Author: harmeet1987

K. Suryanarayanan, P. Patel, A. K. Pathak, and H. Singh

We explore the mechanics of a terminally loaded buckled elastica under frictionless self-contact. With the aid of two integrals associated with the elastica, we propose a scale-invariant condition necessary for the onset of contact. The condition is independent of the boundary conditions, does not involve the position vectors of the material points, and delivers the value of the compressive load at which self-contact initiates. Furthermore, we show that one of the two integrals, namely the Hamiltonian, persists after contact. We compute post-contact configurations of modes three through ten for a pinned-pinned buckled elastica. At a given value of the compressive load, we report multiple post-contact configurations for modes eight and nine. Finally, we show that an infinite force is required to transition from a point contact to a line contact in symmetric post-contact configurations of odd modes.

arXiv

K. Suryanrayanan and H. Singh

We present a reduced order theory of locally impenetrable elastic tubes. The constraint of local impenetrability — an inequality constraint on the determinant of the 3D deformation gradient — is transferred to the Frenet curvature of the centerline of the tube via reduced kinematics. The constraint is incorporated into a variational scheme, and a complete set of governing equations, jump conditions, and boundary conditions are derived. It is shown that with the local impenetrability actively enforced, configurations of an elastic tube comprise segments of solutions of the Kirchhoff rod theory appropriately connected to segments of constant Frenet curvature. The theory is illustrated by way of three examples: a fully flexible tube hanging under self-weight, an elastic tube hanging under self-weight, and a highly twisted elastic tube.

arXiv

K. Suryanrayanan, A.B. Croll, and H. Singh

We present an experimental and theoretical study of the mechanics of an adhesive tape loop, formed by bending a straight rectangular strip with adhesive properties, and prescribing an overlap between the two ends. For a given combination of the adhesive strength and the extent of the overlap, the loop may unravel, it may stay in equilibrium, or open up quasi-statically to settle into an equilibrium with a smaller overlap. We define the state space of an adhesive tape loop with two parameters: a non-dimensional adhesion strength, and the extent of overlap normalized by the total length of the loop. We conduct experiments with adhesive tape loops fabricated out of sheets of polydimethylsiloxane (PDMS) and record their states. We rationalize the experimental observations using a simple scaling argument, followed by a detailed theoretical model based on Kirchhoff rod theory. The predictions made by the theoretical model, namely the shape of the loops the states corresponding to equilibrium, show good agreement with the experimental data. Our model may potentially be used to deduce the strength of self-adhesion in sticky soft materials by simply measuring the smallest overlap needed to maintain a tape loop in equilibrium.

arXiv and journal

H. Singh, K. Suryanarayanan, and E.G. Virga

We study spontaneous deformations of a ribbon made of nematic polymer networks and activated under the action of a mechanical load. We show that when such ribbons are activated appropriately, the deformations produced can pull back and perform work against the externally applied load. We perform two numerical experiments to demonstrate this effect: (1) the pulling experiment, where the ribbon is pulled longitudinally by a point force, and (2) the bending experiment, where the ribbon is bent out of plane by a terminally applied point force. We quantify the capacity of the ribbon to work against external loads, and compute its dependence on both the ribbon thickness and the imprinted nematic texture (that is, the distribution of the nematic directors across the ribbon’s length). Finally, we compute the efficiency of the activation process. Building on the outcomes of our numerical explorations, we formulate two educated conjectures on how the activation efficiency can in general be improved by acting on both the applied load and the imprinted nematic texture.

arXiv and journal

H. Singh and E. G. Virga

We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey a complementarity relation: one is maximum where the other is minimum. Moreover, we identify a bleaching regime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon’s deformation is essentially independent of its thickness.

arXiv and journal