The mechanics and interactions of electrically sensitive mechanoreceptive hair arrays of arthropods

Recent investigations highlight the possibility of electroreception within arthropods through charged mechanosensory hairs. This discovery raises questions about the influence of electrostatic interaction between hairs and surrounding electrical fields within this sensory modality. Here, we investigate these questions by studying electrostatic coupling in arrays of hairs. We establish the notion of sensitivity contours that indicate regions within which point charges deflect hairs beyond a given threshold. We then examine how the contour’s shape and size and the overall hair behaviour change in response to variations in the coupling between hairs. This investigation unveils synergistic behaviours whereby the sensitivity of hairs is enhanced or inhibited by neighbouring hairs. The hair spacing and ratio of a system’s electrical parameters to its mechanical parameters influence this behaviour. Our results indicate that electrostatic interaction between hairs leads to emergent sensory properties for biologically relevant parameter values. The analysis raises new questions around the impact of electrostatic interaction on the current understanding of sensory hair processes, such as acoustic sensing, unveiling new sensory capabilities within electroreception such as amplification of hair sensitivity and location detection of charges in the environment

Bespoke extensional elasticity through helical lattice systems

© 2019 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ℇ > 0, we construct a system whose energy is approximately E up to an additive constant, with L∞-error no more that ℇ. The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability

Adaptive stiffness in lattice metastructures through tensile-buckling inspired topology morphing

This paper explores the use of simultaneous tensile buckling of unit cells to induce a transformation in lattice topology. Under tension, unit cells undergo passive transformation from a rectangle-like to a triangle-/pentagon-like topology, with an associated change in the effective stiffness properties. This behaviour is investigated through finite element analysis and experiments, with analytical results providing insights into the observed behaviour. The analysis identifies (i) that the initial unit cell topology (rectangular) is dominated by membrane effects, (ii) the transformation phase is associated with negative stiffness, and (iii) once formed, the new topology (triangular/pentagonal) exhibits increased stiffness in both compression and tension. Finite element analysis confirms that the unit cell behaviour is also preserved in lattices. Under tension, the lattice undergoes a seven-fold increase in stiffness as it transitions from its initial to the new topology, with a regime of negative stiffness during this transformation accounting for approximately 82% of its total elastic deformation. This new approach to elastically tailor the nonlinear response of (meta-)materials/structures has the potential to contribute to the development of novel tensile energy absorbers

Towards the efficient computation of effective properties of microstructured materials

An algorithm for partially relaxing multiwell energy densities, such as for materials undergoing martensitic phase transitions, is presented here. The detection of the rank-one convex hull, which describes effective properties of such materials, is carried out for the most prominent nontrivial case, namely the so-called Tk-configurations. Despite the fact that the computation of relaxed energies (and with it effective properties) is inherently unstable, we show that the detection of these hulls (T4-configurations) can be carried out exactly and with high efficiency. This allows in practice for their computation to arbitrary precision. In particular, our approach to detect these hulls is not based on any approximation or grid-like discretization. This makes the approach very different from previous (unstable and computationally expensive) algorithms for the computation of rank-one convex hulls or sequential-lamination algorithms for the simulation of martensitic microstructure. It can be used to improve these algorithms. In cases where there is a strict separation of length scales, these ideas can be integrated at a sub-grid level to macroscopic finite-element computations. The algorithm presented here enables, for the first time, large numbers of tests for T4-configurations. Stochastic experiments in several space dimensions are reported here. To cite this article: C.-F. Kreiner et al., C. R. Mecanique 332 (2004). © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved

Algebraic detection of Tk-configurations

The problem of detecting so-called Tk-configurations is addressed here. These configurations are the most prominent examples of sets with nontrivial rank-one convex hulls. Rank-one convex hulls play an important rôle in the calculus of variations and the modelling of effective properties of materials. An efficient algorithm, based on algebraic methods, is presented. Unlike previous work on the computation of rank-one convex hulls, it is not based on discretization and gives exact results. This algorithm enables, for the first time, large numbers of tests for these configurations. Stochastic experiments in several space dimensions are reported here.