Mattia Bacca

This thesis explores two investigations into improving the detachment strength and load distribution at theinterface of dry bio-inspired fibrillar adhesives subjected to normal loading. The first is in how interfacialcurvature affects the load sharing efficiency of engineering prototypes. Previous investigations unraveled thebenefits of backing layer (BL) thickness in counteracting the detrimental load concentration created by interfacialmisalignment. However, little attention was dedicated to the role of interfacial curvature on load distribution andthe resulting adhesive strength. Based on the concavity of the curvature, the adhesive can detach more easily ordevelop stronger adhesion, compared to a flat-on-flat interface. This suggests the possibility to actuate curvatureand better control adhesion. The curvature-induced strengthening/weakening of the adhesive was analyzedin combination to BL thickness, interfacial misalignment, and imperfections in the fibril length distribution.Detrimental load concentrations, created by BL interaction and interfacial misalignment, drastically reduce whenthe curvature prompts larger stretch to the central fibrils. This also mitigates load concentrations created byuneven fibril length distribution. These beneficial effects are reverted when the curvature prompts larger stretchto the peripheral fibrils. The quantitative analysis provides a design tool for stronger and more controllableadhesives.The second investigation is into an asymptotic solution to the optimal compliance distribution attributable tofibrils within the array. The optimal compliance distribution allows the adhesive to achieve equal load sharing(ELS) which is its theoretical maximum strength i.e all fibrils carry the same load and detach simultaneously.The array of fibrils is modelled as a continuum of linear elastic material that cannot laterally transmit load(analogous to a Winkler soil). Ultimately, the closed form solution for the continuum distribution of fibrilcompliance is obtained and compared to the data from a discrete model. The results show improving accuracy foran incremental number of fibrils and smaller center to center spacing. Surprisingly, the approximation introducedby the asymptotic models shows reduced sensitivity of the adhesive strength with respect to misalignment andimproved adhesive strength for large misalignment angles.

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This thesis explores bioadhesion at two scales. In many animals, adhesion plays a critical role to enable their traversal on inclined and inverted surfaces of varying chemistry. This is achieved through arrays of fibrils or micropillars found at the tips of these animals’ appendages. Synthetic mimics inspired by the design of these natural systems are actively developed, studied, and used in applications not limited to adhesion. A common limitation in these mimics is that adjacent micropillars tend to adhere to each other (self-adhere) by lateral van der Waals interactions, impeding on their intended function. Through mathematical modeling, our work demonstrates that slanting micropillars from their vertical arrangement permits them to be longer or more densely packed while avoiding self-adhesion. We derive a criterion to determine the critical angle above which slanting remains beneficial, providing developers of micropillar array devices with a tool to aid in their design. Our analysis further finds that the design of natural micropillar arrays in the ladybird beetle are close to optimal for packing or length, providing justification for the observed natural design. In cell biology, adhesion gives structure to organisms, enabling growth and proliferation. Furthermore, adhesion enables cells to contract against their surroundings, which has been identified as a key factor in cancer progression and metastasis. We developed an experimental platform to alter cellular concentrations of adenosine triphosphate (ATP) – the energetic currency of cells – and measure changes in their contractile response. Our work contributes to existing literature exploring nutritional approaches to cancer therapeutics but also quantifies general metabolic adaptation due to changes in nutrient levels. By processing cell images, we find that glucose deprived cells become less contractile than control cells. Through mathematical modeling, we additionally found that the glucose deprived are 36% less efficient during contraction (they perform 36% less work per ATP consumed). However, by interpolating between the response parameters of glucose deprived and control cells, we postulate that subject to low levels of glucose deprivation, cells maintain and even enhance their contractility and efficiency. Only beyond a critical level of glucose deprivation do both begin to diminish.

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Two projects are included in the thesis. The two projects study different aspects of fracture and damage as the geometry changes. For Project 1, topology optimization is applied to optimize the fracture toughness of fibrillar adhesives towards initiated cracks. Project 1 applies to applications where the crack initiation is unavoidable and the crack initiation location is fixed. Multiple materials are considered. The objective is to minimize a weighted sum of the compliance and the J-integral, which ensures the load carrying ability and reduces the energy release rate at the crack tip. Three cases are analyzed in plane strain: double edge cracks in tension, single center crack in tension, and single edge crack in shear. With more weight put on reducing the J-integral, the load carrying structure is moved away from the crack. Highly similar results can be obtained for short cracks of different lengths. The methods are verified by: a benchmark topology optimization problem, benchmark J-integral computation problems, and the domain independence of the J-integral in topology optimization. For Project 2, deep indentation of hyperelastic materials in axisymmetry is simulated, which is important for predicting fracture. Frictionless contact and no-slip contact are considered. Four types of indenters are used. Effects of friction, indenter geometries and material constants on the potential crack shapes are studied. Among various types of finite elements, the 3-node triangular elements are chosen by analyzing the order of the numerical integration. The accuracy and the stability of the simulation are increased by modifying the traditional displacement conditions of contact to recover existing penetration. Using remeshing, the indentation can be extended to depth uncapable by commercial finite element software. The large deformation formulation is verified by comparing with the solution of Euler-Bernoulli beams in large bending. The hyperelastic formulation is verified by checking the energy conservation, as well as the agreement with linear elasticity when undeformed.

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Fibrillar dry adhesives are state-of-the-art solutions for controllable and reversible attachments, inspired by nature from animals like the gecko. They depend on short-ranged intermolecular bonds, necessitating discrete attachment terminals with low elastic modulus in order to conform to the adhered material's surface roughness. At the same time, high stiffness grants resistance against interfacial crack growth and detachment under external loading. Nature provides us with a solution to this contentious requirement in the form of bi-material composite adhesives consisting of a soft tip confined by a much stiffer backing, significantly improving the adhesive performance. However, different detachment mechanisms introduced by this design and the adhesive strength corresponding to them have not been thoroughly investigated. We study the adhesive strength of an axisymmetric bi-material with a soft tip adhered to a rigid substrate subjected to normal loading, using linear elastic fracture mechanics. Two major detachment mechanisms are noticed: Crack propagation from the perimeter of the interface and from its center. Geometry and incompressibility of the adhesive layer determine the predominant detachment mode. For a geometrically confined tip under certain conditions, the maximum adhesive strength becomes independent of the crack size due to center crack stable propagation. This maximum adhesive strength is ultimately presented in the form of a power-law equation evidencing an increase in adhesive strength for thinner tips. Finally, we found a good agreement between our results and experiments.

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