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Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there have been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

A flexible membrane deforming its shape in time can self-propel in a viscous fluid. Alternatively, if the membrane is anchored, its deformation will lead to fluid transport. Past work in this area focused on situations where the deformation kinematics of the membrane were prescribed. Here we consider models where the deformation of the membrane is not prescribed, but instead the membrane is internally forced. Both the time-varying membrane shape and the resulting fluid motion result then from a balance between prescribed internal active stresses, internal passive resistance, and external viscous stresses. We introduce two specific models for such active internal forcing: one where a distribution of active bending moments is prescribed, and one where active inclusions exert normal stresses on the membrane by pumping fluid through it. In each case, we asymptotically calculate the membrane shape and the fluid transport velocities for small forcing amplitudes, and recover our results using scaling analysis.

Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here, we use a series of simple models to analytically elucidate the propulsive effects of a solid boundary on passively actuated filaments and model flagella. For passive flexible filaments actuated periodically at one end, the presence of the wall is shown to increase the propulsive forces generated by the filaments in the case of displacement-driven actuation, while it decreases the force in the case of force-driven actuation. In the case of active filaments as models for eukaryotic flagella, we demonstrate that the manner in which a solid wall affects propulsion cannot be known a priori, but is instead a nontrivial function of the flagellum frequency, wavelength, its material characteristics, the manner in which the molecular motors self-organize to produce oscillations (prescribed activity model or self-organized axonemal beating model), and the boundary conditions applied experimentally to the tethered flagellum. In particular, we show that in some cases, the increase in fluid friction induced by the wall can lead to a change in the waveform expressed by the flagella, which results in a decrease in their propulsive force.

Intermolecular forces are known to precipitate adhesion events between solid bodies. Inspired by a macroscale experiment showing the hysteretic adhesion of a piece of flexible tape over a plastic substrate, we develop here a model of far-field dry adhesion between two flexible sheets interacting via a power-law potential. We show that phase transitions from unadhered to adhered states occur as dictated by a dimensionless bending parameter representing the ratio of interaction strength to bending stiffness. The order of the adhesion transitions, as well as their hysteretic nature, is shown to depend on the form of the interaction potential between the flexible sheets. When three or more sheets interact, additional geometrical considerations determine the hierarchical or sequential nature of the adhesion transitions.