Dissipative Forces Research Articles

Phase-field method with additional dissipation force for mixed-mode cohesive fracture

This paper develops a thermodynamic framework of phase-field fracture modeling for cases where the toughness depends on the fracture mode. Using a delicately constructed energy density and a novel dissipation force in the thermodynamic framework, we propose a phase-field model that can implement arbitrary mixed-mode cohesive laws for cases where the mode-II fracture energy (GIIc) is larger than the mode-I fracture energy (GIc). Four numerical examples are presented to validate the effectiveness of the proposed method, including a uniaxial tension test, a uniaxial compression test, a mixed-mode test on dogbone specimens, and a series of tests on double-edge notched concrete under mixed-mode loading. In the first three examples, the numerically predicted cohesive laws are extracted and compared with the analytical target cohesive laws. Excellent agreements are observed. In the last example, we show that very wrong crack paths may be obtained without distinguishing GIc and GIIc in phase-field modeling.

Chiral Thermodynamics in Tailored Chiral Optical Environments

We present an optomechanical model that describes the stochastic motion of an overdamped chiral nanoparticle diffusing in the optical bistable potential formed in the standing-wave of two counter-propagating Gaussian beams. We show how chiral optical environments can be induced in the standing-wave with no modification of the initial bistability by controlling the polarizations of each beam. Under this control, optical chiral densities and/or an optical chiral fluxes are generated, associated respectively with reactive vs. dissipative chiral optical forces exerted on the diffusing chiral nanoparticle. This optomechanical chiral coupling bias the thermodynamics of the thermal activation of the barrier crossing, in ways that depend on the nanoparticle enantiomer and on the optical field enantiomorph. We show that reactive chiral forces, being conservative, contribute to a global, enantiospecific, change of the Helmholtz free energy bistable landscape. In contrast, when the chiral nanoparticle is immersed in a dissipative chiral environment, the symmetry of the bistable potential is broken by non-conservative chiral optical forces. In this case, the chiral electromagnetic fields continuously transfer, through dissipation, mechanical energy to the chiral nanoparticle. For this chiral nonequilibrium steady-state, the thermodynamic changes of the barrier crossing take the form of heat transferred to the thermal bath and yield chiral deracemization schemes that can be explicitly calculated within the framework of our model. Three-dimensional stochastic simulations confirm and further illustrate the thermodynamic impact of chirality. Our results reveal how chiral degrees of freedom both of the nanoparticle and of the optical fields can be transformed into true thermodynamics control parameters, thereby demonstrating the significance of optomechanical chiral coupling in stochastic thermodynamics.

Experimental Study on the Behavior of Polyurethane Springs for Compression Members

In this study, the characteristics of the compression behavior of polyurethane springs that can be used as compression members of seismic devices, such as dampers and seismic isolators, were identified, and the effect of the design variables on the performance points of polyurethane springs was investigated. Compressive stiffness and specimen size were set as the design variables of the polyurethane spring, and the performance indicators were set as maximum force, residual strain, and energy dissipation. A total of 40 specimens with different conditions were fabricated and a cyclic loading test was performed to obtain the force-displacement curve of the polyurethane spring and to check the performance indicator. Significant strength degradation was confirmed after the first cycle by repeated loading, and it was confirmed that compressive stiffness and size demonstrated a linear proportional relationship with maximum force. In addition, the design variables did not make a significant change to the recovered strain, including residual strain, and residual strain of about 1% to 3% occurred. Energy dissipation showed a tendency to decrease by about 60% with strength degradation after the first cycle, and this also demonstrated no relationship with the design variables. Finally, the relationship between the design variables and performance indicators set in this study was reviewed and suggestions are presented for developing a simple design formula for polyurethane springs.

An innovative C-shaped yielding metallic dampers for steel structures

This paper proposed a new passive metallic damper, termed C-Shaped Damper (CSD), for a braced frame structure. The proposed system dissipates the earthquake energy using some sacrificial C-Shaped elements and protects the main elements of structures from plastic deformation and failure. This study investigated energy dissipation and behavior of CSD through numerical and analytical methods. For this purpose, parametric investigations were carried out analytically and numerically. Parametric studies considered the effect of vertical and horizontal diameters of CSD, thickness, and depth of the CSD on its behavior. A good agreement was observed between analytical and numerical results. The numerical results demonstrate that the yielding force was directly related to the thickness and depth of the CSD. Also, by the increasing horizontal diameter, yielding force and energy dissipation decreased. The results indicated suitable energy dissipation and steady hysteretic behavior of the CSD under cyclic loading with a salient characteristic such as being easily replaceable after failure.

3D numerical investigation of effects of density and surface tension on mixing time in bottom-blown gas-stirred ladles

In molten phase metallurgical processes, mixing via gas injection has a vital role in obtaining a homogeneous product. The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases. A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath. The molten metal and the slag are modeled by water and oil, respectively. The numerical results, particularly the mixing time, are validated against experimental data. The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases. The mixing time decreases with an increase in the density of the primary phase; however, it increases as the surface tension between air and water increases. A case with properties close to a real molten metal is also modeled. The performance of the system is influenced by the momentum rather than the dissipative forces. Thus, the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.

Kinetic theory of polydisperse gas–solid flow: Navier–Stokes transport coefficients

The particulate phase stress and solid–solid drag force in the multifluid modeling of polydisperse gas–solid flows are usually closed using kinetic theory. This research aims to establish the hydrodynamic equations and constitutive relations of the multifluid model for polydisperse systems via species kinetic theory, in which the non-equipartition of energy and interphase slip velocity between different species are considered. Whereas previous studies have used approximations, such as Taylor series expansions, to simplify the calculation of collision integrals, the present study, for the first time, solves the collision integrals analytically without any approximations to obtain accurate constitutive relations. Explicit expressions for the constitutive laws are obtained, including the particle stress tensor, solid–solid drag force, heat flux, and energy dissipation rate up to the Navier–Stokes order. The present study offers more complete and mathematically rigorous constitutive laws for the multifluid modeling of polydisperse gas–solid flows.

Analyzing the motion of a mass sliding on a sphere with friction

A well-known problem in classical mechanics that is often presented for pedagogical purposes involves a small mass that slides without friction under a gravitational force on the surface of a sphere. Commonly, students are asked to find the angular position where a mass with no azimuthal motion leaves the spherical surface, and this question is easily within the reach of most intermediate physics students. However, a complete solution for more general motion of the mass on the spherical surface (including friction) may be suitable for many advanced undergraduates. Without friction, the problem including azimuthal motion is really an inverted version of an ideal spherical pendulum. This problem is also useful for extending discussion in classical mechanics to more sophisticated topics beyond solving Newton's laws of motion, such as the importance of conservation laws and constants of motion as they relate to symmetry, conservative versus dissipative forces, and the role of constraints.

Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems.

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

Fluctuation-dissipation-type theorem in stochastic linear learning.

The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning dynamics, in which the input vector maps to the output vector by a linear matrix whose elements are the subject of learning, has a stochastic version closely mimicking the Langevin dynamics when a full-batch gradient descent scheme is replaced by that of a stochastic gradient descent. We derive a generalized FDT for the stochastic linear learning dynamics and verify its validity among the well-known machine learning data sets such as MNIST, CIFAR-10, and EMNIST.

Assessment of failure mode and seismic performance of damaged masonry structures retrofitted with grout-injected ferrocement overlay reinforcement (GFOR)

The vulnerability of unreinforced masonry (URM) structures under seismic action has promoted efforts to explore a wide variety of retrofitting and repairing methods. However, most studies have focused on the in-plane response of newly built walls; few have discussed the failure mode and seismic behavior of damaged walls before and after retrofitting. Hence, the present study was conducted to investigate the failure mode and seismic performance of damaged URM walls retrofitted with grout-injected ferrocement overlay reinforcement (GFOR). The main parameters in the experiments were the aspect ratio and the stiffness ratio of the spandrel to the pier. Two groups of URM specimens with different vertical loads were fabricated using identical clay brick units and cement mortar. The specimens in the first group had a length of 2450 mm, a height of 2550 mm, and a thickness of 240 mm, while those in the second group had a length of 3300 mm, a height of 1950 mm, and a thickness of 240 mm. Testing was performed with a gradual increase in the horizontal load and displacement reversals, combined with a constant vertical load. Subsequently, both sets of damaged URM walls with pier failure were retrofitted with GFOR; the retrofitted specimens were designated as ferrocement reinforced masonry (FRM) walls and were retested to their ultimate state under load conditions identical to those in the initial test. Finally, the results for the URM and FRM walls were compared in terms of the failure modes, force–displacement curves, and other experimental parameters. The findings indicate that the spandrel failure mode was more likely in the walls under larger vertical loads. The walls exhibited the spandrel failure mode had a greater lateral force and better energy dissipation. Both sets of damaged walls exhibited a more reasonable failure mode (from “pier before spandrel” to “spandrel before pier”) after the GFOR technique was adopted.

Painting the phase space of dissipative systems with Lagrangian descriptors

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear dynamics literature that this mathematical technique can provide valuable information and insights to develop a more general and detailed understanding of the global behavior and underlying geometry of these systems. In order to achieve this goal, we analyze systems that display dynamical features such as hyperbolic points with different expansion and contraction rates, limit cycles, slow manifolds and strange attractors. Furthermore, we study how this technique can be used to detect transition ellipsoids that arise in Hamiltonian systems subject to dissipative forces, and which play a crucial role in characterizing trajectories that evolve across an index-1 saddle point of the underlying potential energy surface.

Dynamics of nonlinear waves in a Burridge and Knopoff model for earthquake with long-range interactions, velocity-dependent and hydrodynamics friction forces

We investigate the dynamics of nonlinear waves in a long-range extension of the Burridge and Knopoff model for earthquake. We consider the dissipative hydrodynamics forces. The spatio-temporal dynamics of the system is found by introducing in the coupling spring and hydrodynamics forces a linear term that decays as a power-law, with an exponent s such that 1<s≤3. The theoretical framework for the analysis is presented in the rotative wave approximation. Due to the non analytic properties of the dispersion relation, we use the discrete derivative operator technique. The dynamics of the system is governed by the complex Ginzburg-Landau equation, allowing breather-like soliton solutions. We use the relevant case s=2, and results show that the magnitude, the velocity, and area of propagation of nonlinear waves strongly depend on the frictions forces. Our analytical results are in good agreement with numerical experiments and confirm the correctness of the method.

Electronic transport calculations showing electron-phonon separation in directions transverse to high current

An electron-phonon Boltzmann transport equation is formulated which accounts for second order collisions with an electron-phonon vertex and a three-phonon vertex. This approach for electronic transport at second order reveals the existence of two forces perpendicular to the primary direction of electrical current, acting on the electrons and phonons. The force on electrons is equal and opposite to that on the phonons. Solutions for stationary states confirm that charge and thermal energy become separated. The force terms include both conservative and dissipative components, which for the phonons, lead to a modified Guyer-Krumhansl equation. The conservative components exist only when there exist explicit transverse gradients in the dissipated energy, and these terms may be incorporated into a Poisson kinematics. The dissipative force terms can cause threshold induced spontaneous symmetry breaking.

Optimizing the Arrangement of Strain Gauges in Pile Load Testing

Abstract The use of strain gauges in a deep foundation element static load test is a common technique to obtain soil strata mobilized resistance. The typical arrangement is several gauges at each of several discrete depths. The gauges at each depth are averaged, the average is converted to a force, and the forces at various depths are differentiated to compute force dissipation into the soil. A simple error analysis leads to the optimal arrangement of gauges in the element cross section, accounting for uneven distribution of strain across the cross-section plane of the element and the possibility of gauge malfunction. By using a case history as an example, the optimal vertical spacing of gauge levels is discussed.

ТЕОРЕТИЧНЕ ВИЗНАЧЕННЯ ЗАКОНОМІРНОСТІ ЗМІНИ НАПРУЖЕНЬ, ЯКІ ВИНИКАЮТЬ У ПОЛІМЕРНОМУ БЕТОНІ ПРИ ЙОГО УЩІЛЬНЕННІ ВІБРАЦІЙНОЮ ПЛИТОЮ

Purpose. Based on a thorough analysis of the scientific and technical literature, it is established that for the mass production of quality materials and products from polymer concrete compositions, the most effective will be a vibration method of sealing, which means that when they are received, the vibrating working bodies of the forming technological equipment will interact with the polymer concrete mass. Methodology. For the theoretical determination of the nature of the interaction of the surface vibrating working body with polymer concrete, the study of the dynamic system "vibration plate - polymer concrete" was performed. In this dynamic system, compacted polymer concrete is presented in the form of a system with distributed parameters, which takes into account the action of elastic and dissipative resistance forces acting from the polymer concrete side when it is deformed on a vibrating working body. Results. In accordance with the accepted rheological model of polymer concrete for the uniaxial stress condition, the dependence in the individual derivatives be- tween the stress and the deformation of the polymer concrete is proposed, the nature of which depends on the dynamic modulus of elastic deformation, the dynamic modulus of Maxwell's elastic deformation and the coefficient of dynamic viscosity. A wave equation of oscillation is proposed, which describes the propagation of elastic-viscous deformation waves in polymer concrete deformed by a surface vibrating working body. To solve the wave equation of oscillations, boundary conditions are drawn. The first boundary condition describes the interaction of a surface vibrating working body with a compacted concrete. The second boundary condition implies that the displacement of the sealed layer of polymer concrete at a certain distance from the surface of the vibrating working body is zero. We find constant integrations (complex am- plitudes) that satisfy the accepted boundary conditions. Originality. Based on the solution of the wave equation of oscil- lations describing the propagation of deformation waves in the compacted concrete, it is determined: the regularity of propagation of elastic-viscous deformation waves in the polymeric concrete and the expressions for numerically deter- mining the coefficients of rigidity polymer concrete resistance, law and vibration amplitude of surface vibrating working body. The stresses arising on the surface and depth of the polymer concrete when exposed to the surface vibrating working body are determined. Practical value. The obtained theoretical dependences make it possible to reasonably determine the rational parameters of the surface vibrating working body depending on the physical and mechanical properties of the compacted polymer concrete.

Transition criteria and phase space structures in a three degree of freedom system with dissipation

Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape events plays an important role in making use of such phenomenon, particularly when realistic frictional or dissipative forces are present. We aim to extend the study of the escape dynamics around the saddle from two degrees of freedom to three degrees of freedom, presenting both a methodology and phase space structures. Both the ideal conservative system and a perturbed, dissipative system are considered. We define the five-dimensional transition region, , as the set of initial conditions of a given initial energy h for which the trajectories will escape from one side of the saddle to another. Invariant manifold arguments demonstrate that in the six-dimensional phase space, the boundary of the transition region, , is topologically a four-dimensional hyper-cylinder in the conservative system, and a four-dimensional hyper-sphere in the dissipative system. The transition region in the dissipative (conservative) system can be constructed by a solid three-dimensional ellipsoid (solid three-dimensional cylinder) in the three-dimensional configuration space, where at each point, there is a cone of velocity—the velocity directions leading to transition are given by cones, with velocity magnitude given by the initial energy and the direction by two spherical angles with given limits. To illustrate our analysis, we consider an example system which has two potential minima connected by an index 1 saddle.

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension.

The inner viscosity of a biological red blood cell is about five times larger than the viscosity of the blood plasma. In this work, we use dissipative particles to enable the proper viscosity contrast in a mesh-based red blood cell model. Each soft particle represents a coarse-grained virtual cluster of hemoglobin proteins contained in the cytosol of the red blood cell. The particle interactions are governed by conservative and dissipative forces. The conservative forces have purely repulsive character, whereas the dissipative forces depend on the relative velocity between the particles. We design two computational experiments that mimic the classical viscometers. With these experiments we study the effects of particle suspension parameters on the inner cell viscosity and provide parameter sets that result in the correct viscosity contrast. The results are validated with both static and dynamic biological experiment, showing an improvement in the accuracy of the original model without major increase in computational complexity.

Energy-conserving DPD and thermodynamically consistent Fokker–Planck​ equation

The original Fokker–Planck equation does not satisfy most balance equations of continuum mechanics. Dissipative particle dynamics (DPD) is an attempt to remedy the demerits of the Fokker–Planck equation. However, a desirable kinetic equation should satisfy the four balance equations of irreversible thermodynamics, i.e., the balance equations of mass, momentum, energy, and entropy. To the best of the author’s knowledge, only the Boltzmann kinetics fulfills all the conditions. We suggest a modified Fokker–Planck equation that satisfies all the conditions without the assumption of DPD, the pairwise additivity of dissipative and random forces. Our formalism is expected to minimize the number of adjustable functions that must be used in DPD.

A Viscoelastic Contact Analysis of the Ground Reaction Force Differentiation in Walking and Running Gaits Realized in the Simplified Horse Leg Model Focusing on the Hoof—Ground Interaction

In the present study, the systematic method for the forward dynamics associated with the ground contact model was introduced to be able to consider the viscoelastic effect when contacting with the ground. In particular, we focused on the hoof-ground interaction in the simplified horse leg model because walking and running gaits are known to be different in trajectories; however, the force analysis still remains as unsolved issues. The computational experiments in Matlab, elastic and inelastic impact with the ground was resolved by using the dissipative contact force model proposed by Lankarani and Nikravesh and the ground reaction force was clearly examined in four different conditions from the combination of walking/running and elastic/inelastic contact. As result, two peaks during the stance phase in the walking condition were realized as well as the human gait and a single peak was newly observed in running with a time gap in elastic and inelastic condition. The proposed method contributes to the establishment of the detail time course analysis of the ground reaction force for animal and human gaits in a consistent manner.

Large Hall angle of vortex motion in high- Tc cuprate superconductors revealed by microwave flux-flow Hall effect

We investigated the nature of the quasi-particle state in the vortex core by means of the flux-flow Hall effect measurements at 15.8 GHz. We measured the flux-flow Hall effect in cuprate superconductors, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{y}$ and YBa$_{2}$Cu$_{3}$O$_{y}$ single crystals, whose equilibrium $B$-$T$ phase diagrams were different. As a result, we found that the Hall angle is independent of the magnetic field, and reaches an order of unity at low temperatures in BSCCO. However, in YBCO, the angle increases with increasing magnetic field even at low temperatures. We understood that this difference in the magnetic field dependence of the Hall angle is due to the difference in the influence of the pinning, which originated from the difference in the vortex state (liquid vs. solid) between the two materials. However, as a common feature, both materials showed a large tangent of the Hall angle at low temperatures, which was larger by an order of magnitude than those obtained in the effective viscous drag coefficient measurements. We discussed the origin of the discrepancy both in terms of the possible nonlinearity of the viscous drag force and possible hidden dissipation mechanisms. The unexpectedly large Hall angle of the vortex motion in cuprates revealed in our flux-flow Hall effect study poses a serious question on the fundamental understanding of the motion of the quantized vortex in superconductors, and it deserves further investigation.