Bulk Force Research Articles

Elastic response of a cylinder loaded by a Hertzian contact pressure and maintained in equilibrium by its inertia

We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either infinitesimal or finite contact displacements, including partial slip. The developments are illustrated by revisiting a classical example in what could be called The heavy cylinder on a vibrating soil . The four contact resonances and forced response of the system are given in closed form in the quasi-static approximation, and compared against a reference numerical solution. The formulae can also be used as building blocks to assemble the compliance matrix of a system comprising several cylinders.

On the interdependence of insertion forces, insertion speed, and lubrication: Aspects to consider when testing cochlear implant electrodes.

During the insertion of cochlear implant (CI) electrode arrays, forces occur which may cause trauma and poorer hearing outcomes. Unfortunately, research groups investigating factors influencing insertion forces come to contradicting results, especially regarding insertion speed. This study was conducted to investigate the origin of these contradicting results and to determine how different testing conditions influence experimental findings. Repeated, automated insertions with three different FLEX28 CI electrode arrays (MED-EL, Innsbruck, Austria) were performed into a newly developed, anatomically correct and 3D-printed mean scala tympani phantom. The testing protocol for each electrode included variations in insertion speed (v = 0.1-2.0 mm/s) and lubrication (90%, 50%, and 10% liquid soap), resulting in 51 insertions per electrode array and a total of 153 insertions. The test setup and protocol allowed for repeatable insertions with only minimal change in the morphology of the insertion force profiles per testing condition. Strong but varying dependencies of the maximal insertion forces and work were found regarding both lubrication and speed: work-speed dependency is constant for the 10% lubricant, negative for the 50% lubricant and positive for the 90% lubricant. Our results can explain part of the contradicting results found within previous studies by translating interrelations known from lubricated rubber friction to the field of CI electrode array insertion. We show that the main driver behind measured bulk forces are most likely the generated friction forces, which are strongly dependent on insertion speed and lubrication. The employed test setup allows for conducting repeatable and comparable insertion studies, which can be recapitulated by other centers due to the detailed explanation of the test setup as well as the developed and freely available insertion phantom. This study hence represents another important step toward standardizing CI array insertion testing.

Untangling dissipative and Hamiltonian effects in bulk and boundary-driven systems.

Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behavior of nonequilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of a nonequilibrium nondiffusive system, specifically an open linear network on a finite graph. We explicitly calculate the dissipative bulk and boundary forces that drive the system towards the steady state, and the nondissipative bulk and boundary forces that drive the system in orbits around the steady state. Using the fact that these forces are orthogonal in a certain sense, we provide a decomposition of the large-deviation cost into dissipative and nondissipative terms. We establish that the purely nondissipative force turns the dynamics into a Hamiltonian system. These theoretical findings are illustrated by numerical examples.

Resonance Impact of a Periodic Sequence of Plasma Actuators in Flow Control in a Swept-Wing Boundary Layer

The process of flow control in the swept-wing boundary layer using a number of plasma actuators mounted at an angle to the leading edge is theoretically studied. The resonance response of the controlled flow is investigated when the angle of inclination of the actuators is close to the angle of inclination of the stationary vortices of cross-flow instability. The calculation of the controlled flow is carried out within the framework of the parabolic system of Navier–Stokes equations. The stability characteristics of periodic flows formed by the action of a control bulk force are calculated.

Traveling wave solutions to the inclined or periodic free boundary incompressible Navier-Stokes equations

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and above by a moving surface. The fluid is acted upon by a bulk force and a surface stress that are stationary in a coordinate system moving parallel to the fluid bottom. We also assume that the fluid is subject to a uniform gravitational force that can be resolved into a sum of a vertical component and a component lying in the direction of the traveling wave velocity. This configuration arises, for instance, in the modeling of fluid flow down an inclined plane. We also study the effect of periodicity by allowing the fluid cross section to be periodic in various directions. The horizontal component of the gravitational field gives rise to stationary solutions that are pure shear flows, and we construct our solutions as perturbations of these by means of an implicit function argument. An essential component of our analysis is the development of some new functional analytic properties of a scale of anisotropic Sobolev spaces, including that these spaces are an algebra in the supercritical regime, which may be of independent interest.

Issledovanie vliyaniya skorosti nabegayushchego potoka na techenie, indutsiruemoe dielektricheskim bar'ernym razryadom

Plasma actuators based on a dielectric barrier discharge (DBD) are considered as a promising method оf flow control. Their main advantage is the possibility of flow acceleration by the ion wind without using movable elements. The generation of the ion wind by DBD in a settling gas has been studied quite comprehensively. At the same time, almost all aerodynamic applications of this method of flow control presume the presence of an external flow. However, the emergence of a bulk force in DBD in such conditions has not been investigated in detail. This study is devoted to detailed analysis of this effect. We have investigated the influence of DBD on the velocity distribution near electrodes using the PIV method and have calculated the bulk force generated by the ion wind. The results of this study demonstrate a substantial effect of the incoming flow velocity on the ion wind generation.

Spacetime evolutive equilibrium in Nonlinear Continuum Mechanics

In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between the product of area and unit normal vectors relevant to corresponding surfaces in two configurations of a 3D body. A geometric treatment provides equivalent expressions of Nanson formula by direct elaborations on Euler–Jacobi volume change formula. Meaning and limits of Nanson formula are underlined. In the literature this formula has been improperly assumed to be expedient for attempts of imposing equilibrium in a reference shape of the body. A critical revision shows recourse to scaling and parallel transport of surface and bulk forces is impassable in assessing alleged referential equilibrium. A variational formulation of evolutive equilibrium in spacetime is developed and finite step elastic problems guided by control algorithms in computational procedures are illustrated. Step-by-step iterative methods of solution of nonlinear structural problems and simple counterexamples should help in convincing referential equilibria are not conceivable in Nonlinear Continuum Mechanics.

A multiphase model developed for mesoscopic heat and mass transfer in thawing frozen soil based on lattice Boltzmann method

Subgrade engineering in cold region collapsed and settled under the influence of global warming, this was mainly due to the thawing frozen soil. The heat and mass transfers in thawing frozen soils are generally described with continuity equations on the macroscopic scale. However, the processes of ice melting and water migration in soil were rarely described on the mesoscopic scale. In this study, a multiphase pseudo-potential model with enthalpy-based module was developed based on lattice Boltzmann method to predict the distributions of temperature and water content in the thawing process of frozen soil. The force source terms in pseudo-potential model were given as adhesive force, cohesive force, temperature drive force and bulk force to describe the interaction between multiple components in thawing process, and the enthalpy-based module was employed to realize the process of phase transition in soil. The complex initial conditions of thawing process were measured and then set in simulation for the first time. The results showed that as compared with the measured soil temperatures and water contents at different top soil temperature (5 °C and 10 °C) and times (0, 12, and 36 h), the relative errors of model were 0.01 % ∼ 0.72 % and 0.10 % ∼ 19.31 % for the soil temperatures and water contents, respectively. Further, the developed pseudo-potential model can also be used to detail the mesoscopic heat and mass transfers in thawing soils.

Faster Indentation Influences Skin Deformation To Reduce Tactile Discriminability of Compliant Objects.

To discriminate the compliance of soft objects, we rely upon spatiotemporal cues in the mechanical deformation of the skin. However, we have few direct observations of skin deformation over time, in particular how its response differs with indentation velocities and depths, and thereby helps inform our perceptual judgments. To help fill this gap, we develop a 3D stereo imaging method to observe contact of the skin's surface with transparent, compliant stimuli. Experiments with human-subjects, in passive touch, are conducted with stimuli varying in compliance, indentation depth, velocity, and time duration. The results indicate that contact durations greater than 0.4 s are perceptually discriminable. Moreover, compliant pairs delivered at higher velocities are more difficult to discriminate because they induce smaller differences in deformation. In a detailed quantification of the skin's surface deformation, we find that several, independent cues aid perception. In particular, the rate of change of gross contact area best correlates with discriminability, across indentation velocities and compliances. However, cues associated with skin surface curvature and bulk force are also predictive, for stimuli more and less compliant than skin, respectively. These findings and detailed measurements seek to inform the design of haptic interfaces.

Automatic differentiation for orbital-free density functional theory.

Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance burden. Furthermore, fully differentiable simulation tools enable direct evaluation of challenging derivatives-including those directly related to properties measurable by experiment-that are conventionally computed with finite difference methods. Here, we investigate automatic differentiation in the context of orbital-free density functional theory (OFDFT) simulations of materials, introducing PROFESS-AD. Its automatic evaluation of properties derived from first derivatives, including functional potentials, forces, and stresses, facilitates the development and testing of new density functionals, while its direct evaluation of properties requiring higher-order derivatives, such as bulk moduli, elastic constants, and force constants, offers more concise implementations than conventional finite difference methods. For these reasons, PROFESS-AD serves as an excellent prototyping tool and provides new opportunities for OFDFT.

Relativistic theory of elastic bodies in the presence of gravitational waves

The equations of motion governing small elastic oscillations of materials, induced by gravitational waves, are derived from the general framework of Carter and Quintana. In transverse-traceless gauge, no bulk forces are present, and the gravitational wave is found to act as an effective surface traction. For thin rods, an equivalent description is given, in which there is no surface traction, but a bulk acceleration, which is related to the Riemann curvature of the gravitational wave. The resulting equations are compared to those of the Synge–Bennoun elasticity theory.

Study of Energy Dissipation in a Two-Phase Soil System

The dependence of energy dissipation coefficient on filtration properties and on creep characteristics of soil skeleton is examined. The study was carried out on the basis of the general solution of the joint task of creep and consolidation theory for a two-phase soil system obtained on the basis of the generalized model of bulk forces, taking into account the interaction of soil phases, changes over time in the general stress state at any point of the soil and additional pressures in pore water, and incomplete transfer of external pressure to the pore water. Interactions between phases are taken into account in the solution of the one-dimensional joint task of the theory of creep and consolidation, and the creep kernel is taken in the form of an exponential function. The formula for the deformation of two-phase soils is presented as the sum of two syllables due to primary and secondary consolidation of the soil. The strain formula uses experimentally obtained values of filtration characteristics and creep parameters of the soil skeleton. Using the formulas obtained, hysteresis loops under sinusoidal stress changes can be plotted and the energy expended per deformation cycle and the dissipation coefficient for two-phase soil can be obtained.

Insights on Multistage Rock Avalanche Behavior From Runout Modeling Constrained by Seismic Inversions

AbstractInversion of low‐frequency regional seismic records to solve for a time series of bulk forces exerted on the earth by a landslide (a force‐time function) is increasingly being used to infer volumes and dynamics of large, highly energetic landslides, such as rock avalanches and flowslides, and to provide calibration information on event dynamics and volumes for numerical landslide runout models. Much of the work to date using landslide runout modeling constrained by seismic data has focused on using single‐phase models with frictional or velocity‐weakening rheologies. Awareness of multistage landslide initiations is increasing, with discrete failures separated in time contributing to the final impact of an event. Our work utilizes a method for incorporating seismic data as a calibration constraint for landslide runout models, considering variable rheologies and different initiation conditions. This study presents a systematic examination of multiple rheologies and initiation conditions, and shows how these factors affect the force‐time function derived from the landslide runout model. Our work confirms that, while rheology and fragmenting or initially coherent initiations affect the force‐time function, multiple collapses separated by tens of seconds have the greatest impact on the shape and amplitude. We apply this method to the analysis of three real rock avalanches to better constrain plausible initiation conditions and rheology parameters using both seismic and field data. This study provides insights on how assumptions about the initiation dynamics of the source zone and the runout model definition can aid in the interpretation of seismic inversions for multistage rock avalanches.

Unveiling bulk and surface radiation forces in a dielectric liquid

Precise control over light-matter interactions is critical for many optical manipulation and material characterization methodologies, further playing a paramount role in a host of nanotechnology applications. Nonetheless, the fundamental aspects of interactions between electromagnetic fields and matter have yet to be established unequivocally in terms of an electromagnetic momentum density. Here, we use tightly focused pulsed laser beams to detect bulk and boundary optical forces in a dielectric fluid. From the optical convoluted signal, we decouple thermal and nonlinear optical effects from the radiation forces using a theoretical interpretation based on the Microscopic Ampère force density. It is shown, for the first time, that the time-dependent pressure distribution within the fluid chiefly originates from the electrostriction effects. Our results shed light on the contribution of optical forces to the surface displacements observed at the dielectric air-water interfaces, thus shedding light on the long-standing controversy surrounding the basic definition of electromagnetic momentum density in matter.

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field.

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as , where r is the distance between the edge of the string and the current I, and is the Boltzmann constant; ( is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as , which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

A hybrid partitioned deep learning methodology for moving interface and fluid–structure interaction

In this work, we present a hybrid partitioned deep learning framework for the reduced-order modeling of moving interfaces and predicting fluid–structure interaction. Using the discretized Navier–Stokes in the arbitrary Lagrangian–Eulerian reference frame, we generate the full-order flow snapshots and point cloud displacements as target physical data for the learning and inference of coupled fluid–structure dynamics. The hybrid operation of this methodology comes by combining two separate data-driven models for fluid and solid subdomains via deep learning-based reduced-order models (DL-ROMs). The proposed multi-level framework comprises the partitioned data-driven drivers for unsteady flow and the moving point cloud displacements. At the fluid–structure interface, the force information is exchanged synchronously between the two partitioned subdomain solvers. The first component of our proposed framework relies on the proper orthogonal decomposition-based recurrent neural network (POD-RNN) as a DL-ROM procedure to infer the point cloud with a moving interface. This model utilizes the POD basis modes to reduce dimensionality and evolve them in time via long short-term memory-based recurrent neural networks (LSTM-RNNs). The second component employs the convolution-based recurrent autoencoder network (CRAN) as a self-supervised DL-ROM procedure to infer the nonlinear flow dynamics at static Eulerian probes. We introduce these probes as spatially structured query nodes in the moving point cloud to treat the Lagrangian-to-Eulerian conflict together with convenience in training the CRAN driver. To determine these Eulerian probes, we construct a novel snapshot-field transfer and load recovery algorithm. They are chosen in such a way that the two components (i.e., POD-RNN and CRAN) are constrained at the interface to recover the bulk force quantities. These DL-ROM-based data-driven drivers rely on the LSTM-RNNs to evolve the low-dimensional states. A popular prototypical fluid–structure interaction problem of flow past a freely oscillating cylinder is considered to assess the efficacy of the proposed methodology for a different set of reduced velocities that lead to vortex-induced vibrations. The proposed framework tracks the interface description with acceptable accuracy and predicts the nonlinear wake dynamics over the chosen test data range. The proposed framework aligns with the development of partitioned digital twin of engineering systems, especially those involving moving boundaries and fluid–structure interactions.

Moving vesicles in elastic tissues: A model with existence and uniqueness of weak solutions

We describe the transport of vesicles in an elastic body in terms of a phase field. Besides standard forces implied by macroscopic strain, we account for a balance of microstructural actions induced by vesicle-to-vesicle interactions, vesicle self-actions, membrane bending and related nonlinear pressure-type confinement effects on vesicles. For the resulting balance equations, we prove existence and uniqueness of appropriate weak solutions (the so-called regular weak ones). Also, in the absence of bulk forces and under homogeneous Neumann-type boundary conditions, we prove a weak maximum principle for the vesicle phase-field.

Development of Li-ion Battery Bulk Force and Expansion Displacement Test-bench

In order to test the bulk force and expansion displacement of lithium-ion batteries, it is planned to develop a corresponding test-bench, which is mainly composed of a measurement-control system and a mechanical system. To improve the accuracy of the test data, the coupled thermal-structure simulation of the test system in the mechanical system of the test-bench is carried out to select an optimal mechanical structure of the test system. At the same time, for safe and convenient testing, a monitoring-testing system software was developed to ensure the reliability and safety of data collection. Finally, through the test-bench, the battery expansion displacement-SOC curve and the battery bulk force-SOC curve under different discharge rates were tested, providing a basis for the development of a battery management system coupling temperature-current-voltage-displacement-force.

Modeling and Experimental Verification of Heat Dissipation Model for Test System of Li-ion Battery Test-bench

In order to develop a test-bench which can accurately test the mechanical signal of lithium-ion battery under various working conditions, the finite element model of heat dissipation simulation is established for different test systems designed in the mechanical system of the test-bench. At the same time, pulse excitation experiments are used to verify the simulation results, and the bulk force experiments are carried out to verify the optimal test system structure chosen accord to the simulation results. The mechanical structure of a test system is composed of a lithium-ion battery and upper/lower spacer. In its finite element model, the finite element model of the lithium-ion battery is established by the actual measurement after cutting lithium-ion battery by a diamond cutter, and spacers are established according to their actual design. The heat dissipation simulation finite element model can simulate the heat dissipation of an actual test system, which is conducive to the design and selection of an optimal test system, so as to improve the accuracy of test data measured through the test-bench and provide a reliable data basis for the development of the battery management system coupling temperature-current-voltage-swell-force.

Soft topological lattice wheels

We investigate the large deformation and extreme load-management capabilities of a soft topologically polarized kagome lattice mapped to a cylindrical domain through the problem of a lattice wheel rolling on an irregular surface. We test the surface–lattice interaction experimentally by subjecting a 3D-printed topological lattice wheel prototype to localized and distributed boundary loads. This investigation reveals a dichotomy in the force transfer between the two loading scenarios, whereby localized loads are absorbed with limited stress penetration into the bulk and small force transfer to the wheel axle, compared to distributed loads. Through numerical simulations, we compare the lattice wheel against a baseline solid wheel to highlight the unique stress management opportunities offered by the lattice configuration. These findings promote the design of rolling objects enabled by topological mechanics, in which a surplus of softness, activated by local asperities, can coexist with a globally stiff response to distributed loads that ensures satisfactory load-bearing capabilities.