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.

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 loaded in shear, 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 extremely 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.

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

Biological adhesion, in particular the mechanisms by which animals and plants 'stick' to surfaces, has been widely studied in recent years, and some of the structural principles have been successfully applied to bioinspired adhesives. However, modelling of adhesion, such as in single or multiple peeling theories, has in most cases been limited to ideal cases, and due consideration of the role of substrate geometry and mechanical properties has been limited. In this paper, we propose a numerical model to evaluate these effects, including substrate roughness, patterning, curvature, and deformability. The approach is validated by comparing its predictions with classical thin film peeling theoretical results, and is then used to predict the effects of substrate properties. These results can provide deeper insight into experiments, and the developed model can be a useful tool to design and optimize artificial adhesives with tailor-made characteristics.

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. The numerical model is based on a recently developed multiple peeling theory, which extends the energy-based single peeling theory of Kendall, and can be applied to arbitrarily complex structures. In particular, we numerically show 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.