Physics

Adhesive attachment systems consisting of multiple tapes or strands are commonly found in nature, for example in spider web anchorages or in mussel byssal threads, and their structure has been found to be ingeniously architected in order to optimize mechanical properties, in particular to maximize dissipated energy before full detachment. These properties emerge from the complex interplay between mechanical and geometric parameters, including tape stiffness, adhesive energy, attached and detached lengths and peeling angles, which determine the occurrence of three main mechanisms: elastic deformation, interface delamination and tape fracture. In this paper, we introduce a formalism to evaluate the mechanical performance of multiple tape attachments in different parameter ranges, allowing to predict the corresponding detachment behaviour. We also introduce a numerical model to simulate the complex multiple peeling behaviour of complex structures, illustrating its predictions in the case of the staple-pin architecture. We expect the presented formalism and numerical model to provide important tools for the design of bioinspired adhesive systems with tunable or optimized detachment properties.

This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first deduced. Using the displaced Dirac operator, which is closely related to the main vector calculation operators, it is possible to establish a direct connection between the solutions of the Maxwell time-harmonic system and two quaternion equations. Also, the application of the Lorentz condition to transform the time-harmonic Maxwell system into a simple quaternion equation based on the scalar and vector potentials is exposed.

Configurational, or Eshelby-like, forces are shown to strongly influence the nonlinear dynamics of an elastic rod constrained with a frictionless sliding sleeve at one end and with an attached mass at the other end. The configurational force, generated at the sliding sleeve constraint and proportional to the square of the bending moment realized there, has been so far investigated only under quasi-static setting and is now confirmed (through a variational argument) to be present within a dynamic framework. The deep influence of configurational forces on the dynamics is shown both theoretically (through the development of a dynamic nonlinear model in which the rod is treated as a nonlinear spring, obeying the Euler elastica, with negligible inertia) and experimentally (through a specifically designed experimental set-up). During the nonlinear dynamics, the elastic rod may slip alternatively in and out from the sliding sleeve, becoming a sort of nonlinear oscillator displaying a motion eventually ending with the rod completely injected into or completely ejected from the sleeve. The present results may find applications in the dynamics of compliant and extensible devices, for instance, to guide the movement of a retractable and flexible robot arm.

It is pointed out that an electric charge oscillating in a one-dimensional purely-harmonic potential is in detailed balance at its harmonics with a radiation bath whose energy U rad per normal mode is linear in frequency ω , U rad =const×ω, and hence is Lorentz invariant, as seems appropriate for relativistic electromagnetism. The oscillating charge is NOT in equilibrium with the Rayleigh-Jeans spectrum which arises from energy-sharing equipartition ideas which are valid only in nonrelativistic mechanics. Here we explore the contrasting behavior of harmonic oscillators connected to baths in classical mechanics and electromagnetism. It is emphasized that modern physics text are in error in suggesting that the Rayleigh-Jeans spectrum corresponds to the equilibrium spectrum of random classical radiation, and in ignoring Lorentz-invariant classical zero-point radiation which is indeed a classical equilibrium spectrum.

We study here the behaviour of solutions for conjugated (antipodal) points in the 2 -body problem on the two-dimensional sphere M 2 R . We use a slight modification of the classical potential used commonly in \cite{Borisov}, \cite{Diacu} and \cite{Perez}, which avoids the conjugated (antipodal) points as singularities and permit us obtain solutions through these points, as limit of relative equilibria. Such limit solutions behave as relative equilibria because are invariant under Killing vector fields in the Lie Algebra su(2) and are geodesic curves.

In the article, hyperelastic material models which state consistent polynomial expansions of the stored energy function are discussed. The approach follows from the muliplicative decomposition of the deformation gradient. Some advantages of the third order expansion model over the five-parameter Rivlin model using Treloar's experimental data are shown. The models are qualitatively and quantitatively compared to highlight these advantages of the discussed MV model.

In this contribution, the use of discrete simulations to formulate an anisotropic damage model is investigated. It is proposed to use a beam-particle model to perform numerical characterization tests. Indeed, this discrete model explicitly describes cracking by allowing displacement discontinuities and thus capture crack induced anisotropy. Through 2D discrete simulations, the evolution of the effective elasticity tensor for various loading tests, up to failure, is obtained. The analysis of these tensors through bi-dimensional harmonic decomposition is then performed to estimate the tensorial damage evolution. As a by-product of present work we obtain an upper bound of the distance to the orthotropic symmetry class of bi-dimensional elasticity.

The thermal modeling of biological systems has increasing importance in developing more advanced, more precise techniques such as ultrasound surgery. One of the primary barriers is the complexity of biological materials: the geometrical, structural, and material properties vary in a wide range, and they depend on many factors. Despite these difficulties, there is a tremendous effort to develop a reliable and implementable thermal model. In the present paper, we focus on the continuum modeling of heterogeneous materials with biological origin. There are numerous examples in the literature for non-Fourier thermal models. However, as we realized, they are associated with a few common misconceptions. Therefore, we first aim to clarify the basic concepts of non-Fourier thermal models. These concepts are demonstrated by revisiting two experiments from the literature in which the Cattaneo-Vernotte and the dual phase lag models are utilized. Our investigation revealed that using these non-Fourier models is based on misinterpretations of the measured data, and the seeming deviation from Fourier's law originates in the source terms and boundary conditions.

This work is based on the study of the behaviour of flax fibres twill reinforced epoxy composites. The aim of the study is to determine the modulus of elasticity, Poisson coefficients and strength of these composites materials with image correlation. The specimens used in this work were manufactured by the infusion vacuum process and after subjected to quasi-static tensile tests. Two numeric cameras were disposed perpendicular to the front and to the side of the specimen so as to achieve a sequence of visible digital pictures during the test. The recorded pictures were analysed with the image correlation software 7D in order to calculate ad hoc measurements of displacements and strain fields. To check the validity of the results, measurements were compared to those obtained by classical extensometry. We found that, despite the low levels of strains, results of identifications from optical extensometry were very promising.

A magnetized bead in a magnetic field seeks to minimize its magnetic free energy by aligning its magnetic moment with the field direction and by moving towards the maximum of the field's intensity. However, when the bead is coupled to a substrate it is forced to roll. The two otherwise independent degrees of freedom, translation and rotation, become tightly coupled giving rise to subtle and often counterintuitive effects. Here we investigate one such, easily reproducible, yet stunning effect : A neodymium bead placed on top of a laboratory magnetic stirrer. When the stirrer's magnet spins at slow rates the bead naturally follows the field. However, surprisingly, at high spinning rates the bead suddenly inverts its direction and runs, to the surprise of the observer, in the opposite direction, against the driving field direction.This effect, experimentally investigated in [J.Magn.Magn.Matter, 476, 376-381, (2019)], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.