Fibrous metamaterials derive their macroscopic mechanical response from the interplay between fiber deformation and hinge mechanics. This work introduces a novel printable hinge conception for filament-based additive manufacturing that is designed to behave as a perfect pivot and to improve structural stability under compression. Experiments on specimens subjected to bias-extension and compression tests show that the proposed hinges preserve the characteristic second-gradient response of fibrous metamaterials while contributing to delay the onset of transverse instability (qualitative evidence). The improved compressive behavior suggests potential applications in lightweight fibrous composite metamaterials requiring enhanced stability and deformation control. A second-gradient continuum model is calibrated against the experimental bias-extension response and used to perform finite element based numerical simulations. The resulting simulations reproduce the experimental force–displacement behavior with very good accuracy, supporting both the effectiveness of the proposed hinge design and the relevance of the adopted higher-order continuum description.
The Bénard–von Kármán wake is a canonical phenomenon in fluid mechanics, readily identified by its alternating vortex street forming behind a bluff body. Seemingly unrelated, rapidly rotating fluids give rise to elongated, quasi-two-dimensional structures known as Taylor columns. The Taylor–Proudman theorem indeed enforces an invariance of the flow along the rotation axis when inertial and viscous effects are small compared with Coriolis forces. Here, we combine these two seemingly distinct phenomena by studying the formation of what we call phantom wakes: a rotating fluid appears to flow around a non-existent solid obstacle, namely a Taylor column. We address the question of whether a Bénard–von Kármán-type wake can spontaneously emerge under such conditions. To do so, we perform direct numerical simulations of an imposed flow in a rotating channel containing a small cylindrical cavity on one wall, which generates a Taylor column. By systematically varying the Rossby and Reynolds numbers, we analyze the progressive emergence of a wake behind the column and its convergence toward the classical vortex street. As in the non-rotating case, vortex shedding occurs through a Hopf bifurcation, which we characterize for a fixed Rossby number. However, the transition threshold varies non-monotonically with rotation. For intermediate Rossby numbers, elliptical streamlines and a shorter recirculation region are observed, resulting in a critical Reynolds number exceeding the classical value of 47. These findings not only reveal unexpected wake dynamics, but also suggest a mechanism for Taylor column formation that depends sensitively on the cavity geometry.
This article examines the force deduced by Ampère (1775–1826). In 1820 Oersted conducted his revolutionary experiment: a current-carrying wire capable of deflecting a compass needle. To explain this phenomenon Ampère presented two crucial hypotheses: he postulated the existence of forces between current-carrying conductors and suggested that electric currents existed not only in conductive wires, but also inside magnets and even within the Earth. To deduce his force Ampère developed his famous cases of equilibrium in which a mobile circuit is kept at rest between two opposing forces or between two opposing torques. In 1822 Ampère obtained his final expression, a central force consistent with Newton’s third law of motion. According to Ampère’s force, the action between two current elements is proportional to the product of their intensities, to the product of their infinitesimal lengths, and varies inversely with the square of their distance. Furthermore, this force depends on three angles. According to Maxwell, Ampère’s force should always remain the most important formula of electrodynamics. However, despite this positive evaluation, Ampère’s force disappeared from modern textbooks, being replaced by Grassmann’s theoretical force from 1845, which does not comply with Newton’s third law. In 1822 Ampère predicted the existence of longitudinal repulsive forces between two collinear and parallel elements with currents in the same direction. This force should not exist according to Grassmann’s law. Ampère created the bridge experiment to test this prediction and it was successful. Maxwell, while aware of both expressions (Ampère’s and Grassmann’s forces), expressly preferred Ampère’s force.
Nonlocal constitutive models have been widely developed to account for size/gradient effects or to circumvent the difficulties associated with excessive spatial localization. Two main thermodynamic frameworks have been proposed to incorporate some information regarding the spatial distribution of internal variables in a consistent manner: formulations based on an extended energy flux and those relying on an extended entropy flux. Although these approaches are often regarded as equivalent, their respective implications on the thermodynamic structure of the governing equations remain insufficiently understood. In this work, a comparison between nonlocal models formulated with an extended energy flux and with an extended entropy flux is conducted within the general framework of continuum thermodynamics. Both gradient-based and integral-based nonlocal approaches are considered in a unified manner. The corresponding energy and entropy balance equations are derived, along with the associated dissipation inequalities, evolution equations for internal degrees of freedom, and heat diffusion equations. It is shown that the two formulations lead to identical evolution equations under uniform temperature conditions. However, some differences arise in the presence of temperature gradients, notably through the coupling between nonlocal interactions and the temperature field in the extended entropy flux formulation. The analysis also clarifies under which assumptions some formulations presented as extended entropy flux approaches should rather be interpreted as extended energy flux frameworks. The results provide a theoretical basis to assess the relevance and limitations of extended energy and entropy flux formulations of nonlocal constitutive models in thermomechanically coupled problems.
The aim of this work is to study theoretically and numerically the effect of the inhomogeneity of the yield stress on void coalescence for isotropic porous ductile materials. Such inhomogeneities may arise due to strain hardening prior to void coalescence. Sequential limit analysis is applied to a cylindrical unit cell containing a coaxial cylindrical void in a von Mises matrix material with a radially dependent yield stress. An estimate of the coalescence criterion is obtained for combined tensile and shear loading. The criterion relies on 1D integrals, but two approximations are also provided to obtain analytical expressions. Numerical limit analysis based on FFT simulations is performed to get exact, up to numerical errors, coalescence stresses, and to assess the theoretical expressions. A good agreement is found between the analytical coalescence criterion and the numerical results for a large set of void shape, porosities and yield stress distributions. The coalescence criterion is finally used to assess the effect of strain-hardening on the orientation of void coalescence plane, as well as to describe the full yield locus — accounting for both void growth and coalescence — of porous isotropic materials, for axisymmetric loading conditions.
