Adhesion of a tape loop

T. Elder, T. Twohig, H. Singh, and A. B. Croll

In this work, we revisit experimentally and theoretically the mechanics of a tape loop. Using primarily elastic materials (polydimethylsiloxane, PDMS, or polycarbonate, PC) and confocal microscopy, we monitor the shape as well as the applied forces during an entire cycle of compression and retraction of a half-loop compressed between parallel glass plates. We observe distinct differences in film shape during the cycle; points of equal applied force or equal plate separation differ in shape upon compression or retraction. To model the adhesion cycle in its entirety, we adapt the ‘Sticky Elastica’ of [T. J. W. Wagner et al., Soft Matter, 2013, 9, 1025–1030] to the tape loop geometry, which allows a complete analytical description of both the force balance and the film shape. We show that under compression the system is generally not sensitive to interfacial interactions, whereas in the limit of large separation of the confining parallel plates during retraction the system is well described by the peel model. Ultimately, we apply this understanding to the measurement of the energy release rate of a wide range of different cross-linker ratio PDMS elastomer half-loops in contact with glass. Finally, we show how the model illuminates an incredibly simple adhesion measurement technique, which only requires a ruler to perform.


Mechanics of two filaments in tight contact: The orthogonal clasp

P. Grandgeorge, C. Baek, H. Singh, P. Johanns, T. G. Sano, A. Flynn, J. H. Maddocks, and P. M. Reis

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple yet canonical problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with the finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibits strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and the FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small but finite tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.


Pseudomomentum: origins and consequences

H. Singh and J. A. Hanna

The balance of pseudomomentum is discussed and applied to first gradient elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to position, time, and material labels yields bulk balance laws and jump conditions for momentum, energy, and pseudomomentum. The example of first gradient elasticity of space-filling continua is treated at length. Then the pseudomomentum balance is employed to derive several results, beginning with the conservation of vorticity, circulation, and helicity in ideal fluids. A mathematical similarity is noted between the evaluation of circulation along a material loop and the J-integral of fracture mechanics. Integration of the pseudomomentum balance, making use of a prescription for singular sources derived by analogy with the continuous form of the balance, directly provides the propulsive force driving passive reconfiguration or locomotion of confined, inhomogeneous elastic rods. The conserved angular momentum and pseudomomentum are identified in the classification of conical sheets with rotational inertia or bending energy.



Impact-induced acceleration by obstacles

N. Corbin, J. A. Hanna, W. Royston, H. Singh, and R. Warner

We explore a surprising phenomenon in which an obstruction accelerates, rather than decelerates, a moving flexible object. It has been claimed that the right kind of discrete chain falling onto a table falls faster than a free-falling body. We confirm and quantify this effect, reveal its complicated dependence on angle of incidence, and identify multiple operative mechanisms. Prior theories for direct impact onto flat surfaces, which involve a single constitutive parameter, match our data well if we account for a characteristic delay length that must impinge before the onset of excess acceleration. Our measurements provide a robust determination of this parameter.


supplementary videos and data fitting plots
arXiv, journal, and perspective

Partial constraint singularities in elastic rods

J. A. Hanna, H. Singh, and E. G. Virga

We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the configurational balance of material momentum and the concept of a driving traction. The theory is generalizable and can be applied to a wide array of contact, adhesion, gripping, and locomotion problems.


arXiv and journal