by threads ending in plaques, (b) stereo microscope image of a M. californianus plaque under SEM, and (c) a cross section microscopic image of the plaque shows the porous structure of the bulk material and the variance of void sizes and distribution (Reproduced with permission from Filippidi et al. [1], Copyright 2015 the Royal Society; permission conveyed through Copyright Clearance Center, Inc.).

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Fig. 2

Setup of the analytical model for the pulling a porous pillar attached to a rigid substrate: (a) The geometry of the 2D pillar with three near-interface rectangular voids, the pillar is subjected to an upward displacement, (b) the geometry and dimensions of the part of the pillar near the crack tip where the thickness of the horizontal strip is th, the thickness of the vertical strip is tv, the void width is W, the void height is L, and the crack length a, (c) the simplified beam on elastic foundation model for the pillar with three rectangular voids, and (d) Dugdale's traction separation relation for the cohesive interface

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Fig. 3

Different cases of crack propagation under the elastic beam: (a) edge crack propagates under the void and (b) onset of local crack initiation under the inner leg

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Fig. 4

Results from the approximate analytical model and finite element simulations: (a) force versus crack length from analytical and numerical solutions for th=5 mm, th/tv=1.0,W/th= 5.0 showing that the total force may continue to increase even though the crack is expanding, (b) force versus crack length for the analytical model for various values of the interfacial horizontal strip to vertical web thickness ratio th/tv and the same void width, (c) force versus crack length for the analytical model for the same interfacial horizontal to vertical strip thickness ratio th/tv and various values of void width, and (d) maximum force in the inner leg versus interfacial horizontal strip to vertical strip thickness ratio for two different values of W/tv from both the numerical and analytical solutions

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Fig. 5

The geometry of the numerical model, which is composed of a porous plate attached to a rigid substrate, throws a zero-thickness layer of cohesive material

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Fig. 6

Effect of void size: (a) normalized nominal stress versus nominal strain curves for the different plates with uniform voids. The void diameter to characteristic length ratios are listed in the legend. The result for a solid plate with the same material volume and in-plane dimension (but reduced thickness, i.e., reduced contact area) is also added for reference, (b) Normalized stress distribution along the interface at different nominal strain levels: (top) case of uniform voids with D/Lch=1.8, and (bottom) Case of uniform voids with D/Lch=0.6, and (c) maximum stretch and total energy versus relative void size.

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Fig. 7

Effect of void size to interfacial horizontal strip thickness ratio: (a) the maximum stretch and total energy versus void diameter to interfacial horizontal strip thickness ratio and (b) normalized stress distribution along the interface at different nominal strain levels for.D/th=6

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Fig. 8

Effect of void pattern: (a) normalized nominal stress versus nominal strain curves for the two plates with graded voids, the plates geometries are shown in the legend, also the normalized nominal stress versus nominal strain for two plates with equal void sizes D/Lch=0.7, and D/Lch=1.2 are added for comparison, and (b) normalized stress distribution along the interface at nominal strain levels: (top) case of graded voids with larger voids (D/Lch=1.2) at the interface, and (bottom) case of graded voids with smaller voids (D/Lch=0.7) at the interface

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Fig. 9

Numerical results for plates with uniform voids for three different voids volume fraction 60, 45, and 30%. The numbers in the plot indicate the total area under the curve. The case of solid plate is added for reference.

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Fig. 10

Comparison of strain energy and external work versus separation length for plates with different void diameter to characteristic length ratios: (a) strain energy of the whole plate versus separation length along the interface, and (b) the total cumulative external work exerted on the plate versus separation length along the interface

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Fig. 11

Energy components of the plate during the growth of the interfacial separation versus separation length along the interface for a plate with uniform distribution of voids with D/Lch=1.8



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