A two-scale strategy for the modeling of hook and loop fasteners

Abstract

Hook-and-loop-like joints have been widely used in many engineering applications and even observed in nature. The demand for computational models to predict the behavior of fasteners is increasing as they will be key for reducing design process time and manufacturing costs. Here, we develop a bottom-up two-scale modeling strategy, which enables us to capture the mechanical performance of a hook-and-loop fastener at both micro- and macroscales. In particular, we employ a two-scale homogenization approach capable of predicting the mechanical behavior of the hook-and-loop fastener. The model starts with a micromechanical model of a hook-and-loop fastener which considers the detailed geometry of the individual building blocks of the hook-and-loop fastener and their statistical geometrical variability through a so-called Representative Hook and Loop Element (RHLE) computational domain. The second scale considers the homogenization of the micromechanical model into a Detachment Process Zone (DPZ) which reveals an emerging length scale. The resulting effective traction-separation law concept is then employed at the macroscale with a Double Cantilever Beam (DCB) test using a macroscale model, which is then validated with experiments. The results suggest that the two-scale model strategy is able to predict the mechanical behavior of hook-and-loop fastener and to capture the main deformation and dissipative mechanisms at the relevant length scales.

Introduction

Natural organisms have evolved several strategies to thrive in their local environment. In terms of structural support and additional functionality, such as protection and predation, nature has developed exceptional lightweight, strong, and tough materials through hierarchical architectures and material composition (Huang et al., 2019). These architectures have design features that range from cellular structures that offer lightweight solutions for energy absorption, to solid fibrous architectures that contribute to tensile strength (Naleway et al., 2015). Among these features, nature has found very efficient ways to connect and bond materials employing gradients, geometry and interlocking mechanisms (i.e. sutures, patterned interfaces, etc.). Examples of these interfaces have been found in sea urchins, alligators, and turtles (Hosseini et al., 2019; Naleway et al., 2015), helical architectures found in crabs and mantis shrimp (Shishehbor and Zavattieri, 2019; Suksangpanya et al., 2017, 2018) and nacre-like composites (Espinosa et al., 2009).

Other functionalities include the ability of some species to adhere to surfaces for locomotion such as geckos, lizards, and spiders (Sun et al., 2005). The study by Autumn et al. (2000) revealed the exceptional ability of geckos to climb vertical surfaces due to the presence of a hundred thousand keratinous hairs or setae (Autumn et al., 2000). Similarly, the ventral leg segments in spiders are covered by microtrichia with spatula-like tips and result in considerably high friction when climbing steep surfaces (Niederegger and Gorb, 2006). Although the presence of hook-like surfaces in the structure of some species can facilitate movement in high, steep surfaces by enhancing adhesion and friction, other species such as Stylasterias forreri (also called “Velcro” sea stars) are known to use hook-like teeth inside their flexible arms to hunt mollusks and small fish (Dejean et al., 2010) as shown in Fig. 1(a). Similarly, Azteca Andreae ants developed hook-shaped claws to capture prey (Fig. 1(b)).

The feathers of birds are also a good example of hook-like connections in nature. Their architecture contains barbs branching out from the main shaft. These barbs also contain small barbules with microhooks that facilitate the connection between barbs (Fig. 1(c)). This type of connection provides a self-repair mechanism through the re-attachment of unhooked junctions (Sullivan et al., 2016). Hui et al. (2011) studied the crack trapping effect enabled by the architecture of the base plate of Balanus amphitrite, which allows them to attach strongly to submerged surfaces in tidal waters. Recently, Morano et al. (2018, 2020) used computational modeling and additive manufacturing to explain the mechanisms that contribute to such strong adhesion.

Perhaps one of the first bio-inspired mechanical adhesives gave birth to the widely used hook-and-loop fasteners. The hooks in these fasteners were inspired by the burrs of burdocks which tend to attach to the fur of animals and fabric (see Fig. 1(d)). Burdocks are small plant usually found in the mountains in Europe, and their burrs are hard to remove if they come in contact with fibrous surfaces. The surface of the burdock burr is covered by several spines with hook- shaped ends, as shown in Fig. 1(d) (Kapsali, 2018). This observation resulted in the development of hook-and-loop fasteners as the one shown in Fig. 1(e). Hook-and-loop fasteners consist of two components: i) hooks tape and ii) loops with fibrous surfaces. Once contact occurs (i.e., by pressing two tape surfaces together), the loops in the fibrous surface engage and become entangled with the hooks providing a strong connection and bonding based on mechanical interlocking. Separation can be attained by either pulling-out or peeling-off the two surfaces (Kennedy and Rocha, 1994).

Mechanical hook-and-loop fasteners have been widely employed in the clothing, automotive and aerospace industry, and have been proposed as clever design concepts in other disciplines. For example, Meislin (2000) demonstrated how surgical muscle repair can be accomplished by connecting separated tendons and muscles using hook-and-loops fasteners. Also, the supramolecular technique was used as a solution for enhancing strength in underwater adhesion using Velcro-like connections (Ahn et al., 2013). They have also been used in geotechnical design as a way to improve the interface between geomembrane and geotextile that contains hook-and-loops fasteners (Hebeler et al., 2005). Recently, Restrepo and Martinez (2021) proposed reconfigurable hook-and-loop cementitious brick-and-mortar structures with the capability to distribute loading forces and accommodate deformation. Although these examples illustrate the benefits of using hook-and-loop fasteners and the demands for such fasteners keeps increasing with new applications, there are not many computational models and tools that can be employed to study and understand their mechanical behavior (Berber et al., 2003; Pugno, 2007; Vokoun et al., 2011; Williams et al., 2007). The development of such computational models would enable the analysis of these fasteners and help shorten the design and production process. For instance, such models can assist designers in making decisions and provide a virtual test bed to evaluate the performance of a new fastener.

Predictive models that can connect the geometry and mechanical behavior of the individual hooks and loops with the macroscopic mechanical performance of the fastener will need a multiscale strategy. Previous works have demonstrated the ability of multiscale homogenization technique as an effective way to predict the behavior of the large homogenized systems by considering the details and heterogeneities at lower scales. Nguyen et al. (2012a, 2012b) and Esmaeeli et al. (2019) successfully predicted the macroscopic failure behavior of the concrete by considering microscale details using a multistep model. In these models, the time-dependent mechanical properties of the cement paste, as a purely brittle material, were first defined at the microscale (i.e., the lowest length scale). Following a continuous-discontinuous multiscale method that employs cohesive models, they were able to predict the quasi-brittle mechanical properties of concrete at the macroscale. Using this approach, the first step considered the mesoscale geometry of the mortar, (e.g., a composite with cement paste and fine aggregates) and the second step consisted of a composite with the homogenized mortar (obtained from the mesoscale simulations) and coarse aggregates. Cracks were then allowed to initiate, propagate, and interact on the cement paste fine/coarse aggregates, mortar and in their respective interfaces (Esmaeeli et al., 2019). In general, these multiscale approaches allow us to couple both micro- and macroscales and predict the homogenized behavior even when fracture and other mechanisms of localization are present (Aragón et al., 2013; Kulkarni et al., 2009; Matouš et al., 2008).

In this paper, we propose a two-scale computational model for hook-and-loop fasteners based on the real geometry of their most fundamental building blocks and their material properties at the microscale and will enable the prediction of the macroscopic mechanical behavior of hook-and-loop fasteners. In the first part of this study, we provide details of the proposed micromechanical models of both hooks and loops, which includes both geometry of hooks and fibrous loops, and their corresponding material properties. Following a two-step homogenization technique, the results from the micromechanical models are used as an input in the macromechanical model to predict the performance of a Double Cantilever Beam (DCB) specimen under mode-I loading. For both micromechanical and macromechanical models, the results from the numerical simulations are validated with the experiments.