Unearthing real-time 3D ant tunneling mechanics.

Granular excavation is the removal of solid, discrete particles from a structure composed of these objects. Efficiently predicting the stability of an excavation during particle removal is an unsolved and highly nonlinear problem, as the movement of each grain is coupled to its neighbors. Despite this, insects such as ants have evolved to be astonishingly proficient excavators, successfully removing grains such that their tunnels are stable. Currently, it is unclear how ants use their limited information about the environment to construct lasting tunnels. We attempt to unearth the ants' tunneling algorithm by taking three-dimensional (3D) X-ray computed tomographic imaging (XRCT), in real time, of Pogonomyrmex ant tunnel construction. By capturing the location and shape of each grain in the domain, we characterize the relationship between particle properties and ant decision-making within an accurate, virtual recreation of the experiment. We discover that intergranular forces decrease significantly around ant tunnels due to arches forming within the soil. Due to this force relaxation, any grain the ants pick from the tunnel surface will likely be under low stress. Thus, ants avoid removing grains compressed under high forces without needing to be aware of the force network in the surrounding material. Even more, such arches shield tunnels from high forces, providing tunnel robustness. Finally, we observe that ants tend to dig piecewise linearly downward. These results are a step toward understanding granular tunnel stability in heterogeneous 3D systems. We expect that such findings may be leveraged for robotic excavation.

Edge States and Topological Pumping in Spatially Modulated Elastic Lattices.

Spatial stiffness modulations defined by the sampling of a two-dimensional surface provide one-dimensional elastic lattices with topological properties that are usually attributed to two-dimensional crystals. The cyclic modulation of the stiffness defines a family of lattices whose Bloch eigenmodes accumulate a phase quantified by integer valued Chern numbers. Nontrivial gaps are spanned by edge modes in finite lattices whose location is determined by the phase of the stiffness modulation. These observations drive the implementation of a topological pump in the form of an array of continuous elastic beams coupled through a distributed stiffness. Adiabatic stiffness modulations along the beams' length lead to the transition of localized states from one boundary, to the bulk and, finally, to the opposite boundary. The first demonstration of topological pumping in a continuous elastic system opens new possibilities for its implementation on elastic substrates supporting surface acoustic waves, or to structural components designed to steer waves or isolate vibrations.

A study of deformation localization in nonlinear elastic square lattices under compression.

The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where a variety of localized deformations were found depending on loading configuration, lattice parameters and boundary conditions. These studies are conducted on other lattice structures, with the objective of identifying and investigating minimal models that exhibit localization, hysteresis and path-dependent behaviour. To this end, we first consider a two-dimensional square lattice consisting of point masses connected by in-plane axial springs and vertical ground springs, which may be considered as a discrete description of an elastic membrane supported by an elastic substrate. Results illustrate that, depending on the relative values of the spring constants, the lattice exhibits in-plane or out-of-plane instabilities leading to localized deformations. This model is further simplified by considering the one-dimensional case of a spring-mass chain sitting on an elastic foundation. A bifurcation analysis of this lattice identifies the stable and unstable branches and sheds light on the mechanism of transition from affine deformation to global or diffuse deformation to localized deformation. Finally, the lattice is further reduced to a minimal four-mass model, which exhibits a deformation qualitatively similar to that in the central part of a longer chain. In contrast to the widespread assumption that localization is induced by defects or imperfections in a structure, this work illustrates that such phenomena can arise in perfect lattices as a consequence of the mode shapes at the bifurcation points.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Amplitude-dependent topological edge states in nonlinear phononic lattices.

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

Wave tailoring by precompression in confined granular systems.

We present a granular system whose response under an impact load can be varied from rapidly decaying to almost constant amplitude waves by an external regulator. The system consists of a granular chain of larger spheres surrounded by small spheres, confined in a hollow cylindrical tube and supporting wave propagation along the axis of the cylinder. We demonstrate using numerical simulations that the response can be controlled by applying radial precompression. These observations are then complemented by an asymptotic analysis, which shows that the decay in the leading wave is due to energy leakage to the oscillating small beads in the tail of the wave. This system has potential applications in systems requiring tuning of elastic waves.

Characterization of wave propagation in elastic and elastoplastic granular chains.

For short duration impulse loadings, elastic granular chains are known to support solitary waves, while elastoplastic chains have recently been shown to exhibit two force decay regimes [ Pal, Awasthi and Geubelle Granular Matter 15 747 (2013)]. In this work, the dynamics of monodisperse elastic and elastoplastic granular chains under a wide range of loading conditions is studied, and two distinct response regimes are identified in each of them. In elastic chains, a short loading duration leads to a single solitary wave propagating down the chain, while a long loading duration leads to the formation of a train of solitary waves. A simple model is developed to predict the peak force and wave velocity for any loading duration and amplitude. In elastoplastic chains, wave trains form even for short loading times due to a mechanism distinct from that in elastic chains. A model based on energy balance predicts the decay rate and transition point between the two decay regimes. For long loading durations, loading and unloading waves propagate along the chain, and a model is developed to predict the contact force and particle velocity.