Elastic Degrees Of Freedom Research Articles

Defect-induced electronic smectic state at the surface of nematic materials

Due to the intertwining between electronic nematic and elastic degrees of freedom, lattice defects and structural inhomogeneities commonly found in crystals can have a significant impact on the electronic properties of nematic materials. Here, we show that defects commonly present at the surface of crystals generally shift the wave-vector of the nematic instability to a non-zero value, resulting in an incommensurate electronic smectic phase. Such a smectic state onsets above the bulk nematic transition temperature and is localized near the surface of the sample. We argue that this effect may explain not only recent observations of a modulated nematic phase in iron-based superconductors, but also several previous puzzling experiments that reported signatures consistent with nematic order before the onset of a bulk structural distortion.

Detection of relativistic fermions in Weyl semimetal TaAs by magnetostriction measurements

Thus far, a detection of the Dirac or Weyl fermions in topological semimetals remains often elusive, since in these materials conventional charge carriers exist as well. Here, measuring a field-induced length change of the prototype Weyl semimetal TaAs at low temperatures, we find that its c-axis magnetostriction amounts to relatively large values whereas the a-axis magnetostriction exhibits strong variations with changing the orientation of the applied magnetic field. It is discovered that at magnetic fields above the ultra-quantum limit, the magnetostriction of TaAs contains a linear-in-field term, which, as we show, is a hallmark of the Weyl fermions in a material. Developing a theory for the magnetostriction of noncentrosymmetric topological semimetals and applying it to TaAs, we additionally find several parameters characterizing the interaction between the relativistic fermions and elastic degrees of freedom in this semimetal. Our study shows how dilatometry can be used to unveil Weyl fermions in candidate topological semimetals.

Anchoring-induced nonmonotonic velocity versus temperature dependence of motile bacteria in a lyotropic nematic liquid crystal.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

Actuation and Motion Control of Flexible Robots: Small Deformation Problem

AbstractThis paper introduces a new computational approach for the articulated joint/deformation actuation and motion control of robot manipulators with flexible components. Oscillations due to small deformations of relatively stiff robot components which cannot be ignored, are modeled in this study using the finite element (FE) floating frame of reference (FFR) formulation which employs two coupled sets of coordinates: the reference and elastic coordinates. The inverse dynamics, based on the FFR formulation, leads to driving forces associated with the deformation degrees of freedom. Because of the link flexibility, two approaches can be considered to determine the actuation forces required to achieve the desired motion trajectories. These two approaches are the partially constrained inverse dynamics (PCID) and the fully constrained inverse dynamics (FCID). The FCID approach, which will be considered in future investigations and allows for motion and shape control, can be used to achieve the desired motion trajectories and suppress undesirable oscillations. The new small-deformation PCID approach introduced in this study, on the other hand, allows for achieving the desired motion trajectories, determining systematically the actuation forces and moments associated with the robot joint and elastic degrees of freedom, and avoiding deteriorations in the vibration characteristics as measured by the differences between the inverse- and forward-dynamics solutions. A procedure for determining the actuation forces associated with the deformation degrees of freedom is proposed and is exemplified using piezoelectric actuators. The PCID solution is used to define a new set of algebraic equations that can be solved for the piezoelectric actuation voltages required to maintain the forward-dynamics oscillations within their inverse-dynamics limits. A planar two-link flexible-robot manipulator is presented to demonstrate the implementation of the joint/deformation actuation approach. The results obtained show deterioration in the robot precision if the deformation actuation is not considered.

Topological solitons and bulk polarization switch in collinear type-II multiferroics

We introduce a microscopic model for collinear multiferroics capable to reproduce, as a consequence of magnetic frustration and easy-axis anisotropy, the so-called "uudd" (or antiphase) magnetic ordering observed in several type II multiferroic materials. The crucial role of lattice distortions in the multiferroic character of these materials is entered into the model via an indirect magnetoelectric coupling, mediated by elastic degrees of freedom through a pantograph mechanism. Long range dipolar interactions set electric dipoles in the antiferroelectric order. We investigate this model by means of extensive DMRG computations and complementary analytical methods. We show that a lattice dimerization induces a spontaneous Z2 ferrielectric bulk polarization, with a sharp switch off produced by a magnetic field above a critical value. The topological character of the magnetic excitations makes this mechanism robust.

Monopole matter from magnetoelastic coupling in the Ising pyrochlore

Ising models on a pyrochlore oxide lattice have become associated with spin ice materials and magnetic monopoles. Ever more often, effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O−2 ions mediating superexchange; we call it the magnetoelastic spin ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite of its simplicity and classical approach, it describes the double-layered monopole crystal observed in Tb2Ti2O7. Additionally, the dipolar electric moment of single monopoles emerges as a probe for magnetism. As an example we show that some Coulomb phases could, in principle, be detected through pinch points associated with O−2-ion displacements.

Wetting transitions on soft substrates

Within mean-field theory we study wetting of elastic substrates. Our analysis is based on a grand canonical free energy functional of the fluid number density and of the substrate displacement field. The substrate is described in terms of the linear theory of elasticity, parametrized by two Lamé coefficients. The fluid contribution is of the van der Waals type. Two potentials characterize the interparticle interactions in the system. The long-ranged attraction between the fluid particles is described by a potential , and characterizes the substrate-fluid interaction. By integrating out the elastic degrees of freedom we obtain an effective theory for the fluid number density alone. Its structure is similar to the one for the wetting of an inert substrate. However, the potential is replaced by an effective potential which, in addition to , contains a term bilinear in . We discuss the corresponding wetting transitions in terms of an effective interface potential , where ℓ denotes the thickness of the wetting layer. We show that in the case of algebraically decaying interactions the elasticity of the substrate may suppress critical wetting transitions, and may even turn them first order.

Spectral energy transfer in a viscoelastic homogeneous isotropic turbulence

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.

Probing magneto-elastic phenomena through an effective spin-bath coupling model

A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the present work, the consequences of identifying the effects of dissipation as resulting from interactions with a bath of spins are explored, in addition to elastic, degrees of freedom. The corresponding stochastic differential equations are solved numerically and the moments of the magnetization are computed. The stochastic equations implicitly define a measure on the space of spin configurations, whose moments at equal times satisfy a hierarchy of deterministic, ordinary differential equations. Closure assumptions are used to truncate the hierarchy and the same moments are computed. We focus on the advantages and problems that each approach presents, for the approach to equilibrium and, in particular, the emergence of longitudinal damping.

Numerical and Experimental Analysis of the Dynamic Behavior of Piezoelectric Stiffened Composite Plates Subjected to Airflow

In this paper, the authors present results on dynamic behavior analysis of the stiffened composite plate with piezoelectric patches under airflow by finite element method and experimental study. The first-order shear deformation plate theory and nine-noded isoparametric piezoelectric laminated plate finite element with five elastic degrees of freedom at each node and one electric degree of freedom per element per piezoelectric layer were used in the dynamic analysis of plates by finite element method. The modern equipment was used in the dynamic behaviors analysis of plates subjected to airflow load by experimental method. In this study, the results of the theoretical method have been compared with experimental studies.

Coupling magneto-elastic Lagrangians to spin transfer torque sources

The consequences of coupling magnetic and elastic degrees of freedom, where spins and deformations are carried by point-like objects subject to local interactions, are studied, theoretically and by detailed numerical simulations. From the constrained Lagrangians we derive consistent equations of motion for the coupled dynamical variables. In order to probe the dynamics of such a system, we consider external perturbations, such as spin transfer torques for the magnetic part, and homogeneous stresses for the elastic part, associated to their corresponding damping. This approach is applied to the study of ultrafast switching processes in anti-ferromagnetic systems, which have recently attracted attention as candidates for anti-ferromagnetic spintronic devices. Our strategy is then checked in simple, but instructive, situations. We carried out numerical experiments to study, in particular, how the magnetostrictive coupling and external stresses affect the nature of the switching processes in a prototype anti-ferromagnetic material.

Ultrafast electron-phonon coupling and photo-induced strain in the morphotropic phase boundary of BixDy1\u2212xFeO3 films

The interplay among ferroelectric, magnetic and elastic degrees of freedom in multiferroics is the key issues in condensed matters, which has been widely investigated by various methods. Here, using ultrafast two-color pump-probe spectroscopy, the picosecond electron-phonon and spin-lattice coupling process in Dysprosium doped-BiFeO3 (BDFO) films on SrTiO3 (STO) substrate have been investigated systematically. The Dy-doping induced structural transition and magnetic enhancement in BDFO is observed by ultrafast electron-phonon and spin-lattice interaction, respectively. The elastic anomalies in BDFO films are revealed by the photo-induced coherent acoustic phonon. With increasing the Dy doping ratio, the frequencies of the acoustic phonon in the films are modulated, and the phonon transmission coefficient between films and substrate is found to approach unity gradually. The ultrafast observation of the tunability of the ferroelectric, magnetic and the elastic properties in the morphotropic phase boundary of rare-earth doped BFO films provides new insights into the integration of BFO in next-generation high frequency electro-magnetic and electroacoustic devices.

Microscopic Description of Electric and Magnetic Toroidal Multipoles in Hybrid Orbitals

We present a general formalism of multipole descriptions under the space-time inversion group. We elucidate that two types of atomic toroidal multipoles, i.e., electric and magnetic, are fundamental pieces to express electronic order parameters in addition to ordinary electric and magnetic multipoles. By deriving quantum-mechanical operators for both toroidal multipoles, we show that electric (magnetic) toroidal multipole higher than dipole (monopole) can become a primary order parameter in a hybridized-orbital system. We also demonstrate emergent cross-correlated couplings between electric, magnetic, and elastic degrees of freedom, such as magneto-electric and magneto(electro)-elastic couplings, under toroidal multipole orders.

Monte Carlo Simulations of Thermal Hysteresis in Ni‐Mn‐Based Heusler Alloys

We present a study of the thermal hysteresis that takes place across the magnetostructural phase transition of the Ni‐Mn‐based Heusler alloys. The results have been obtained by means of first‐principles calculations and Monte Carlo simulations based on the proposed Potts‐Blume‐Emery‐Griffiths Hamiltonian involving magnetic and elastic degrees of freedom. First, separating the structural and magnetic contributions, we calculate the phase diagram including the martensitic transformation as a function of ratio between exchange structural constants in martensite and austenite (K/J). It is shown that the width of the thermal hysteresis depends on K/J and it is found to increase at a ratio of K/J between 0.20 and 0.37. A similar trend is also observed for the Landau free energy expansion. The evolutions of the magnetization and deformation order parameter of alloys studied under various applied magnetic fields are simulated as functions of temperature upon heating and cooling cycles. Furthermore, under high applied fields the nonlinear shift of and change of hysteresis width according to the relation between magnetostructural interaction constants ( and ) are observed. The results obtained with the Monte Carlo routine are discussed and demonstrated a good agreement with experimental data.

Longitudinal spin fluctuation contribution to thermal lattice expansion of paramagnetic Fe

Using an efficient first-principles computational scheme for paramagnetic body-centered cubic (bcc) and face-centered cubic (fcc) Fe, we investigate the impact of thermal longitudinal spin fluctuations (LSFs) on the thermal lattice expansion. The equilibrium physical parameters are derived from the self-consistent Helmholtz free energy, in which the LSFs are considered within the adiabatic approximation and the anharmonic lattice vibration effect is included using the Debye-Gr\"uneisen model taking into account the interplay between thermal, magnetic, and elastic degrees of freedom. Thermal LSFs are energetically more favorable in the fcc phase than in the bcc one giving a sizable contribution to the linear thermal expansion of $\ensuremath{\gamma}$-Fe. The present scheme leads to accurate temperature-dependent equilibrium Wigner-Seitz radius, bulk modulus, and Debye temperature within the stability fields of the two phases and demonstrates the importance of thermal spin fluctuations in paramagnetic Fe.

Interpolation-based parametric model order reduction for material removal in elastic multibody systems

One essential step in the simulation of elastic multibody systems is the model order reduction of the elastic degrees of freedom. For simulations of material removal, the system matrices can be described as parameter dependent. In this contribution, parametric model reduction methods based on interpolation are applied for this type of problem. Thereby, the interpolation of the reduced system matrices, interpolation of projection matrices, interpolation of subspaces and the interpolation of the transfer functions are investigated. The advantages and disadvantages of these techniques, especially for the application in elastic multibody systems are carved out and illustrated for the manufacturing of a T-shaped workpiece which varies in its thickness due to material removal. In this contribution, we focus on the investigation of the methods in the frequency domain.

MATLAB-Based Flight-Dynamics and Flutter Modeling of a Flexible Flying-Wing Research Drone

A relatively low-order linear dynamic model is developed for the longitudinal flight-dynamics analysis of a flexible flying-wing research drone, and results are compared to previously published results. The model includes the dynamics of both the rigid-body and elastic degrees of freedom, and the subject vehicle is designed to flutter within its flight envelope. The vehicle of interest is a 12–lb, unmanned flying-wing aircraft with a wingspan of 10 ft. In the modeling, the rigid-body degrees of freedom are defined in terms of motion of a vehicle-fixed coordinate frame, as required for flight-dynamics analysis. As a result, the state variables corresponding to the rigid-body degrees of freedom are identical to those used in modeling a rigid vehicle, and the additional states are associated with the elastic degrees of freedom. Both body-freedom and bending–torsion flutter conditions are indicated by the model, and it is shown that the flutter speeds, frequencies, and genesis modes suggested by this low-order model agree very well with the analytical predictions and flight-test results reported in the literature. The longitudinal dynamics of the vehicle are characterized by a slightly unstable phugoid mode, a well-damped pitch-dominated elastic-short-period mode, and the stable or unstable aeroelastic modes. A classical rigid-body short-period mode does not exist.

Stability Augmentation and Active Flutter Suppression of a Flexible Flying-Wing Drone

Integrated control laws are developed for stability augmentation and active flutter suppression of a flexible flying-wing research drone. The vehicle is a 12 lb unmanned flying-wing research aircraft with a 10 ft wingspan. Active flutter suppression is flight critical, since the subject vehicle is designed to flutter within its flight envelope. The critical flutter condition involves aeroelastic interactions between the rigid body and elastic degrees of freedom; hence, the control laws must simultaneously address both rigid-body stability augmentation and flutter suppression. The conventional control-synthesis approach is motivated by the concept of identically located force and acceleration, which was successfully applied on some previous operational aircraft. Based on the flutter characteristics and on conventional stability-augmentation concepts, two simple loop closures are suggested. It is shown that this control architecture robustly stabilizes the body-freedom-flutter condition, increases the damping of the second aeroelastic mode (which becomes a second flutter mode at higher velocity), and provides a reasonably conventional vehicle pitch-attitude response. The critical factors limiting the performance of the feedback system are identified to be the bandwidth of the surface actuators and the pitch effectiveness of the control surfaces.

General framework for acoustic emission during plastic deformation

Despite the long history, so far there is no general theoretical framework for calculating the acoustic emission spectrum accompanying any plastic deformation. We set up a discrete wave equation with plastic strain rate as a source term and include the Rayleigh-dissipation function to represent dissipation accompanying acoustic emission. We devise a method of bridging the widely separated time scales of plastic deformation and elastic degrees of freedom. The efficacy of the framework is illustrated by considering three distinct cases of plastic deformation. The first one is the acoustic emission during a typical continuous yield exhibiting a smooth stress-strain curve. We first construct an appropriate set of evolution equations for two types of dislocation densities and then show that the shape of the model stress-strain curve and accompanying acoustic emission spectrum match very well with experimental results. The second and the third are the more complex cases of the Portevin-Le Chatelier bands and the L\"uders band. These two cases are dealt with in the context of the Ananthakrishna model since the model predicts the three types of the Portevin-Le Chatelier bands and also L\"uders-like bands. Our results show that for the type-C bands where the serration amplitude is large, the acoustic emission spectrum consists of well-separated bursts of acoustic emission. At higher strain rates of hopping type-B bands, the burst-type acoustic emission spectrum tends to overlap, forming a nearly continuous background with some sharp acoustic emission bursts. The latter can be identified with the nucleation of new bands. The acoustic emission spectrum associated with the continuously propagating type-A band is continuous. These predictions are consistent with experimental results. The acoustic emission spectrum of the L\"uders-like band matches with recent experiments as well.

Strong Improper Ferroelasticity and Weak Canted Ferroelectricity in a Martensitic-Like Phase Transition of Diisobutylammonium Bromide.

Diisobutylammonium bromide is found to be a unique improper ferroelastic in which the elastic degrees of freedom seem to play the essential role, giving rise to a domain pattern resembling that of martensitic phase transitions. A weak canted ferroelectricity turns out switchable by an electric field.