Emergence of the interplay between hierarchy and contact splitting in biological adhesion highlighted through a hierarchical shear lag model

Contact unit size reduction is a widely studied mechanism as a means to improve adhesion in natural fibrillar systems, such as those observed in beetles or geckos. However, these animals also display complex structural features in the way the contact is subdivided in a hierarchical manner. Here, we study the influence of hierarchical fibrillar architectures on the load distribution over the contact elements of the adhesive system, and the corresponding delamination behaviour. We present an analytical model to derive the load distribution in a fibrillar system, including hierarchical splitting of contacts, i.e. a "hierarchical shear-lag" model that generalizes the well-known shear-lag model used in mechanics. The influence on the detachment process is investigated introducing a numerical procedure that allows the derivation of the maximum delamination force as a function of the considered geometry, including statistical variability of local adhesive energy. Our study suggests that contact splitting generates improved adhesion only in the ideal case of infinitely compliant contacts. In real cases, to produce efficient adhesive performance, contact splitting needs to be coupled with hierarchical architectures to counterbalance high load concentrations resulting from contact unit size reduction, generating multiple delamination fronts and helping to avoid detrimental non-uniform load distributions. We show that these results can be summarized in a generalized adhesion scaling scheme for hierarchical structures, proving the beneficial effect of multiple hierarchical levels. The model can thus be used to predict the adhesive performance of hierarchical adhesive structures, as well as the mechanical behaviour of composite materials with hierarchical reinforcements.Comment: 33 pages, 7 figures, 1 table in pres

The influence of substrate roughness, patterning, curvature, and compliance in peeling problems

NMP is supported by the European Commission under the Graphene FET Flagship (WP14 'Polymer composites' No. 604391) and FET Proactive 'Neurofibres' grant No. 732344. FB is supported by 'Neurofibres' grant No. 732344

An experimental and numerical study on the mechanical properties of carbon nanotube-latex thin films

This research was supported by the U.S. National Science Foundation (NSF) under grant number CMMI-CAREER 1253564 and supplement CMMI-CAREER 1542532. In addition, N.M.P. acknowledges support by the European Research Council (ERC StG Ideas 2011 BIHSNAM no. 279985, ERC PoC 2013-2 KNOTOUGH no. 632277, ERC PoC 2015 SILKENE no. 693670), by the European Commission under the Graphene Flagship (WP10 ‘Nanocomposites’, no. 604391) and by the Provincia Autonoma di Trento (‘Graphene nanocomposites’, no. S116/2012-242637 and reg. delib. no. 2266). L.B. and F.B. are supported by BIHSNAM. Computational resources were provided by HPC@POLITO (http://www.hpc.polito.it

Optimal adhesion control via cooperative hierarchy, grading, geometries and non-linearity of anchorages

Optimization of dry adhesion in biological organisms is achieved using various strategies at different scale levels. In the past, studies have shown how contact splitting is used effectively by animals such as geckos and insects to increase the total peeling line of contacts and therefore the adhesion force. Also, tapering of contacts or grading of their mechanical properties has been shown to be instrumental in the achievement of improved adhesion efficiency. On a more macroscopic scale, structures such as spider web anchorages exploit hierarchical structure or nonlinear constitutive material properties to improve resilience and to achieve tunability in adhesion/detachment characteristics. Here, we analyse some of these properties and propose some mechanisms for the optimization of adhesion that have thus far been neglected in modelling approaches, and could be potentially exploited for the design of bioinspired adhesives. We consider hierarchical structure, contact tapering, grading of mechanical properties, and their interaction. It emerges that these mechanisms contribute on various size scales to the achievement of optimal adhesive properties through structural complexity and hierarchical organization

Numerical implementation of multiple peeling theory and its application to spider web anchorages

Adhesion of spider web anchorages has been studied in recent years, including the specific functionalities achieved through different architectures. To better understand the delamination mechanisms of these and other biological or artificial fibrillar adhesives, and how their adhesion can be optimized, we develop a novel numerical model to simulate the multiple peeling of structures with arbitrary branching and adhesion angles, including complex architectures. We validate the numerical model by comparing predictions with the recently developed Multiple Peeling Theory (MPT), which extends the energy-based single peeling theory of Kendall, finding excellent agreement even for complex structures. In particular we numerically confirm that a multiple peeling problem can be treated as the superposition of single peeling configurations even for complex structures. Finally, we apply the developed numerical approach to study spider web anchorages, showing how their function is achieved through optimal geometrical configurations

Numerical implementation of multiple peeling theory and its application to spider web anchorages

Adhesion of spider web anchorages has been studied in recent years, including the specific functionalities achieved through different architectures. To better understand the delamination mechanisms of these and other biological or artificial fibrillar adhesives, and how their adhesion can be optimized, we develop a novel numerical model to simulate the multiple peeling of structures with arbitrary branching and adhesion angles, including complex architectures. We validate the numerical model by comparing predictions with the recently developed Multiple Peeling Theory (MPT), which extends the energy-based single peeling theory of Kendall, finding excellent agreement even for complex structures. In particular we numerically confirm that a multiple peeling problem can be treated as the superposition of single peeling configurations even for complex structures. Finally, we apply the developed numerical approach to study spider web anchorages, showing how their function is achieved through optimal geometrical configurations

Competition between delamination and tearing in multiple peeling problems

Adhesive attachment systems consisting of multiple tapes or strands are commonly found in nature, for example in spider web anchorages or in mussel byssal threads, and their structure has been found to be ingeniously architected in order to optimize mechanical properties: in particular, to maximize dissipated energy before full detachment. These properties emerge from the complex interplay between mechanical and geometric parameters, including tape stiffness, adhesive energy, attached and detached lengths and peeling angles, which determine the occurrence of three main mechanisms: elastic deformation, interface delamination and tape fracture. In this paper, we introduce a formalism to evaluate the mechanical performance of multiple tape attachments in different parameter ranges, where an optimal (not maximal) adhesion energy emerges. We also introduce a numerical model to simulate the multiple peeling behaviour of complex structures, illustrating its predictions in the case of the staple-pin architecture. Finally, we present a proof-of-principle experiment to illustrate the predicted behaviour. We expect the presented formalism and the numerical model to provide important tools for the design of bioinspired adhesive systems with tuneable or optimized detachment properties