Nonlinear Energy Dissipation Research Articles

Failure mode transition in nacre and bone-like materials

Mineralized biological materials such as nacre or bone achieve remarkable combinations of stiffness and toughness by way of staggered arrangements of stiff components (nanoscale or microscale fibers or tablets) bonded by softer materials. Under applied stress these components slide on one another, generating inelastic deformations and toughness on the macroscale. This mechanism is prominent in nacre, a remarkable material which is now serving as a model for biomimetic materials. In order to better identify which type of nacre should serve as a biomimetic model, the toughness of nacre from four different mollusk species was determined in this study. Nacre from the pearl oyster was found to be toughest, and for the first time remarkable deformation and fracture patterns were observed using in situ optical and atomic force microscopy. Under stress, stair-like deformation bands deformed at an angle to the loading direction, forming a dense, tree-like network. This marks a clear difference from the now well-documented "columnar" failure mode, in which deformation bands are perpendicular to the loading direction. Analytical and numerical models reveal the conditions for the transition between the columnar and stair failure modes, namely large or random overlap between inclusions and local shear stress generated by inhomogeneities in the material. "Stair" failure promotes spreading of non-linear deformation and energy dissipation, which translates into a greater toughness overall. A similar mechanism may also occur in bone, which has a microstructure which is in many ways similar to sheet nacre.

Nonlinear Damping Identification in Precast Prestressed Reinforced Concrete Beams

Abstract: This article presents a damage detection method for prestressed reinforced concrete (PRC) elements based on free vibration tests and nonlinear damping identification. Integrated static and dynamic experiments were carried out on three precast PRC beam specimens. The static loading induced different levels of damage to the beams. At each damage level, impulsive loading was applied to the beams and the free vibration response was measured. The dynamic response data were processed using different methods including the multi‐input multi‐output (MIMO) curve fitting and the Hilbert transform techniques. A strong correlation is observed between the level of concrete damage (cracks) and the amount of nonlinear energy dissipation that can be modeled by means of quadratic damping. The nonlinear damping can be extracted from the free vibration response for each vibration mode. The proposed method is suited for quality control when manufacturing precast PRC members, and can be further extended for in situ detection of damage in concrete structures under ambient vibration.

Saturation of the Internal Tides and Induced Mixing in the Abyssal Ocean

Abstract As part of an ongoing effort to develop a parameterization of wave-induced abyssal mixing, the authors derive an heuristic model for nonlinear wave breaking and energy dissipation associated with internal tides. Then the saturation and dissipation of internal tides for idealized and observed topography samples are investigated. One of the main results is that the wave-induced mixing could be more intense and more confined to the bottom than previously assumed in numerical models. Furthermore, in this model wave breaking and mixing clearly depend on the small scales of the topography below 10 km or so, which is below the current resolution of global bathymetry. This motivates the use of a statistical approach to represent the unresolved topography when addressing the role of internal tides in mixing the deep ocean.

Strain localization in a shear transformation zone model for amorphous solids

We model a sheared disordered solid using the theory of shear transformation zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi [Phys. Rev. Lett. 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

Quasi-stationary form of the spectrum of intense seismic waves at the surface of the ground

Transformations of spectra of intense seismic waves propagating in ground columns are studied in numerical experiments. It was found that transformation of spectra to the form E ( f ) ~ f – k in the ground occurs due to nonlinear (hysteresis) energy dissipation and redistribution of the energy of oscillations in the spectrum by means of interaction between waves. Emphasizing the low-frequency components agrees with the Manley‐Row relations of decay instability, according to which energy transport of low-frequency oscillations to high-frequency oscillations is hampered, but decay of high-frequency oscillations and transport of their energy to low-frequency oscillations is facilitated. The authors of papers [1, 2] devoted to accelograms of earthquakes in 1995 in Kobe and 2000 in Tottori (Japan), which were recorded by borehole seismic groups, developed numerical models of the behavior of ground layers in situ; i.e., they estimated the stresses and strains excited by strong motions in the upper ~100 m of the ground. The numerical models describe the behavior of ground layers in ten 1.5-s time intervals during 15 strong motions. The authors of [3] used these models in numerical experiments to study the propagation of intense noise (transverse) waves in the ground layers. The obtained results characterize the statistical phenomena observed during the propagation of intense seismic waves in nonlinear media (the near-surface ground). The interactions between individual spectral components lead to multiplication of spectral lines, nonlinear widening of spectra, and the appearance of a constant component of the seismic field. Figure 1 illustrates transformation of the spectra of intense seismic waves propagating in the ground layers: the results of testing the numerical models are presented for the behavior of the ground in Port Island and the SJK site (a conventional name of the location of vertical groups) during the Kobe earthquake 1995 by the Gaussian white noise (the duration of test signals was chosen to be sufficiently large (~40 min) to obtain smooth spectra; their intensity was chosen so that the stresses and strains excited in the ground coincided on average with the stresses and strains generated during earthquakes to estimate the degree of the response of the ground to earthquakes). The results are presented for five 1.5-s intervals (first, third, …) among ten intervals studied. It is seen in the figure that the spectra of oscillations at the surface take a form close to E ( f ) ~ f – k . In the layers at intermediate depths (16 and 32 m in Port Island; 24.9 m in SJK), the forms of spectra demonstrate a resonance intensification of individual components. Interaction between spectral components takes place along with the resonance intensification. Highand low-frequency combination harmonics are formed. The energy of the propagating seismic waves is redistributed over the spectral band. The spectral peaks are smoothed, and the resulting spectrum of the signal at the surface of the ground tends to obtain the limiting form E ( f ) ~ f – k . Relative deformations in the ground at both points reached ~10 ‐3 in the surface layers and

Orientational Dynamics and Energy Dissipation in a Liquid Dispersion of Single-Domain Ferroparticles on Exposure to a Linearly Polarized Field

A theoretical investigation of the nonlinear orientational dynamics and energy dissipation in a suspension of noninteracting single-domain ferroparticles with a magnetic hysteresis on exposure to a linearly polarized magnetic field has been performed. The bifurcation properties of the system have been studied; the amplitude and frequency dependences of the powers of total and viscous dissipation have been obtained.

Highly nonlinear contact interaction and dynamic energy dissipation by forest of carbon nanotubes

Mechanical response and energy dissipation of an array of carbon nanotubes under high-strain rate deformation was studied using a simple drop-ball test with the measurement of the dynamic force between the ball and forest of nanotubes. This convenient process allows extracting force–displacement curves and evaluating dissipated energy by the nanotubes. The contact force exhibits a strongly nonlinear dependence on displacement being fundamentally different than the Hertz law. The forest of vertically aligned nanotubes may be used as a strongly nonlinear spring in discrete systems for monitoring signal propagation speed, and as a microstructure for localized energy absorption.

Energy spectra of developed superfluid turbulence

The spectrum of turbulence in superfluid liquid is modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. In some region of two Reynolds parameters characterizing the flow of a superfluid, we found the new state of the fully developed turbulence. This state displays both the Kolmogorov-Obukhov 5/3-scaling law $E_k \propto k^{-5/3}$ and the new "3-scaling law" $E_k \propto k^{-3}$, each in a well separated range of $k$.

Non-linear propagation of unidirectional wave fields over varying topography

The present study aims at investigating the non-linear triad interaction process affecting shoaling surface gravity wave fields. The triad interaction phenomenon being enhanced towards the shore, the domain of study is extended up to the surf zone. Three 1D non-linear wave models (one phase-resolving and two phase-averaged spectral models) have been implemented and compared to laboratory experiments performed in a wave flume. This set of models includes two existing models and a new one which has been developed in the frame of this work. The models include a breaking dissipation term based on the parametrical model of Battjes and Janssen [Battjes, J.A., Janssen, P.A.E.M., 1978. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. (ASCE), Vol. 1, pp. 569–587.]. The investigations concern the evolution of variance spectra, spectral significant wave height and mean period over a barred bathymetric profile. In addition, the performances of the different models are analysed by computing the spectral source term for triad interactions. We found that all models are able to reproduce the main features of non-linear mechanisms affecting a wave field in the near-shore zone. The phase-resolving model gives the most accurate results for non-breaking situations. It correctly reproduces the non-linear coupling effect in decreasing water depths due to wave–wave interactions, as well as the harmonic release after a bar. However, the model is computationally time-consuming. The CPU time is considerably reduced using phase-averaged models. They give satisfactorily results on harmonic generation. However, they do not reproduce the release of harmonics as water depth increases. In breaking conditions, the variance spectra undergo significant changes under the combined effects of non-linear energy transfers and dissipation. The depth-induced wave breaking model included in the equations provides a good estimate of the energy decay in the surf zone.

Nonlinear energy dissipation in a cellular automaton magnetotail field model

A magnetic field model of the magnetotail current sheet based on cellular automaton (CA) is presented. The present isotropic model is a continuously driven, two‐dimensional running CA. The model has a physical interpretation in terms of magnetohydrodynamic (MHD) equations, and features self‐organized critical (SOC) behavior with power‐law scalings both in durations and sizes of instabilities (avalanches). The model has nonlinear energy dissipation, and shows avalanches with and without an external trigger. Thus the model reproduces some of the statistical features recently observed in the magnetotail.

Non-linear waves in complex structures modelled by elastic-viscoplastic stochastic media

Wave propagation in complex engineering structures is addressed. Particular attention is paid to modelling of such intrinsic properties of complex structures as parameter uncertainty, essential heterogeneity, non-linear energy dissipation and resonant absorption at high frequencies. A complex structure is modelled by a random medium with a special rheoiogical model composed of a dashpot and an infinite number of elastic-plastic elements in parallel. The Dyson integral equation is employed to handle the problem of wave propagation in essentially heterogeneous random media. It is shown that the considerable spatial decay of the propagating wave is caused by (i) dispersion and scattering, (ii) resonant absorption in secondary systems attached to the primary structure and (iii) non-linear material damping and dry friction between the structural members. The latter causes various non-linear effects, for example, the vibration saturation in complex structures.

A mathematical model of an over-running sprag clutch

This paper gives a complete mathematical model for an over-running sprag clutch. It considers the inertias of the sprags and the output race, the Hertzian contact forces between the sprags and the races, as well as a non-linear energy dissipation approach, previously developed by the authors. Comparison with experiment showed that the normally assumed line contact between the races and the sprags is not valid and that a two-point contact assumption gives a better description of the existing Hertzian forces. In order to express these forces in terms of the windup angle, the work of Stoelzle and Hart [3] is adapted. It assumes that the motion of all clutch components can be expressed by way of an epicyclic train model in which an imaginary arm rolls the planet wheel (sprag) between a sun wheel (inner race) and a ring wheel (outer race), as the local deformations between sprags and races provide the needed “clearance” for motion. The resulting differential equations allow the determination of the clutch output rotation and of the windup angle histories for a given input motion and a known external load.

Research on Wave Phenomena in Hydraulic Lines : 10th Report, Experimental Discussion on Unsteady Nonlinearity of Orifice Flows

This report intends to experimentally reveal the fundamental differences between the steady and unsteady nonlinearities of orifice flows. The same measurements as in the foregoing paper are conducted in pulsating oil flows through orifices. Separating nonlinear components from total pressure drops and plotting them versus flow rates yields another hysteresis curve which represents the unsteady nonlinearity alone. It turns out that this curve invariably takes on similar inflection and counterclockwise hysteresis, and on the average lies below the steady-state loss. These findings lead to a hypothesis that eddies which bring about nonlinear energy dissipation in orifice flows tend to resist the change of magnitude, which is here called 'eddy inertia'. An idea of time lag inherent in the nonlinear loss helps embody this hypothesis as an empiric formula. This formula successfully explains the peculiar behaviors of hysteresis curves and Bolt's observation that the nonlinearity reduces the orifice reactances.

On the spectral dissipation of ocean waves due to white capping

The effect of white capping on the spectral energy balance of surface waves is investigated by expressing the white-cap interactions in terms of an equivalent ensemble of random pressure pulses. It is shown first that the source function for any non-expansible interaction process which is weak-in-the-mean is quasi-linear. In the case of white capping, the damping coefficient is then shown to be proportional to the square of the frequency, provided the wave scales are large compared with the white-cap dimensions. The remaining free factor is determined indirectly from consideration of the spectral energy balance. The proposed white-capping dissipation function is consistent with the structure of the energy balance derived from JONSWAP, and the existence of a δ−5 spectrum governed by a non-local energy balance between the atmospheric input, the nonlinear energy transfer and dissipation. However, closure of the energy balance involves hypotheses regarding the structure of the atmospheric input function which need to be tested by further measurements. The proposed set of source functions may nevertheless be useful for numerical wave-prediction. According to the model, nearly all the momentum transferred across the air-sea interface enters the wave field. For fetchlimited and fully developed spectra in a stationary, uniform wind field, the drag coefficient remains approximately constant. However, for more general wind conditions, this will not be the case and the wave spectrum should be included in an accurate parameterisation of the air-sea momentum transfer.