Displacement Variance Research Articles

High robust eddy current tuned tandem mass dampers-inerters for structures under the ground acceleration

In this work, a novel eddy current tuned tandem mass dampers-inerters, referred to as EC-TTMDI is proposed, a theoretical analysis model of the vibration control mechanism is established, and parameterized analysis and design are conducted using the intelligent optimization algorithm. This model is the single-degree-of-freedom (SDOF) structure with EC-TTMDI subjected to Gaussian white noise base excitation. Specifically, the expression for the displacement variance of the SDOF structure-EC-TTMDI system was firstly obtained with resorting to both the equivalent linearization of eddy current damper (ECD) and residue theorem. The optimization objective function was then defined as minimization of the displacement variance, which is product of the white noise intensity and the square of H2 norm of the model transfer function. Employing the pattern-search algorithm, the variation trends of the objective function and the optimum design parameters were subsequently scrutinized. The vibration damping mechanism of EC-TTMDI is then revealed in terms of control effectiveness, robustness, structural frequency response, suppression bandwidth, and stroke. Finally, the time history response analysis of the SDOF structure-EC-TTMDI system subjected to the near-field impulse, near-field non-impulse, and far-field earthquakes was conducted to further confirm the performance superiority of EC-TTMDI. Results demonstrates that EC-TTMDI offers higher robustness and better control effectiveness compared to TTMDI and TMDI. Furthermore, EC-TTMDI features the damping force limiting characteristic, which enhances the integrity and reliability of TTMDI.

Robustness of highly complex radial carpet beams in turbulent atmospheres

In this study, we report observations of propagating radial carpet beams (RCBs) through a turbulent atmosphere at ground level with a 120 m path length. RCBs are a class of nondiffracting, accelerating, self-healing, and self-amplifying beams, and generated in the diffraction of a plane wave from amplitude/phase radial gratings having different spoke numbers. Observations were made at different times of the day. The intensity profile of an RCB becomes complicated when the number of grating spokes used to generate the beam is large, and includes high intensity spots, called main intensity spots (MISs), which are symmetrically placed at the central area around the beam axis and whose number is equal to (twice) the number of spokes of the amplitude (phase) grating used to generate the beam. With the aid of a telescope and a CCD camera, successive frames of the intensity pattern of the RCBs having different levels of structural complexity are recorded at the end of the path. For the data recorded at different times of the day, we calculate the variance of displacements of MISs along the radial direction. We observe that displacements of the MISs increase with increasing mean temperature of the air; on the other hand, as the complexity of the beam intensity pattern increases, the displacements of the MISs decrease. In order to compare the resilience of different RCBs and a well-known structured beam against atmospheric turbulence, we investigate deformation of the intensity profiles of a Laguerre–Gaussian (LG) beam having a topological charge 20 and different RCBs at the end of the path. It is shown that under the same turbulence condition, highly complex RCBs are more resilient to the destructive effects of the atmospheric turbulence. In particular, for the RCBs generated with gratings having 30 spokes and more, the number of MISs of the received intensity patterns is changed by less than 1% even when the turbulence strength is high. But for the LG beam, its intensity ring is clearly broken in different places, which makes it impossible to follow its maximum intensity in the radial direction

Langevin Equation in Heterogeneous Landscapes: How to Choose the Interpretation.

The Langevin equation is a common tool to model diffusion at a single-particle level. In nonhomogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases, the solution to a Langevin equation is not unique unless the interpretation of stochastic integrals involved is selected. We analyze the diffusion of particles in such systems and evaluate the mean, the mean square displacement, and the distribution of particles, as well as the variance of the time-averaged mean-square displacements. Our analytical results provide a method to choose the interpretation parameter from single-particle tracking experiments.

Vibration control and energy harvesting of offshore wind turbines installed with TMDI under dynamical loading

This study investigates the performance of multiple tuned mass-damper-inerter with multiple electromagnetic motor (TMDI-EM) for the dual objectives of enhancing energy harvesting and dynamic performance in offshore wind turbines (OWTs). OWTs, inherently susceptible to dynamic sensitivity under lateral loads such as wind and waves, necessitate effective solutions for vibration mitigation while harnessing energy from dynamic excitations. The TMDI-EM configuration integrates an electromagnetic motor (EM) as a shunt damper between a secondary mass and an inerter element in series. The scalable inertance of the inerter element allows for adaptability in practical device implementations. Genetic Algorithm (GA) is employed to find optimum parameters for the TMDI-EM system. The research focuses on the dynamic response of OWTs under real-world conditions, where wind and wave forces act as correlated random excitations. Parametric analyses assess the available energy for harvesting at the EM and the displacement variance of the OWT structure as the inertance of the TMDI-EM varies. The study employs methods to optimize the TMDI-EM parameters using Genetic Algorithm, ensuring the system's optimal performance for both enhanced energy harvesting and dynamic response. The findings indicate that lightweight TMDI-EMs, representing only 1.5 % of the OWT structure's mass, demonstrate improved vibration suppression and energy harvesting performance with increasing inertance. This study contributes into the potential integration of TMDI-EMs to enhance the dynamic performance and energy harvesting capabilities of offshore wind turbines under dynamical loading conditions. The use of Genetic Algorithm ensures the identification of optimal parameters for the TMDI-EM system, enhancing its practical applicability.

Seismic performance enhancement of small modular reactors using optimal design of inerter-based vibration absorbers

Nuclear power plant (NPP) structures face significant challenges in ensuring structural resilience subjected to earthquake motions. The inerter-based vibration absorbers (IVAs) have been proven to control structural vibration, but they have not been applied in small modular reactor (SMR) structures. In this study, the optimal IVA parameters are investigated for SMR structures, which focus on reducing the seismic response of the first floor and fifth floor. By using a genetic algorithm (GA), the IVAs parameters are optimized to minimize the storey displacement variance and storey acceleration variance. Besides, the robustness analysis is performed to ensure the optimized parameters are practical. The various ground motions are selected for time history analysis (THA) to illustrate the seismic response of SMR equipped with the optimal IVAs. The results of THA demonstrate that the optimal IVAs enhance the seismic performance of the SMR compared with traditional SMR structures. By positioning optimal IVAs, significant mitigation of both storey displacement and storey acceleration are achieved. This study explores to a deeper understanding of IVAs' efficacy in SMR structures, which is beneficial to the practical use of IVAs in SMR structures.

Variance sum rule: proofs and solvable models

We derive, in more general conditions, a recently introduced variance sum rule (VSR) (Di Terlizzi et al 2024 Science 383 971) involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion 2Dt, with D the diffusion constant and t the time. From the VSR, we also derive formulas for the entropy production rate σ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for σ in an overdamped NESS.

Ternary Solid Polymer Electrolytes at the Electrochemical Interface: A Computational Study.

Polymer-based solid-like gel electrolytes have emerged as a promising alternative to improve battery performance. However, there is a scarcity of studies on the behavior of these media at the electrochemical interface. In this work, we report classical MD simulations of ternary polymer electrolytes composed of poly(ethylene oxide), a lithium salt [lithium bis(trifluoromethanesulfonyl)imide], and different ionic liquids [1-butyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide and 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide] confined between two charged and uncharged graphene-like surfaces. The molecular solvation of Li+ ions and their diffusion as well as the polymer conformational picture were characterized in terms of the radial distribution functions, coordination numbers, number density profiles, orientations, displacement variance, polymer radius of gyration, and polymer end-to-end distance. Our results show that the layering behavior of the ternary electrolyte in the interfacial region leads to a decrease of Li+ mobility in the direction perpendicular to the electrodes and high energy barriers that hinder lithium cations from coming into direct contact with the graphene-like surface. The nature of the ionic liquid and its concentration were found to influence the structural and dynamic properties at the electrode/electrolyte interface, the electrolyte with low amounts of the pyrrolidinium-based ionic liquid being that with the best performance since it favors the migration of Li+ cations toward the negative electrode when compared to the imidazolium-based one.

Dynamic response of asymmetric suspended structure subjected to random wind excitation

SummarySuspended structures, regarded as the expression of structural beauty, have attracted the focus of many architects and engineers. With the complexity of dynamic responses of the asymmetric suspended structures subjected to the random alongside wind excitation, an innovative method was proposed through combining the finite element method (FEM), the complex mode method (CMM), the pseudo excitation method (PEM), and the quadratic decomposition method (QDM) of frequency response function. The method could obtain unified closed‐form solutions of spectral moment and variance of node displacement and velocity and acceleration of asymmetric structures and its correctness was verified by existing numerical approaches. The proposed method is applicable to the random wind‐induced vibration response analysis of diverse linear complex structures. Notably, its efficacy lies in its circumvention of numerical integration, endowing it with high computational efficiency and accuracy. Extended comparative studies and discussion were also performed on effect of suspended span and comparisons of normal framed structure and symmetry structure. The results showed that the suspended span presented positive relation to horizontal displacement and inverse tendency to horizontal acceleration of the whole structure and vertical and horizontal acceleration of the columns near to suspended part should also be considered in engineering design.

Variance sum rule for entropy production.

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Line simplification with sidedness relationship consistency using the constrained total least squares method

AbstractThe simplification of lines plays a crucial role in map generalization and multiscale representation; however, addressing inconsistent sidedness relationships between the simplified lines and their neighboring features poses a persistent challenge. In order to preserve correct and consistent sidedness relationships following simplification, this study introduces a novel line simplification method. This method incorporates topological constraints pertaining to left–right sidedness relationships, formulated as an optimization procedure based on the proposed partial total least squares method with constraints. The primary objective is to minimize the positional difference between the line features before and after simplification, with the sidedness relationship represented as an inequality constraint. Moreover, an optimization algorithm is derived to address the simplification problem effectively while adhering to the specified constraints. The proposed method is then applied to simplify the lines within three distinct datasets. Experimental results validate the efficacy of the proposed method in maintaining sidedness consistency across all tested datasets. In comparison to the Douglas–Peucker (DP) method, the proposed method exhibits minimal vertical displacement variance in the line feature points post‐simplification. Additionally, it achieves a smaller overall positional difference between the simplified and original lines compared to the DP method. These findings underscore the superior performance of the proposed method in maintaining sidedness relationships and minimizing positional differences during the line simplification process.

A portable S-DIMM developed for preliminary measurement of seeing for Solar Site Survey: Theory and one case study

Imaging quality is highly important for astronomical observations. The imaging quality of a telescope depends not only on the capabilities of the telescope itself but also on its location. When distant stars pass the atmosphere, due to the presence of atmospheric turbulence, the imaging quality becomes degraded. The atmospheric coherence length is the most commonly used parameter to evaluate the influence of the local atmospheric turbulence on telescopes. It is used to describe the degree of atmospheric attenuation of image quality. For the preliminary estimation of atmospheric daytime seeing from a lot of candidate sites, we have developed a portable S-DIMM (PS-DIMM),which is mainly composed of a light-duty tracking mount, a 9 cm aperture lens barrel and a Canon 60D SLR camera. With the PS-DIMM the daytime seeing of a site can be well estimated by measuring the relative displacement variance of the edge positions at both ends of the Sun’s diameter. The principle of PS-DIMM is introduced in this paper. The simultaneous seeing measurements by it and the traditional S-DIMM were carried out at the Fuxian Lake Solar Station, showing a very well correlated between them but with an offset of 2.6 cm. In contrast to the traditional S-DIMM, PS-DIMM offers the advantages of reduced weight and enhanced portability. The utilization of PS-DIMM has played an important role in the early stages of the site survey for the next-generation solar telescopes.

Investigations on seismic performance of nuclear power plants equipped with an optimal BIS-TMDI considering FSI effects

This paper introduces a base isolation system-tuned mass damper inerter (BIS-TMDI) hybrid system to the AP1000 nuclear power plant (NPP), which reduces seismic damage potential of the NPP structure. The effects of fluid-structure interaction (FSI) caused by the passive containment cooling system water storage tank (PCCWST) on NPP's seismic performance are investigated. The FSI of water tank theoretical model is considered based on the Housner's model, and a series of time history analyses are performed to prove the rationality of the proposed model. Three single-objective optimization strategies are employed to minimize the relative displacement variance and absolute acceleration variance of the upper structure, as well as the filtered energy index (FEI). Furthermore, a multi-objective optimization strategy considering all these three indexes is proposed to obtain optimal parameters of vibration control. The influence of vibration control strategies on the relative deformation and acceleration of the upper structure is explored with various water level ratios. The analytical results indicate that the proposed BIS-TMDI strategy has significantly reduced the NPP structure's seismic response. The effectiveness of the vibration control strategy is influenced by the water level ratio, emphasizing the significance of designing an appropriate water level ratio to reduce NPP structure's seismic response.

The Role of a Simple Inerter in Seismic Base Isolation

The present study investigates the role of a simple inerter in supplemental devices for possible implementation in the mature seismic base isolation technique. Firstly, the response of the base-isolated structure with an optimally tuned mass damper inerter (TMDI) is investigated to see the tuning effects. The time required to tune the TMDI was found to be significantly longer than the duration of a strong-motion earthquake. There was still a reduction in the response of the isolated structure, which is primarily due to the added damping and stiffness (ADAS) of TMDI and not because of the tuning effects. Hence, it is proposed that the corresponding ADAS of the TMDI be directly added to the isolation device. Secondly, the response of the base-isolated structures to the fluid inerter damper (FID) is studied. It was observed that the inerter of the FID does not influence the displacement variance of an isolated structure under broadband earthquake excitation. It implies that the response of the isolated structure to FID is primarily controlled by its counterpart fluid damper (FD). The performance of optimal TMDI, ADAS, FID, and FD to mitigate the seismic response of the flexible multi-story base-isolated structure under real earthquake excitations is also investigated. In terms of suppressing the displacement and acceleration responses of the isolated structure, it has been found that TMDI and ADAS perform similarly. Comparing the response of the isolated structure with FID and FD demonstrated that the inerter in the FID has detrimental effects on the isolated structures, in which the top floor’s acceleration and base shear are substantially increased.

Assessing brain microstructural changes in chronic kidney disease: a diffusion imaging study using multiple models.

To explore the effectiveness of diffusion quantitative parameters derived from advanced diffusion models in detecting brain microstructural changes in patients with chronic kidney disease (CKD). The study comprised 44 CKD patients (eGFR<59 mL/min/1.73 m2) and 35 age-and sex-matched healthy controls. All patients underwent diffusion spectrum imaging (DSI) and conventional magnetic resonance imaging. Reconstructed to obtain diffusion MRI models, including diffusion tensor imaging (DTI), neurite orientation dispersion and density imaging (NODDI) and Mean Apparent Propagator (MAP)-MRI, were processed to obtain multi-parameter maps. The Tract-Based Spatial Statistics (TBSS) analysis was utilized for detecting microstructural differences and Pearson correlation analysis assessed the relationship between renal metabolism markers and diffusion parameters in the brain regions of CKD patients. Receiver operating characteristic (ROC) curve analysis assessed the diagnostic performance of diffusion models, with AUC comparisons made using DeLong's method. Significant differences were noted in DTI, NODDI, and MAP-MRI parameters between CKD patients and controls (p < 0.05). DTI indicated a decrease in Fractional Anisotropy(FA) and an increase in Mean and Radial Diffusivity (MD and RD) in CKD patients. NODDI indicated decreased Intracellular and increased Extracellular Volume Fractions (ICVF and ECVF). MAP-MRI identified extensive microstructural changes, with elevated Mean Squared Displacement (MSD) and Q-space Inverse Variance (QIV) values, and reduced Non-Gaussianity (NG), Axial Non-Gaussianity (NGAx), Radial Non-Gaussianity (NGRad), Return-to-Origin Probability (RTOP), Return-to-Axis Probability (RTAP), and Return-to-Plane Probability (RTPP). There was a moderate correlation between serum uric acid (SUA) and diffusion parameters in six brain regions (p < 0.05). ROC analysis showed the AUC values of DTI_FA ranged from 0.70 to 0.793. MAP_NGAx in the Retrolenticular part of the internal capsule R reported a high AUC value of 0.843 (p < 0.05), which was not significantly different from other diffusion parameters (p > 0.05). The advanced diffusion models (DTI, NODDI, and MAP-MRI) are promising for detecting brain microstructural changes in CKD patients, offering significant insights into CKD-affected brain areas.

Vibration reduction performance for the novel grounded inerter-based dynamic vibration absorber controlling a primary structure under random excitation

This paper investigates the control performance of a novel grounded inerter-based dynamic vibration absorber (GI-DVA) for random vibration reduction. First, the dynamics equations of the coupled system are written and the transfer function is obtained based on the Laplace transform. Then, assuming that the primary structure is under random white noise excitation, the displacement variance of the primary structure is calculated based on the exact definition of the H2 norm, by solving the Lyapunov equation. By imposing that the partial derivatives of the response variance of the primary structure with respect to the system parameters are simultaneously equal to zero, the optimum design values of the H2 optimized GI-DVA were derived numerically for given different mass ratio. It can be found that the optimal design parameters as the inerter-to-mass ratio, the stiffness ratio and the damping ratio increase, while the frequency ratio decreases with the increase in the mass ratio. Under the optimal conditions, the response analysis showed that the primary structure response controlled by the H2 optimized GI-DVA can decrease with the increase in the mass ratio, but is less sensitive to large mass ratios, and can be robust to the mistuning on the optimum design parameters. Then, the control performance evaluation is first performed in the frequency domain, which reveal that the dynamic response reduction capacity of the H2 optimized GI-DVA are significantly 62% and 48% superior to the H2 optimized classic DVA (CDVA) and high-performance passive nontraditional inerter-based DVA (NIDVA-C4), respectively. Furthermore, for the root mean square response evaluation (H2 performance), the H2 optimized GI-DVA can provide significantly H2 performance 58% and 50% than the H2 optimized CDVA and NIDVA-C4, respectively. To obtain more realistic results, the time domain simulation is performed, which showed that the GI-DVA can provide significantly performance for random vibration reduction.

Internal wave activity in the deep Gulf of Mexico

Internal wave activity in the Gulf of Mexico (GoM) is investigated using a fleet of profiling floats. The floats continuously measured temperature and salinity as they drifted at a parking depth of 1500 dbar, allowing for the reconstruction of 2615 time series of isopycnal displacements. Thanks to the dense sampling of the eastern part of the GoM (east of 90°W), the geographical distribution of the internal waves displacement variance and available potential energy (APE) is revealed. The Loop Current (LC) influence region, between the Yucatan shelf to the west and the southern West Florida shelf to the east exhibits increased displacement variance and APE both in the continuum and near-inertial bands, while the north-eastern and central GoM show reduced internal wave activity. As the LC position fluctuates between a retracted and extended mode, we assessed the impact of the presence or absence of the LC in the increased internal wave activity region. It is shown that in the LC influence region, APE is increased (decreased) when the LC is present (absent), suggesting a strong control of the LC on deep internal waves activity. The 1500 dbar flow velocity, bottom roughness, and float altitude also seem to contribute to increased internal waves APE, but their influence is more subtle. Oppositely, no correlation with wind speed or wind intermittency is found.

Stochastic Dynamics of Two‐Dimensional Particle Motion in Darcy‐Scale Heterogeneous Porous Media

AbstractWe study the upscaling and prediction of ensemble dispersion in two‐dimensional heterogeneous porous media with focus on transverse dispersion. To this end, we study the stochastic dynamics of the motion of advective particles that move along the streamlines of the heterogeneous flow field. While longitudinal dispersion may evolve super‐linearly with time, transverse dispersion is characterized by ultraslow diffusion, that is, the transverse displacement variance grows asymptotically with the logarithm of time. This remarkable behavior is linked to the solenoidal character of the flow field, which needs to be accounted for in stochastic models for the two‐dimensional particle motion. Here, we derive an upscaled model based on the statistical characterization of the motion of solute particles. To this end, we analyze particle velocities and orientations through equidistant sampling along the particle trajectories obtained from direct numerical simulations. This sampling strategy respects the flow structure, which is organized on a characteristic length scale. Perturbation theory shows that the longitudinal particle motion is determined by the variability of travel times, while the transverse motion is governed by the fluctuations of the space increments. The latter turns out to be strongly anticorrelated with a correlation structure that leads to ultraslow diffusion. Based on this analysis, we derive a stochastic model that combines a correlated Gaussian noise for the transverse motion with a spatial Markov model for the particle speeds. The model results are contrasted with detailed numerical simulations in two‐dimensional heterogeneous porous media of different heterogeneity variances.

Adaptive Flexible Controller Frequency Optimization for Reducing Structural Response of a 10 Mw Floating Offshore Wind Turbine

This study presents the adaptive flexible controller frequency optimization method (AFCFOM) as a means of minimizing dynamic loads and structural response in large-scale floating wind turbines, with the goal of enhancing reliability and reducing the frequency of failures. AFCFOM employs a flexible proportional integral (PI) controller frequency, allowing the wind turbine to autonomously adapt to different wind and wave conditions while minimizing structural response. The AFCFOM framework utilizes Latin hypercube sampling for spatial compression, two Bayesian neural networks (BNN) for training and mapping, and particle swarm optimization (PSO) for controller frequency seeking, along with the extreme response surface method for processing the response dataset. OpenFSAT was used for raw data collection and method effect validation. The simulation results demonstrate that the application of AFCFOM effectively reduces the extreme values and variance of the axial displacement at the blade top of the floating offshore wind turbine blade and enhances the robustness of the floating platform. The study provides an overview of the potential effects of adaptive flexible controller frequency on wind turbines, serving as a reference for future wind turbine control optimization research.

Estimating the robust optimal parameters of tuned mass damper

The tuned mass damper (TMD) is one of the oldest and most extensively used passive vibration control systems in dynamically excited buildings. However, the uncertainties or randomness in the loading and the primary structure parameters (i.e., stiffness and damping coefficient) significantly affected the TMD performance. In this framework, Robust Design Optimization (RDO) technique is advantageous, aiming to simultaneously minimize the performance function’s mean and variance. Simulation-based RDO techniques are particularly effective at solving difficult nonconvex and multimodal issues. Therefore, in the present study, a stochastic simulation-based approach is proposed for the RDO of TMD. The performance function’s mean and variance are considered robustness measures. The TMD’s frequency and damping ratios are considered design parameters. TMD attached to a Multiple-Degree-of-Freedom (MDOF) structural system is analyzed to demonstrate the efficacy of the proposed approach. The top floor displacement variance ratio of the protected structural system to that of the unprotected structural system is adopted as the performance function. The simulation results show that the proposed strategy successfully identifies the optimal design for all levels of uncertainty. The necessity of considering the uncertainties is well highlighted. In conclusion, the proposed approach is found to be effective and offers the designer more information for an optimal design decision.

Characterization of the L4/L5 rat facet capsular ligament macromechanical and microstructural responses to tensile failure loading

Low back pain is a prevalent condition that affects the global population. The lumbar facet capsular ligament is a source of pain since the collagenous tissue of the ligament is innervated with sensory neurons that deform with the capsule’s stretch. Regional differences in the microstructural and macrostructural anatomy of the spinal facets affect its capsule’s mechanical behavior. Although there are many studies of the cervical facet in human and rodent models, the lumbar capsular ligament’s multiscale behavior is less well-defined. This study characterizes the macroscale and fiber-scale changes of the rat lumbar facet capsule during tensile failure loading. An integrated polarized light imaging setup captured local fiber alignment during 0.08 mm/s distraction of 7 lumbar facets. Force, displacement, strain, and circular variance were measured at several points along the failure curve: the first instance when the local collagen fiber network realigns differentially (anomalous realignment), yield, the first peak in force corresponding to the capsule’s first failure, and peak force, defined as ultimate rupture. Those outcomes were compared across events. While each of force, displacement, and average maximum principal strain increased with applied tension, so did the circular variance of the collagen, suggesting that the fibers were becoming more disorganized. From the fiber alignment maps collected at each mechanical event, the number of anomalous realignment events were counted and found to increase dramatically with loading. The increased collagen disorganization and increasing regions of such disorganization in the facet capsule during loading can provide insights about how loading to the ligament afferent nerves may be activated and thereby produce pain.