Quasi-static Displacement Research Articles

Displacement measurement with nanoscale resolution using a coded micro-mark and digital image correlation

A method for simple and reliable displacement measurement with nanoscale resolution is proposed. The measurement is realized by combining a common optical microscopy imaging of a specially coded nonperiodic microstructure, namely two-dimensional zero-reference mark (2-D ZRM), and subsequent correlation analysis of the obtained image sequence. The autocorrelation peak contrast of the ZRM code is maximized with well-developed artificial intelligence algorithms, which enables robust and accurate displacement determination. To improve the resolution, subpixel image correlation analysis is employed. Finally, we experimentally demonstrate the quasi-static and dynamic displacement characterization ability of a micro 2-D ZRM.

Quasi-static displacement calibration system for a “Violin-Mode” shadow-sensor intended for Gravitational Wave detector suspensions

This paper describes the design of, and results from, a calibration system for optical linear displacement (shadow) sensors. The shadow sensors were designed to detect "Violin-Mode" (VM) resonances in the 0.4 mm diameter silica fibre suspensions of the test masses/mirrors of Advanced Laser Interferometer Gravitational Wave Observatory gravitational wave interferometers. Each sensor illuminated the fibre under test, so as to cast its narrow shadow onto a "synthesized split photodiode" detector, the shadow falling over adjacent edges of the paired photodiodes. The apparatus described here translated a vertically orientated silica test fibre horizontally through a collimated Near InfraRed illuminating beam, whilst simultaneously capturing the separate DC "shadow notch" outputs from each of the paired split photodiode detectors. As the ratio of AC to DC photocurrent sensitivities to displacement was known, a calibration of the DC response to quasi-static shadow displacement allowed the required AC sensitivity to vibrational displacement to be found. Special techniques are described for generating the required constant scan rate for the test fibre using a DC motor-driven stage, for removing "jitter" at such low translation rates from a linear magnetic encoder, and so for capturing the two shadow-notch signals at each micrometre of the test fibre's travel. Calibration, across the four detectors of this work, gave a vibrational responsivity in voltage terms of (9.45 ± 1.20) MV (rms)/m, yielding a VM displacement sensitivity of (69 ± 13) pm (rms)/√Hz, at 500 Hz, over the required measuring span of ±0.1 mm.

Seismic behavior of slender reinforced concrete walls

Residential reinforced concrete buildings performed well during the 2010 Mw 8.8 Maule, Chile earthquake. However, brittle damage was observed in reinforced concrete structural walls. The most frequent observed damage in such walls was crushing of concrete due to flexural-compressive interaction, buckling and fracture of longitudinal reinforcement, and opening of the horizontal reinforcement. The main objective of this study is to understand the observed damage in slender walls after 2010 Maule earthquake and to reproduce and analyze experimentally the seismic behavior of such walls. The second objective is to provide recommendations to estimate the lateral displacement and the effective stiffness of slender walls. To achieve these objectives, six ½-scale slender reinforced concrete walls were tested using a conventional quasi-static cyclic incremental lateral displacement test protocol with a constant axial load. The test results are compared to a reference wall tested previously in the same research project. The variables analyzed in this study are: wall thickness, wall aspect ratio, use of uniformly distributed vertical reinforcement, detailing of 135-degree hooks for the horizontal reinforcement, addition of closed stirrups in the wall boundaries, and addition of transverse cross-ties. The observed damage in the tested walls was similar to that observed in walls of buildings damaged during the 2010 Maule earthquake. The behavior of the tested walls was dominated by bending due to their relatively large aspect ratio. The failure, determined by the loss of ability to carry axial load, occurred suddenly as a compression failure along the entire cross section at the base of the tested walls. Test results showed that a 25% reduction in wall thickness reduced the ultimate displacement capacity, ductility, and energy dissipation ability of the wall. Closed stirrups and cross-ties were effective in increasing displacement capacity and ductility, and closed stirrups were effective in preventing out-of-plane buckling of the wall after compression failure. The average effective stiffness ratio of the tested walls was 0.39, which is slightly larger than the ACI 318 suggestion of 0.35.

Inertial effects during irreversible meniscus reconfiguration in angular pores

In porous media, the dynamics of the invading front between two immiscible fluids is often characterized by abrupt reconfigurations caused by local instabilities of the interface. As a prototype of these phenomena we consider the dynamics of a meniscus in a corner as it can be encountered in angular pores. We investigate this process in detail by means of direct numerical simulations that solve the Navier–Stokes equations in the pore space and employ the Volume of Fluid method (VOF) to track the evolution of the interface. We show that for a quasi-static displacement, the numerically calculated surface energy agrees well with the analytical solutions that we have derived for pores with circular and square cross sections. However, the spontaneous reconfigurations are irreversible and cannot be controlled by the injection rate: they are characterized by the amount of surface energy that is spontaneously released and transformed into kinetic energy. The resulting local velocities can be orders of magnitude larger than the injection velocity and they induce damped oscillations of the interface that possess their own time scales and depend only on fluid properties and pore geometry. In complex media (we consider a network of cubic pores) reconfigurations are so frequent and oscillations last long enough that increasing inertial effects leads to a different fluid distribution by influencing the selection of the next pore to be invaded. This calls into question simple pore-filling rules based only on capillary forces. Also, we demonstrate that inertial effects during irreversible reconfigurations can influence the work done by the external forces that is related to the pressure drop in Darcy’s law. This suggests that these phenomena have to be considered when upscaling multiphase flow because local oscillations of the menisci affect macroscopic quantities and modify the constitutive relationships to be used in macro-scale models. These results can be extrapolated to other interface instabilities that are at the origin of fast pore-scale events, such as Haines jumps, snap-off and coalescence.

Multiobjective topology optimization of energy absorbing materials

A method for the multiobjective optimization of local-scale material topology is presented. The topology optimization scheme is based on a constructive solid geometry-like representation, in which convex polygons--defined as the convex hull of arbitrary-length lists of points--are combined using an overlapping function. This data structure is tree-shaped and so genetic programming is used as the optimizer. The forward problem is solved with a multiscale finite element method with automatic cohesive zone insertion to model damage. As a multiscale method, loads and boundary conditions are applied and objective functions measured at a global scale, while the local scale material structure is optimized. The global scale geometry is assumed fixed. Pareto optimal designs are generated, representing optimal tradeoffs between conflicting goals: quasi-static displacement and dynamic strain energy. Results demonstrate the efficacy of the proposed algorithm.

Investigating the quasi-static axial crushing behavior of polymeric foam-filled composite pultrusion square tubes

The capability of structures to absorb large amounts of energy is a crucial factor, particularly for structural components of vehicles, in reducing injury in case of collision. In this study, an experimental investigation was conducted to study the crashworthiness of polymeric foam-filled structures to the pultruded square cross-section E-Glass fiber-reinforced polyester composite tube profiles. Quasi-static compression was applied axially to composite tubes to determine the response of the quasi-static load displacement curve during progressive damage. Three pultruded composite tube wall thicknesses at different sizes were examined, and the effects of crushing behavior and failure modes were analyzed and discussed. Experimental results indicated that the foam-filled profile is superior to the non-filled foam composite tube profile in terms of the capacity to absorb specific energy.

Tensile Testing of Hybrid Composite Joints

In the present paper, results of experimental tests carried out on hybrid (bonded/bolted) and adhesive composite single-lap joints are showed. The laminate adherends were made by unidirectional carbon fiber/epoxy with symmetric stacking sequence. In particular, the tests were carried out to evaluate strength and failure mode of the different joints. These joints were subjected to quasi-static tensile displacement and tests were conducted using a universal testing machine. The maximum tension load that the specimen can bear is determined and the failure process is correlated to the lay-up of the composite and joint type.

Computation of Relative Permeability from Imaged Fluid Distributions at the Pore Scale

Image-based computations of relative permeability for capillary-dominated quasi-static displacements require a realistic description of the distribution of the fluids in the pore space. The fluid distributions are usually computed directly on the imaged pore space or on simplified representations of the pore space extracted from the images using a wide variety of models which capture the physics of pore-scale displacements. Currently this is only possible for uniform strongly wetting conditions where fluid–fluid and rock–fluid interactions at the pore-scale can be modelled with a degree of certainty. Recent advances in imaging technologies which make it possible to visualize the actual fluid distributions in the pore space have the potential to overcome this limitation by allowing relative permeabilities to be computed directly from the imaged fluid distributions. The present study explores the feasibility of doing this by comparing laboratory measured capillary-dominated drainage relative permeabilities with relative permeabilities computed from micro-CT images of the actual fluid distributions in the same rock. The agreement between the measurements and the fluid image-based computations is encouraging. The paper highlights a number of experimental difficulties encountered in the study which should serve as a useful guide for the design of future studies.

Design of Reinforced Concrete Infilled Frames

AbstractThe work presented in this paper aimed to evaluate the diagonal strut model for the design of reinforced concrete (RC) infilled frames, already broadly used as a design tool in the case of masonry infilled RC frames. The assumptions on which the strut model provisions in codes are based are reviewed. In parallel, some of the results of an experimental study on the response of eight 1/3-scale RC infilled frames subjected to quasi-static cyclic horizontal displacements are summarized. Two different aspect ratios and different types of connection of the infill to the frame have been investigated. Design provisions for infilled frames included in codes are applied to describe the behavior of the specimens tested in terms of stiffness, ultimate strength, and expected mode of failure. The results are discussed and some suggestions are made for improving the design procedures.

Boundary condition-free elastic modulus reconstructions from ultrasound measured quasi-static displacements

Quantitative elastic modulus imaging from quasi-static displacement data requires the solution of an inverse elasticity problem. The inverse problem formulation generally requires specification of either displacement or traction boundary conditions. Most current ultrasound devices are not capable of measuring traction data, and the measured displacement field is noisy. The incomplete and imprecise nature of the available boundary information often necessitates that educated guesses be made in order to have adequate knowledge of the boundary conditions to compute mechanical properties. These assumed boundary conditions, however, can to lead to errors in the reconstructions. This abstract proposes a method to perform reconstructions without knowing the boundary conditions a priori. This method relies on using the constrain imposed by the equilibrium equation and an optimization algorithm to estimate the modulus field. This method was verified with simulated displacement data, validated with phantom displacement data, and applied to in-vivo displacement data measured from patients with breast masses. [Authors gratefully acknowledge funding from NSF and NIH (NSF Grant No. 50201109; NIH NCI-R01CA140271).]

Mechanics of CNT-palladium Interfaces for Sensor Applications Simulated with Molecular Dynamics

We present force-displacement data simulated with molecular dynamics of quasi-static displacement controlled pull-out tests of single-walled carbon nanotubes (CNT) embedded in palladium. With our simulations we focus on the mechanical interface behavior at the atomic scale which is of importance for thermo-mechanical reliability predictions and failure-mechanistic treatment of future CNT devices. In general, an incommensurate interface structure can be predicted, when a chiral CNT is in contact with a noble metal like palladium. This originates in lattices with different basis and periodicities as well as a strong metal interaction, a strong carbon interaction and a weak metal carbon interaction, which in this paper is assumed to be of van der Waals type. We report on an interface fracture with a complete detachment of CNT and palladium. The pull-out forces we calculated are in the nano Newton range for models with CNTs embedded 5 to 10nm and increase when the CNT has intrinsic defects or functional groups are attached. Furthermore, for ideal cases the pull-out behavior is independent of the embedding length and although bond breaking and forming occurs, there is no associated energy dissipation. Due to the incommensurate interface some atoms assist while others resist the pull-out displacement. In effect the pull-out force is then a restoring force, which is fed by the surface potential energy that is lowered when the CNT shares maximum contact area with the palladium. In contrast, defects in the CNT like kinks or functional groups alter this behavior and then energy dissipation becomes a pronounced effect due to sudden changes of unstable atomic configurations.

Numerical modelling of dissipative pin devices for brace-column connections

In this paper, the behaviour of dissipative brace-column connection devices is emphasized. The computation is carried out for a single- and double-pin connection device, where the pins are displaced in two configurations: in-parallel and in-line. The study is conducted by using the theoretical and the OpenSees beam model under monotonic and cyclic quasi-static displacement loading. The proposed OpenSees model of the single-pin connection was calibrated against experimental test results found in the literature and the validation was completed when both the experimental and simulated models provided a good match in terms of hysteresis loops and cumulative dissipated energy. Using the same approach, the double-pin connection, in both configurations, was studied through numerical modelling only. The purpose of installing dissipative single- or double-pin connections at the brace-column joints is to preserve brace members to behave in the elastic range, while maintaining their buckling resistance.

Fabrication and characterization of a piezoelectric micromirror using for optical data tracking of high-density storage

A micromirror actuated by three piezoelectric microcantilevers is presented for optical data tracking of high-density storage application. The microcantilevers are actuated by 2.5-μm-thick lead zirconate titanate (PZT) films which are deposited on the silicon-based substrate by a compatible sol–gel route. The X-ray diffraction result shows that the PZT film is perovskite structure and has a typical good ferroelectric loop. The quasi-static displacement of the mirror plate increases linearly with increasing the driving voltage and the tracking resolution on disk is as high as 8 nm/V. The micromirror also provides a high bandwidth of about 21 kHz, which is high enough to support the optical data tracking of future high-density storage.

Finite-size effects on the quasistatic displacement pulse in a solid specimen with quadratic nonlinearity

There is an unresolved debate in the scientific community about the shape of the quasistatic displacement pulse produced by nonlinear acoustic wave propagation in an elastic solid with quadratic nonlinearity. Early analytical and experimental studies suggested that the quasistatic pulse exhibits a right-triangular shape with the peak displacement of the leading edge being proportional to the length of the tone burst. In contrast, more recent theoretical, analytical, numerical, and experimental studies suggested that the quasistatic displacement pulse has a flat-top shape where the peak displacement is proportional to the propagation distance. This study presents rigorous mathematical analyses and numerical simulations of the quasistatic displacement pulse. In the case of semi-infinite solids, it is confirmed that the time-domain shape of the quasistatic pulse generated by a longitudinal plane wave is not a right-angle triangle. In the case of finite-size solids, the finite axial dimension of the specimen cannot simply be modeled with a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. More profoundly, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second order harmonic pulses generated by the same transducer.

Numerical and experimental characterizations of longitudinally polarized piezoelectric d 15 shear macro-fiber composites

This contribution presents original numerical and experimental characterizations for prototyped longitudinally polarized piezoelectric d 15 shear macro-fiber composites (MFC). The numerical characterization consists of a finite element (FE) simulation based on a representative volume element. It implements an enthalpy-based homogenization method (EBHM), recently proposed by the authors, as an extension of the so-called strain energy method to orthotropic piezoelectric fiber-reinforced composites. The numerical validation is carried out on a previously assumed layout of shear MFC. Later on, the EBHM is used to get the effective electromechanical material parameters of the shear MFC actual layout. These parameters are further validated experimentally through their use in the FE simulation of an original actuation benchmark that is proposed for the manufactured shear MFC experimental characterization. The latter is based on low-frequency (quasi-static) displacement measurements where the shear MFC serves as a voltage-driven actuator. Due to the small overall dislocation, a laser vibrometer is used for the measurements. The comparison of experimental and numerical results shows a reasonably good agreement and a nonlinear actuation response is observed. This work’s major outcomes are the experimental validation of the EBHM and the actuation functional operability of the manufactured longitudinally polarized piezoelectric d 15 shear MFC. This opens the possibility for their application as actuator and sensor of shear-induced bending and torsion for vibration, shape and health control, or as a transducer for energy harvesting.

Protocol for testing of cold-formed steel wall in regions of low-moderate seismicity

Loading protocols have been developed for quasi-static cyclic testing of structures and components. However, it is uncertain if protocols developed for conditions of intense ground shaking in regions of high seismicity would also be applicable to regions of low-moderate seismicity that are remote from the tectonic plate boundaries. This study presents a methodology for developing a quasi-static cyclic displacement loading protocol for experimental bracing evaluation of cold-formed steel stud shear walls. Simulations presented in the paper were based on conditions of moderate ground shaking (in Australia). The methodologies presented are generic in nature and can be applied to other regions of similar seismicity conditions (which include many parts of China, Korea, India and Malaysia). Numerous response time histories including both linear and nonlinear analyses have been generated for selected earthquake scenarios and site classes. Rain-flow cycle counting method has been used for determining the number of cycles at various ranges of normalized displacement amplitude. It is found that the number of displacement cycles of the loading protocol increases with increasing intensity of ground shaking (associated with a longer return period).

Wavelet based multi-step filtering method for bridge health monitoring using GPS and accelerometer

Effective monitoring, reliable data analysis, and rational data interpretations are challenges for engineers who are specialized in bridge health monitoring. This paper demonstrates how to use the Global Positioning System (GPS) and accelerometer data to accurately extract static and quasi-static displacements of the bridge induced by ambient effects. To eliminate the disadvantages of the two separate units, based on the characteristics of the bias terms derived from the GPS and accelerometer respectively, a wavelet based multi-step filtering method by combining the merits of the continuous wavelet transform (CWT) with the discrete stationary wavelet transform (SWT) is proposed so as to address the GPS deformation monitoring application more efficiently. The field measurements are carried out on an existing suspension bridge under the normal operation without any traffic interference. Experimental results showed that the frequencies and absolute displacements of the bridge can be accurate extracted by the proposed method. The integration of GPS and accelerometer can be used as a reliable tool to characterize the dynamic behavior of large structures such as suspension bridges undergoing environmental loads.

Loading and fracture response of CFRP-to-steel adhesively bonded joints with thick adherents – Part I: Experiments

There is a gap in the existing standardized testing procedures (ASTM and ISO) for evaluating the stiffness and strength of composite-to-metal adhesively bonded joints. Thus, there is much effort made in this field towards understanding the impact of the geometric parameters to the loading and fracture response of such joints, but limited to joints with thin adherents. On this basis, the present work provides an experimental parametric study of adhesively bonded Single Lap Joint geometries between thick dissimilar adherents. For this purpose, mild steel and CFRP laminates have been considered as the structural adherent materials. Seven SLJ geometries have been considered for fabrication and experimental testing. The SLJ specimens were tested under a uni-axial tensile quasi-static displacement. Strain gage sensors were used, in order to study their potential for monitoring damage initiation occurring in the adhesive bondline. The global response was recorded and corresponding results are presented. It was concluded that for the current material systems and geometries tested, the effect of the adhesive thickness and stiffness ratio is negligible compared to the effect of the overlap length to the stiffness and strength of the joints. The results can be utilized for analysis and design purposes of practical adhesive joints.

A new efficient procedure to solve the nonlinear dynamics of a cracked rotor

The dynamic analysis of a cracked rotor with a breathing crack leads to the formulation of a nonlinear time-dependent problem. For the simple Jeffcott rotor model, this problem has been addressed using numerical integration methods that are very time consuming. A first simplification can be done assuming that the stiffness is a time-dependent function obtained with the quasi-static displacements of the shaft. In this study, we propose a new procedure to analyze the nonlinear dynamic of such a kind of cracked rotors using an iterative technique that transforms the full nonlinear problem in a succession of time-dependent linear ones. We show with different examples that this technique virtually gives the same results as the classical integration methods, but being much more efficient and achieving a significant saving of computation time. The calculations using the proposed method are over a 100 times faster than the corresponding to integrate the full nonlinear problem, being very helpful in on-line crack identification procedures. Also, this analysis shows that, in cases for which the vertical whirl amplitude is greater than the shaft weight static deflection, the use of simplified methods based on the quasi-static stiffness matrix could not be adequate.

Dual-modulation fiber Fabry-Perot interferometer with double reflection for slowly-varying displacements

This Letter describes a dual-amplitude modulation technique incorporated into a double reflection extrinsic-type fiber Fabry-Perot interferometer to measure periodic, nonperiodic as well as quasi-static displacements. The modulation scheme simultaneously maintains the interference signal pair in quadrature and provides a reference signal for displacements inferior to a quarter of the source wavelength. The control and phase demodulation of the interferometer carried out via software enable quasi-real-time measurement and facilitates sensor alignment. The sensor system can be exploited in the low frequency range from 10(-3) to ∼500 Hz and has a resolution better than 2.2 nm, targeting applications in geophysics.