Force-displacement Model Research Articles

Eliminating the surface location from soft matter contact mechanics measurements

The material properties of soft materials can be measured with rheometers and tensile testing instruments whenever there exist few limitations on sample volume, fixturing and general sample preparation, where samples often need to be prepared specifically to work with the hardware of a given instrument. By contrast, indentation methods are well suited for measuring material properties when sample preparation and geometry are highly constrained, as is the case with living cells, confluent cell layers, tissue samples, hydrogel coatings or soft objects with defined shapes like contact lenses. For example, indentation can be performed directly on cells grown in a Petri dish, without modifying typical cell culture protocols or materials. However, the low elastic modulus of these soft materials make it extremely difficult to determine when an indentation instrument first makes contact with a sample, which is critically important to know if material properties are to be determined with confidence. Here, we present an analysis method that eliminates the need to identify when an instrument makes contact with a sample. The method recasts the traditional force–displacement models of contact mechanics in terms of the first derivative of applied normal force with respect to indenter position, which automatically removes the unknown point of contact. This approach enables the selection of appropriate theoretical models for a given data-set and allows the measurement of sample material properties with the only fitting parameter being the elastic modulus.

An investigation of dimensional scaling using cervical spine motion segment finite element models.

The paucity of experimental data for validating computational models of different statures underscores the need for appropriate scaling methods so that models can be verified and validated using experimental data. Scaling was investigated using 50th percentile male (M50) and 5th percentile female (F05) cervical spine motion segment (C4-C5) finite element models subject to tension, flexion, and extension loading. Two approaches were undertaken: geometric scaling of the models to investigate size effects (volumetric scaling) and scaling of the force-displacement or moment-angle model results (data scaling). Three sets of scale factors were considered: global (body mass), regional (neck dimensions), and local (segment tissue dimensions). Volumetric scaling of the segment models from M50 to F05, and vice versa, produced correlations that were good or excellent in both tension and flexion (0.825-0.991); however, less agreement was found in extension (0.550-0.569). The reduced correlation in extension was attributed to variations in shape between the models leading to nonlinear effects such as different time to contact for the facet joints and posterior processes. Data scaling of the responses between the M50 and F05 models produced similar trends to volumetric scaling, with marginally greater correlations. Overall, the local tissue level and neck region level scale factors produced better correlations than the traditional global scaling. The scaling methods work well for a given subject, but are limited in applicability between subjects with different morphology, where nonlinear effects may dominate the response.

Dynamic analysis of beam-soil interaction systems with material and geometrical nonlinearities

In this paper a Hybrid Domain Boundary Element Method is developed for the geometrically nonlinear dynamic analysis of inelastic Euler-Bernoulli beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on viscous inelastic Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse dynamic loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. A displacement based formulation is developed and inelastic redistribution is modelled through a distributed plasticity (fibre) approach. A uniaxial hysteretic law is considered for the evolution of the plastic part of the normal stress following the phenomenological hysteresis model, while hysteretic force-displacement model is also employed in order to describe the inelastic behaviour of the Winkler springs. Numerical integration over the beam cross sections is performed in order to resolve the hysteric parts of the stress resultants. Application of the boundary element technique yields a system of nonlinear Differential-Algebraic Equations, which are written in state-space form and solved by an incremental–iterative solution strategy. Numerical examples are worked out confirming the accuracy and the computational efficiency of the proposed beam formulation, as well as the significant influence of material and geometrical nonlinearities in the response of beam-soil interaction systems.

Arc-Surfaced Frictional Damper for Vibration Control in Container Crane

In this paper, a new arc-surfaced frictional damper (AFD) is proposed and its hysteretic behavior is experimentally studied. Then the device is applied to container crane based on a seesaw mechanism. The major advantage of the seesaw damping system is that the long tension cables can be utilized as bracing between the seesaw member and the portal legs to avoid compression and buckling of the cables. A simplified trilinear force-displacement model on the basis of experimental results is adopted to represent the hysteretic behavior of AFD. After that, seismic responses of container crane with and without dampers to four earthquakes are studied using nonlinear dynamic time-history analysis. Besides this system, a diagonal-brace-AFD system is studied for comparison. A method based on the displacement and energy dissipation ratio is proposed to find the optimum slip force for seesaw damping system. Performance of AFD control system is assessed though various parameters including displacement and maximum portal frame drift angle. Results prove a feasible application of AFD control system to absorb large amounts of seismic energy and significantly reduce the structural responses.

Dynamic response of flexible rockfall barriers under different loading geometries

Flexible steel barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible barriers is conventionally performed using full-scale field tests by dropping a weight onto the barriers in accordance with the European test standard ETAG 27. The weight typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. A rigid slab may load a barrier over a larger area and its effect has not been investigated. In this study, a calibrated three-dimensional finite-element model was developed to study the performance of vertically and horizontally orientated rockfall barriers under concentrated areal impact loads. A new bilinear force-displacement model was incorporated into the model to simulate the behavior of the energy-dissipating devices on the barriers. The effect of different weight geometries was studied by considering impacts by a rigid single spherical boulder and a rigid slab. Results reveal that areal loading induced by a rigid slab increases the loading on the barrier foundation by up to 40 % in both horizontally and vertically positioned barriers when compared to a concentrated load scenario with a single boulder. This indicates that barriers tested under the current test standard does not give the worst-case scenario in terms of foundation loads, and barrier designers should take into account the possible effect of increased foundation loads by reinforcing the barrier posts and/or increasing their spacing.

Vision-based deformation recovery for intraoperative force estimation of tool–tissue interaction for neurosurgery

PurposeIn microsurgery, accurate recovery of the deformation of the surgical environment is important for mitigating the risk of inadvertent tissue damage and avoiding instrument maneuvers that may cause injury. The analysis of intraoperative microscopic data can allow the estimation of tissue deformation and provide to the surgeon useful feedback on the instrument forces exerted on the tissue. In practice, vision-based recovery of tissue deformation during tool–tissue interaction can be challenging due to tissue elasticity and unpredictable motion.MethodsThe aim of this work is to propose an approach for deformation recovery based on quasi-dense 3D stereo reconstruction. The proposed framework incorporates a new stereo correspondence method for estimating the underlying 3D structure. Probabilistic tracking and surface mapping are used to estimate 3D point correspondences across time and recover localized tissue deformations in the surgical site.ResultsWe demonstrate the application of this method to estimating forces exerted on tissue surfaces. A clinically relevant experimental setup was used to validate the proposed framework on phantom data. The quantitative and qualitative performance evaluation results show that the proposed 3D stereo reconstruction and deformation recovery methods achieve submillimeter accuracy. The force–displacement model also provides accurate estimates of the exerted forces.ConclusionsA novel approach for tissue deformation recovery has been proposed based on reliable quasi-dense stereo correspondences. The proposed framework does not rely on additional equipment, allowing seamless integration with the existing surgical workflow. The performance evaluation analysis shows the potential clinical value of the technique.

Performance of Seismic Restrainer with SMA Springs for Sliding Isolation of Single-Layer Spherical Lattice Shells

The seismic response of a single-layer spherical lattice shell controlled by restorable sliding isolator is studied under different seismic excitations. The isolation system consists of flat steel-Teflon sliding isolators and superelastic SMA spring restrainers. The NiTi-SMA is used to fabricate helical spring for recentering control of the isolation system. In the first step of this investigation, the configuration scheme and functioning mechanism of a novel SMA spring restrainer are introduced briefly. Then, realistic mechanical behavior of large-scale superelastic NiTi helical spring is studied through a set of cyclic experimental tests. According to the obtained hysteresis loops, a mechanical model combining multilinear model and hysteresis model is developed to simulate the overall response of the SMA-based seismic restrainer. Besides, the sliding isolator is evaluated using a bilinear force-displacement hysteresis model. Finally, a 60 m span single-layer spherical lattice shell with substructure is modeled with finite element program. Nonlinear time history analyses of the controlled and uncontrolled lattice shell are performed considering multidimensional seismic inputs. The study shows that the seismic response of the controlled lattice shell can be effectively reduced by using isolation and control devices. Furthermore, the seismic response of the isolation system such as peak displacement and residual displacement can be effectively controlled by using the developed SMA spring restrainers.

A Phenomenological Model for Superelastic Shape Memory Alloy Helical Springs

Due to their capabilities of large recoverable deformation, energy dissipation and self-recovery, Nitinol superelastic shape memory alloy (SMA) helical springs can be used as base isolation components to protect isolated structures. In such applications, to design the specific isolation component which consists of SMA helical springs, it is essential to study the force-displacement relationship model of the SMA springs under cyclic loading. In this paper, two types of SMA springs are trained using Nitinol superelastic SMA wires. Based on the data of a series of cyclic loading tests, a phenomenological model is established to model the superelasticity or pseudoelasticity of the SMA springs. The developed model describes the force-displacement relationship of SMA springs subjected to general dynamic load. Comparative studies show that for the proposed phenomenological model, the simulation results of force-displacement relationship of the SMA springs agree very well with the experimental ones, which demonstrates the effectiveness of the proposed model.

Guided Impact Mitigation in 2D and 3D Granular Crystals

We simulate the dynamics of impacts on 1D, 2D and 3D arrays of metallic spheres in order to design novel granular protection systems. The dynamics of these highly organized systems of spheres, commonly called granular crystals, are governed by the contact law that describes how each particle interacts with the others. We use our recently developed force-displacement model of the dynamic compression of elastic-plastic spheres as the building block to investigate the response of systems comprised of metallic spheres to an impact. We first provide preliminary experimental results using a drop tower as validation of our numerical approach for 2D and 3D systems. We then use simulations of large periodic granular crystals in order to determine which particle properties govern the velocity of stress waves in these materials. We show that the properties of 1D systems can be scaled to predict the behavior of more complex 2D and 3D granular crystals. Because we can choose the material properties of each of the constituent particles and design how the particles are geometrically packed, we can leverage the heterogeneity of the system to create materials with unique properties such as anisotropic local stiffnesses and wave propagation velocities. We show that these materials allow us to design the dispersion and dissipation properties within the material in order to influence the propagation of a stress wave. Using these materials, we can therefore design protection systems or armor that directs damage away from sensitive parts or localizes damage to an unimportant area after impact from a projectile or a blast.

Bayesian uncertainty quantification and propagation for discrete element simulations of granular materials

Predictions in the behavior of granular materials using Discrete Element Methods (DEM) hinge on the employed interaction potentials. Here we introduce a data driven, Bayesian framework to quantify DEM predictions. Our approach relies on experimentally measured coefficients of restitution for single steel particle–wall collisions. The calibration data entail both tangential and normal coefficients of restitution, for varying impact angles and speeds of the bouncing particle. The parametric uncertainty in multiple Force–Displacement models is estimated using an enhanced Transitional Markov Chain Monte Carlo implemented efficiently on parallel computer architectures. In turn, the parametric model uncertainties are propagated to predict Quantities of Interest (QoI) for two testbed applications: silo discharge and vibration induced mass-segregation. This work demonstrates that the classical way of calibrating DEM potentials, through parameter optimization, is insufficient and it fails to provide robust predictions. The present Bayesian framework provides robust predictions for the behavior of granular materials using DEM simulations. Most importantly the results demonstrate the importance of including parametric and modeling uncertainties in the potentials employed in Discrete Element Methods.

Alternating current-gas metal arc welding for application to thin sheets

The metal transfer in alternating current-gas metal arc welding (AC-GMAW) was analyzed in order to predict the drop size. The effects of complex waveforms of the process, involving both the electrode positive (EP) and the electrode negative (EN) pulse regions, were investigated analytically. The force-displacement model was modified to predict the drop size in AC-GMAW. Experiments were conducted using different types of wires for validating the predicted results. The effect of EN pulse parameters on the drop size was modeled, eliminating the need for experimental trial and error. The drop size information can be used to predict the range of the joint gap that can be bridged effectively. The proposed technique was found to be equally applicable to both direct current-gas metal arc welding and P-GMAW.

Strain-rate-dependent model for the dynamic compression of elastoplastic spheres.

We present a force-displacement contact model for the compressive loading of elastoplastic spheres. This model builds from the well known Hertz contact law for elastic, quasistatic compression to incorporate a material's strain-rate-dependent plasticity in order to describe collisions between particles. In the quasistatic regime, finite-element analysis is used to derive an empirical function of the material properties. A Johnson-Cook strain rate dependence is then included into the model to study dynamic effects. We validate the model using split Hopkinson bar experiments and show that the model can accurately simulate the force-displacement response of strain-rate-dependent elastoplastic spheres during dynamic compression and unloading.

Single particle contact versus particle packing behavior: model based analysis of chemically modified glass particles

Smooth spherical micro glass particles are the reference particle system to demonstrate the correlation between single contacts and the particle packing properties. To investigate the influence of the van der Waals attraction force, the particles will be functionalized to obtain hydrophilic and hydrophobic surfaces. To remove the impurities and hydrophilize the particle surfaces a very strong oxidizing agent is used—the peroxymonosulfuric acid. In order to generate a hydrophobic glass surface, the process of silanization is applied. The comprehensive force displacement model of elastic-plastic and adhesive contacts are discussed. Therefore the model ‘stiff particles with soft contacts’ is used to quantify and compare the elastic-plastic contact properties. In this work, the particle contacts are experimentally investigated by means of atomic force microscopy (AFM), nanoindentation and shear tests. While the AFM and nanoindenter measurements are aimed to analyse single particle contacts, shear tests are used for particle packing studies. The fundamental challenge and question is addressed and answered: How do the micro mechanical material properties change when the glass surfaces are functionalized? Do we obtain the same behavior for the used micro glass particles when we compare the different methods?

Development and validation methodology of the Nuss procedure surgical planner

Surgical planners are used to achieve the optimal outcome for surgery. They are especially desired in procedures where a positive aesthetic outcome is the primary goal, such as the Nuss procedure which is a minimally invasive surgery for correcting pectus excavatum (PE) – a congenital chest wall deformity which is characterized by a deep depression of the sternum. The Nuss procedure consists of placement of a metal bar(s) underneath the sternum, thereby forcibly changing the geometry of the ribcage. Because of the prevalence of PE and the popularity of the Nuss procedure, the demand to perform this surgery is greater than ever. Therefore, a Nuss procedure surgical planner is an invaluable planning tool ensuring an optimal physiological and aesthetic outcome. We propose the development and validation of the Nuss procedure planner. First, a generic model of the ribcage is developed. Then, the computed tomography (CT) data collected from actual patients with PE is used to create a set of patient-specific finite element models (FEM). Based on finite element analyses (FEA) a force–displacement data set is created. This data is used to train an artificial neural network (ANN) to generalize the data set. In order to evaluate the planning process, a methodology which uses an average shape of the chest for comparison with results of the Nuss procedure planner is developed. Haptic feedback and inertial tracking is also implemented. The results show that it is possible to utilize this approximation of the force–displacement model for a Nuss procedure planner and trainer.

Electro-Thermal Response of 2G HTS Coated Conductors Subjected to Current Pulses

Triangular-shaped current pulses were used to obtain the electrical characteristics ( E-I curves) of second-generation high-temperature superconductor coated conductors above their critical current. The dependence of these E-I curves on magnetic field was also characterized (up to 150 mT). Current pulses with rising rates of hundreds of amperes per millisecond were used to minimize the heat generated in the samples. When a transverse magnetic field is applied before the current pulse, an inductive voltage is measured during the rise of the current, whose origin is explained by the presence of an asymmetric flux profile in the high-temperature superconductor layer. Results from finite-elements calculations based on a force-displacement model of the flux lines reproduced this inductive voltage, as well as the rise in samples temperature.

Experimental Study on Stiffness of Dougong in Chinese Ancient Buildings

As an important structural member in Chinese timber structure system, Dougong has an excellent capability in earthquake resistance. Through low cyclic loading experiment of single Dougong, two Dougongs and four Dougongs, the degrading rule of lateral stiffness of Dougong was studied. According to that, the hysteresis curve and skeleton curve of force –displacement were researched and the formula of resilience model and mechanical model were established. The experiment data show that slippage is the main deformation of Dougong. Energy dissipation due to frictional slippage is an important reason for the excellent seismic behavior of ancient wooden structure. The shape of hysteretic loops of Dougong assumes to be parallelogram. Plump area of hysteretic loop accounts for its excellent energy dissipation performance. The mechanic model of Dougong belongs to linear strengthen elastic-plastic model. Both the fitting equation of force-displacement and resilience model reflect stiffness changes of Dougong. These basic theories provide a theoretical basis for the study on the seismic performance, repair and strengthening of ancient wooden structures.

CONFIRMATION OF PSEUDODYNAMIC TECHNIQUE FOR BIDIRECTIONAL LOADING

R eliable prediction of inelastic structural performance during an earthquake is a difficult task because the inelastic behavior of a structure is very complex. Although various analytical methods are available to predict the inelastic response of a structure, the accuracy of the response prediction is limited by the assumptions used in the mathematical description of the force-displacement model. Therefore, experimental methods remain the most reliable means to evaluate the inelastic behavior of a structural system. The pseudodynamic test method has been developed for evaluating the inelastic seismic performance of large-scale structural specimens, which usually cannot be tested by conventional methods, such as quasi-static tests, forced-vibration tests, and shaking table tests. In fact, this method has been applied to many actual seismic performance tests.1–3 Thus, it has become a widely used testing method in a structural laboratory. In general, a reliable test result can be achieved if the test setup is properly adjusted, and the pseudodynamic error is controlled within a certain limit.4–9

Optimizing the shape of a bumper beam section considering pedestrian protection

This paper presents a design technique to optimize the shape of a vehicle bumper beam that satisfies both the safety requirements for a front rigid-wall impact and the regulations protecting pedestrians from lower leg injuries caused by bumper impacts. An intermediate response surface modeling (IRSM) technique was introduced to approximate the non-linear force-displacement curves obtained from the front impact analysis of a vehicle bumper. The accuracy of the IRSM model was tested by comparing its results with those of the non-linear finite element analysis. The maximum displacement error between the two models did not exceed 3%. Using pedestrian impact analyses based on the experimental arrangement of the Plackett-Burman design, the approximate functions describing the response values acting on the lower legs were calculated. The shape of the bumper beam was optimized by integrating the IRSM with the force-displacement model and the approximate functions on lower leg impact. The optimization results satisfied safety regulations on the maximum allowable displacement of the vehicle bumper, and also the regulations protecting pedestrians from lower leg injuries caused by bumper impacts.

힘-변위 모델을 이용한 펄스 GMAW의 해석

In order to determine the One-Drop One-Pulse(ODOP) condition of the pulsed gas metal arc(GMA) welding, the drop detaching phenomenon during the peak time is investigated using the force-displacement model. The drop detaching criterion is established based on the displacement of the pendant drop, and the forces exerted on the drop are calculated using the Modified Force Balance Model(MFBM). The effects of wire melting on the drop size and force are included in the force-displacement model. While the peak current has most significant effects on the drop detaching time, the initial drop mass prior to the peak time also influences drop transfer. The calculated results show good agreements with the experimental data, which implies that the ODOP condition can be predicted using the force-displacement method.

Force–displacement model for analysis of pulsed-GMAW

A force–displacement model (FDM) is introduced in this work to analyse pulsed gas metal arc welding (GMAW). The drop detaching criterion is established based on the displacement of the pendant drop instead of the previous force balance criterion. The displacement of the drop is calculated by integrating the acceleration of the drop, and the force exerted on the drop is predicted using the modified force balance model coupled with wire melting. When the peak current, base current and time of pulsed-GMAW are given, the peak time for the one-drop one-pulse condition is determined using the FDM. While the peak current has the most significant effect on drop detachment, the initial drop mass prior to the peak time also influences the drop transfer. The FDM is applied to the dc as well as pulsed-GMAW, and the calculated results show good agreement with the experimental data.