Force-displacement Data Research Articles

Low force, high noise: Isolating indentation forces through autocorrelation analysis

Simple contact models are often used in combination with indentation measurements to determine the elastic moduli of materials in the limits of small strain and linear-elastic deformation. However, for soft biological samples these limits can occur at indentation forces comparable to detection noise from the instrument. Here we describe a data analysis method for determining the moduli of soft materials when the measured forces are comparable to the level of instrumental noise; relationships between the force and displacement autocorrelation functions enable the elastic modulus to be determined from indentation curves with large uncertainties in the measured force. In simulations of force-displacement indentation data using the Hertz and Winkler foundation contact models with added noise, we find the autocorrelation analysis enables the accurate measurement of known elastic moduli, even when the noise-to-signal ratio is large throughout an indentation experiment. We also find that this analysis method is more accurate at measuring the modulus at high noise levels compared to directly fitting the model curve to the data. We further validate this approach experimentally by testing a series of polyacrylamide hydrogel slabs prepared within a wide polymer concentration range, finding the measured modulus to be in agreement with the moduli determined through rheological characterization.

Prediction of displacement in the equine third metacarpal bone using a neural network prediction algorithm

Bone is a nonlinear, inhomogeneous and anisotropic material. To predict the behavior of bones expert systems are employed to reduce the computational cost and to enhance the accuracy of simulations. In this study, an artificial neural network (ANN) was used for the prediction of displacement in long bones followed by ex-vivo experiments. Three hydrated third metacarpal bones (MC3) from 3 thoroughbred horses were used in the experiments. A set of strain gauges were distributed around the midshaft of the bones. These bones were then loaded in compression in an MTS machine. The recordings of strains, load, load exposure time, and displacement were used as ANN input parameters. The ANN which was trained using 3,250 experimental data points from two bones predicted the displacement of the third bone (R2 ≥ 0.98). It was suggested that the ANN should be trained using noisy data points. The proposed modification in the training algorithm makes the ANN very robust against noisy inputs measurements. The performance of the ANN was evaluated in response to changes in the number of input data points and then by assuming a lack of strain data. A finite element analysis (FEA) was conducted to replicate one cycle of force-displacement experimental data (to gain the same accuracy produced by the ANN). The comparison of FEA and ANN displacement predictions indicates that the ANN produced a satisfactory outcome within a couple of seconds, while FEA required more than 160 times as long to solve the same model (CPU time: 5 h and 30 min).

Effect of a continuous epitendinous suture as adjunct to three-loop pulley and locking-loop patterns for flexor tendon repair in a canine model.

To evaluate the effect of combining a continuous epitendinous suture with three-loop pulley (3LP) and locking-loop (LL) core patterns for flexor tendon repair. Ex vivo biomechanical study. Seventy-two cadaveric superficial digital flexor musculotendon (SDFT) units. Tendons were divided into four groups (n = 18/group). After sharp transection, SDFT were repaired with 3LP, LL, 3LP + epitendinous (E), or LL + E suture patterns. After preloading, repaired constructs were tested to failure. Video data acquisition allowed evaluation of failure mode and quantitation of gap formation. Yield, peak, and failure force were measured from force-displacement data. Significance was set at P < .05. Mode of failure did not differ between repairs with or without an epitendinous suture (P = .255). Gap formation was best prevented with 3LP compared with LL when used alone (P = .001). Mean yield force for 3LP, LL, 3LP + E, and LL + E were 91.4 N ± 25.4, 61.3 N ± 18.4, 195.2 N ± 66.0, 165.3 N ± 46.8, respectively. Tenorrhaphies combined with an epitendinous suture achieved higher yield (P < .0001), peak (P < .0001), and failure forces (P < .0001), without gapping between tendon ends. Addition of an epitendinous suture eliminated gapping between tendon ends until failure and increased resistance to loads tolerated at the repair site. The addition of an epitendinous suture may increase the strength of tendon repairs and resistance to gap formation over core suture use alone. The influence of epitendinous suture placement on tendinous healing and blood supply warrants in-vivo testing.

Sampling-dependent systematic errors in effective harmonic models

Effective harmonic methods allow for calculating temperature dependent phonon frequencies by incorporating the anharmonic contributions into an effective harmonic Hamiltonian. The systematic errors arising from such an approximation are explained theoretically and quantified by density functional theory based numerical simulations. Two techniques with different approaches for sampling the finite temperature phase space in order to generate the force-displacement data are compared. It is shown that the error in free energy obtained by using either can exceed that obtained from 0 K harmonic lattice dynamics analysis which neglects the anharmonic effects.

Nonlinear contact mechanics for the indentation of hyperelastic cylindrical bodies

The mechanical properties of biological materials are commonly found through the application of Hertzian theory to force-displacement data obtained through micro-indentation techniques. Due to their soft nature, biological specimens are often subjected to large indentations, resulting in a nonlinear deformation behavior that can no longer be accurately described by Hertzian contact. Useful models for studying the large deformation response of cylindrical specimens under indentation are not readily available, and the morphologies of biological materials are often closer to cylinders than spheres (e.g., cellular processes, fibrin, collagen fibrils, etc.). In this study, a computational model is used to analyze the large deformation indentation of an incompressible hyperelastic cylinder in order to provide a generalized formulation that can be used to extract mechanical properties from indentation into soft cylindrical bodies. The effects of specimen size and indentation depth are examined in order to quantify the deformation at which the proposed force-displacement relationship remains accurate.

Hyperelastic modeling of sino-nasal tissue for haptic neurosurgery simulation

The aim of this research was to provide a simple yet realistic model of the sino-nasal tissue as a major requirement for developing more efficient endoscopic neurosurgery simulation systems. Ex-vivo indention tests were performed on the orbital floor soft tissue of four sheep specimens. The resulting force-displacement data was incorporated into an inverse finite element model to obtain the hyperelastic mechanical properties of the tissue. Material characterization was performed for Polynomial, Yeoh, Mooney-Rivlin and Neo-Hookean hyperelastic models, using a Sequential Quadratic Programming algorithm. Experimental results indicated a relatively large elastic deformation, up to 6mm, during indentation test with a considerable nonlinearity in the force-displacement response. All hyperelastic models could satisfy the convergence criteria of the optimization procedure, with the highest convergence rate and a close fittings accuracy associated with the Yeoh hyperelastic model. The initial guess of the material constants was found to affect the number of iterations before converging, but not the optimization results. The normalized mean square errors of fitting between the model and experimental curves were obtained as 2.39%, 4.26% and 4.65% for three sheep samples, suggesting that the Yeoh model can adequately describe the typical hyperelastic mechanical behavior of the sino-nasal tissue for surgery simulation.

The Use of Genetic Algorithms to Calibrate Johnson–Cook Strength and Failure Parameters of AISI/SAE 1018 Steel

Johnson–Cook (JC) strength and failure models have been widely used in finite element analysis (FEA) to solve a variety of thermo-mechanical problems. There are many techniques to determine the required JC parameters; however, a best practice to obtain the most reliable JC parameters has not yet been proposed. In this paper, a genetic-algorithm-based optimization strategy is proposed to calibrate the JC strength and failure model parameters of AISI/SAE 1018 steel. Experimental data were obtained from tensile tests performed for different specimen geometries at varying strain rates and temperatures. FEA was performed for each tensile test. A genetic algorithm was used to determine the optimum JC parameters that best fit the experimental force-displacement data. Calibrated JC parameters were implemented in FEA to simulate the impact tests of standard V-notch Charpy bars to verify the damage mechanism in the material. Considering good agreement of the experimental and FEA results, the current strategy is suggested for calibration proposes in other kind of materials in which plastic behavior could be represented by the JC strength and failure models.

Stiffness and energy storage characteristics of energy storage and return prosthetic feet.

Mechanical properties of prosthetic feet can significantly influence amputee gait, but how they vary with respect to limb loading and orientation is infrequently reported. The objective of this study is to measure stiffness and energy storage characteristics of prosthetic feet across limb loading and a range of orientations experienced in typical gait. This study included mechanical testing. Force-displacement data were collected at combinations of 15 sagittal and 5 coronal orientations and used to calculate stiffness and energy storage across prosthetic feet, stiffness categories, and heel wedge conditions. Stiffness and energy storage were highly non-linear in both the sagittal and coronal planes. Across all prosthetic feet, stiffness decreased with greater heel, forefoot, medial, and lateral orientations, while energy storage increased with forefoot, medial, and lateral loading orientations. Stiffness category was proportional to stiffness and inversely proportional to energy storage. Heel wedge effects were prosthetic foot dependent. Orientation, manufacturer, stiffness category, and heel wedge inclusion greatly influenced stiffness and energy storage characteristics. These results and an available graphical user interface tool may help improve clinical prescriptions by providing prosthetists with quantitative measures to compare prosthetic feet.

Medially-stabilized total knee arthroplasty does not alter knee laxity and balance in cadaveric knees.

Instability after total knee arthroplasty (TKA) can lead to suboptimal outcomes and revision surgery. Medially-stabilized implants aim to more closely replicate normal knee motion than other implants following TKA, but no study has investigated knee laxity (motion under applied loads) and balance (i.e., difference in varus/valgus motion under load) following medially-stabilized TKA. The primary purposes of this study were to investigate how medially-stabilized implants change knee laxity in non-arthritic, cadaveric knees, and if it produces a balanced knee after TKA. Force-displacement data were collected on 18 non-arthritic cadaveric knees before and after arthroplasty using medially-stabilized implants. Varus-valgus and anterior-posterior laxity and varus-valgus balance were compared between native and medially-stabilized knees at 0°, 20°, 60°, and 90° under three different loading conditions. Varus-valgus and anterior-posterior laxities were not different between native and medially-stabilized knees under most testing conditions (p ≥ 0.068), but differences of approximately 2° less varus-valgus laxity at 20° of flexion and 4 mm more anterior-posterior laxity at 90° were present from native laxities (p < 0.017) Medially-stabilized implant balance had ≤1.5° varus bias at all flexion angles. Future studies should confirm if the consistent laxity afforded by the medially-stabilized implant is associated with better and more predictable postoperative outcomes. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:335-349, 2019.

A comparative study of mode I delamination behavior of unidirectional glass fiber-reinforced polymers with epoxy and polyurethane matrices using two methods

The mode I delamination behavior of a unidirectional glass-fiber reinforced polymer with a prototype elasto-plastic polyurethane matrix (GF/PU) was investigated and compared with that of glass/epoxy (GF/EP) using double cantilever beam specimens. Fracture resistance was assessed using experimental data based on the strain energy release rate (ERR), G, calculated by means of the modified compliance calibration, and the J-integral, calculated using the applied force and arm rotations measured by digital image correlation. The fracture energies given by the two methods differed by ∼5%. In both systems large scale bridging was observed and fracture resistance at initiation and steady state was about 4 times greater in GF/PU and correlated to adhesive failure in GF/EP and cohesive in GF/PU. Since the fiber sizing was the same, the higher ERR of GF/PU was attributed to strong glass/PU interface allowing higher local matrix strains and larger fiber bundles to develop. Traction-separation relations were determined by the direct and an indirect method using Fiber Bragg Grating sensors to construct numerical models to simulate the delamination process. The simulated force-displacement and R-curve data were in good agreement with experiments.

One-time determination of 20 material parameters in a strain-compensated constitutive model and its application in extrusion for an Al-Zn-Mg thin-walled profile

A reasonable constitutive model is the key for accurate numerical simulation of extrusion process of aluminum alloy profiles. In this work, 20 material parameters in a fourth-order strain-compensated constitutive model of an Al-Zn-Mg alloy were determined by the inverse analysis method. Firstly, taking the minimization of shape error of specimens under different compression extents (10–60%) at the temperature of 475 °C and the strain rate of 1 s−1 as the optimization objective, the friction coefficient in hot compression test was determined by inverse analysis. Results showed that the friction coefficient was 0.031 and the global error was merely 1.001%, which demonstrated the practical lubrication condition between specimen and tool head could be reflected by the acquired friction coefficient. Then, based on the obtained friction coefficient, the inverse analysis was also used to identify 20 unknown material parameters in the fourth-order strain-compensated constitutive model at once by minimizing the difference between predicted and experimental force-displacement data. The predicted force-displacement curves matched the experimental ones well with the global error of only 6.07%. Finally, the developed constitutive model was applied in simulating the porthole and piercing extrusion for a hollow thin-walled profile and corresponding verified experiments were also carried out.

Data-Driven Elasticity Imaging Using Cartesian Neural Network Constitutive Models and the Autoprogressive Method.

Quasi-static elasticity imaging techniques rely on model-based mathematical inverse methods to estimate mechanical parameters from force-displacement measurements. These techniques introduce simplifying assumptions that preclude exploration of unknown mechanical properties with potential diagnostic value. We previously reported a data-driven approach to elasticity imaging using artificial neural networks (NNs) that circumvents limitations associated with model-based inverse methods. NN constitutive models can learn stress-strain behavior from force-displacement measurements using the autoprogressive (AutoP) method without prior assumptions of the underlying constitutive model. However, information about internal structure was required. We invented Cartesian NN constitutive models (CaNNCMs) that learn the spatial variations of material properties. We are presenting the first implementation of CaNNCMs trained with AutoP to develop data-driven models of 2-D linear-elastic materials. Both simulated and experimental force-displacement data were used as input to AutoP to show that CaNNCMs are able to model both continuous and discrete material property distributions with no prior information of internal object structure. Furthermore, we demonstrate that CaNNCMs are robust to measurement noise and can reconstruct reasonably accurate Young's modulus images from a sparse sampling of measurement data. CaNNCMs are an important step toward clinical use of data-driven elasticity imaging using AutoP.

Determination of Mechanical Properties of Polymer Interphase Using Combined Atomic Force Microscope (AFM) Experiments and Finite Element Simulations

In polymer nanocomposites (PNCs), the physical and chemical interactions at the polymer matrix–filler interface lead to local variations in polymer properties over a substantial “interphase” region in the vicinity of the interface. Characterization of mechanical properties in the polymer interphase region is essential for informed modeling and design of advanced PNCs. Direct contact measurement of the mechanical properties in the interphase region has been performed via high-resolution scanning probe nanoindentation experiments on model polymer–substrate samples. However, the force–displacement data from indentation experiments are affected by the interaction of the elastic stress field with the substrate, which limits determination of the interphase properties close to the polymer–substrate boundary. To extract the mechanical properties of the interphase from experimentally measured data, three-dimensional finite element analysis (3D FEA) models are developed in this study to simulate the indentation exp...

Anelasticity Influence of Wire Rope on the Calculation of Freight Ropeway Bearing Cable

The force-displacement data during loading and unloading process is obtained by wire rope stretch experiment, which includes 7 different diameters ropes. Based on the data, deformation curves of elastic extension are established. It is shown that the loading and unloading curves compose of the elastic hysteresis loop because the wire rope during unloading shows obvious anelasticity. Analysing the elastic deformation curve characteristics, the values of loading and unloading curve parameters are provided by fitting the experimental data. The loading elastic modulus is constant independent of initial load, and the unloading elastic modulus is non-linear which is related with the maximum load. The elastic modulus is applied to the calculation of freight ropeway bearing cable. Compared the result with the actual project data, it shows that the method considering the wire rope anelasticity can improve the precision of bearing cable calculation.

An empirical approach for nonlinear modelling and deformation capacity assessment of RC columns with plain bars

This study proposes an empirical-based approach for the nonlinear modelling and deformation capacity assessment of flexure-controlled Reinforced Concrete (RC) columns with plain bars, providing an estimate of the expected post-elastic response backbone through formulations based on regression of experimental data. To this end, a database of tests on RC columns with plain bars is collected from literature. The specimens have different axial load, material properties, geometry, and longitudinal and transverse reinforcement ratio. Force-displacement data are collected and processed for each specimen. The backbone of the experimental base moment-chord rotation response is evaluated for each test, and characteristic points corresponding to yielding, maximum, “ultimate”, and zero resistance conditions are identified. Potential predictors are investigated and empirical predictive equations are proposed for these points, based on a statistical analysis of data. Predictions of the proposed model are compared with literature and code provisions.

Additive manufacturing and computed tomography of bio-inspired anchorage systems

Using additive manufacturing, computer-assisted models can be rapidly transformed into physical objects. When combined with X-ray imaging, minimally attenuating three-dimensional (3D) printed objects can allow for enhanced insight into soil processes, whether this is through the design of novel testing devices, prototypes or soil surrogates. In this study, this methodology is exploited to investigate the pullout mechanics of bio-inspired anchors. The purpose of this paper is twofold: (1) to demonstrate the value of the union of 3D printing and X-ray computed tomography (CT) technologies; and (2) to evaluate the effect of geometry on the pullout behaviour of plant root-inspired anchor elements. The results of the experimental investigations demonstrate how X-ray CT was used to effectively capture the evolution of soil behaviour during the uplift of three unique 3D printed prototypes. The analysis of the soil response was completed from both a global perspective, through an interpretation of the force–displacement data, and a local perspective, through an image correlation investigation of image sets at sequential displacement increments. The results provide insight into not only the means to design a more optimised anchor element, but also the efficacy of additive manufacturing-assisted X-ray tomography in investigating geotechnical problems.

Un enfoque de los Formatos Común y Conciso para la construcción de una curva maestra para generar valores de extensión de grieta en probetas C(T)

La construcción de curvas J-R para un material dúctil, acorde con la Norma ASTM E1820-15 (2015), requiere de información del proceso de extensión estable de grieta. Según la Norma, la curva de resistencia puede ser obtenida de un ensayo con solo una probeta, en el cual el tamaño de grieta es medido simultáneamente con fuerza y desplazamiento por los métodos de cambios de flexibilidad, caída de potencial, y normalización. Basándose en los Formatos Común y Conciso, Donoso y Landes desarrollaron la “ley de crecimiento de grieta” y el “método del intercepto” como alternativas para obtener tamaños de grieta de un ensayo que exhibe extensión estable de grieta, pero del cual se dispone solo de datos fuerza-desplazamiento, y tamaños de grieta inicial y final. Ambos métodos alternativos se ven complementados por la construcción de una curva maestra, basada en estos Formatos, aplicada a probetas C(T) en las cuales los valores experimentales de extensión de grieta son insuficientes para producir una curva J-R válida.

Mode I traction-separation measured using rigid double cantilever beam applied to structural adhesive

ABSTRACTAdhesive joining facilitates the development of multi-material vehicle structures; however, widespread adoption requires material properties to characterize adhesive joints for implementation in finite element (FE) models. Specifically, modeling adhesive joints using the cohesive zone method requires measuring the Mode I traction-separation response, which currently requires multiple tests. To address this need, a new method to determine the Mode I response was developed using the Rigid Double Cantilever Beam (RDCB) test, where the steel adherend geometry was designed to ensure high stiffness compared to structural epoxy adhesives. The samples were tested in tension with displacements measured from high-resolution imaging of the test. A new analysis method was developed with resulting Mode I traction-separation response within the expected range for this structural adhesive. The analysis was verified using a FE model of the test and compared to Tapered Double Cantilever Beam test data. Importantly, the predicted force-displacement response from the FE model, using the measured traction-separation curve, compared well to the measured force-displacement data. The proposed RDCB test demonstrated the ability to determine the Mode I response of a toughened structural adhesive using a single test, the results of which can then be readily implemented into FE simulations.

Determination of in-situ engineering properties of soil using an inverse solution technique and limited field tests

The goal of this research is to develop a response surface based inverse solution technique to determine in-situ engineering properties of soil for use in mobility and traction prediction models from the force displacement data generated by a cone penetrometer device. The nonlinear elasto-plastic behavior of soil was characterized by a six-parameter constitutive model – two elastic parameters (i.e., bulk modulus, K and the Poisson’s ratio, υ), three plastic parameters (i.e., angle of internal friction φ, cohesion c, and soil hardening parameter λ), and one soil physical condition parameter (i.e. initial void ratio, e∗). Soil failure was represented by the Drucker-Prager yield criterion and associated flow rule. LS-DYNA FEM software package was used to model the soil-cone interaction problem. FEM simulations were conducted for a set of soil properties properly selected within the defined parameter space. The analysis of FEM simulations indicated that the cone penetration force-displacement curves could be represented by two piecewise smooth functions – a parabola followed by a straight line. The coefficients of these two curves were used to create fourth order response surfaces using a stepwise multiple linear regression technique. The results showed both cohesion and soil hardening parameter could be predicted using this methodology.

Estimation of the Young's moduli of fresh human oropharyngeal soft tissues using indentation testing.

Finite element (FE)-based biomechanical simulations of the upper airway are promising computational tools to study abnormal upper airway deformations under obstructive sleep apnea (OSA) conditions and to help guide minimally invasive surgical interventions in case of upper airway collapse. To this end, passive biomechanical properties of the upper airway tissues, especially oropharyngeal soft tissues, are indispensable. This research aimed at characterizing the linear elastic mechanical properties of the oropharyngeal soft tissues including palatine tonsil, soft palate, uvula, and tongue base. For this purpose, precise indentation experiments were conducted on freshly harvested human tissue samples accompanied by FE-based inversion schemes. To minimize the impact of the probable nonlinearities of the tested tissue samples, only the first quarter of the measured force-displacement data corresponding to the linear elastic regime was utilized in the FE-based inversion scheme to improve the accuracy of the tissue samples' Young's modulus calculations. Measured Young's moduli of the oropharyngeal soft tissues obtained in this study are presented. They include first estimates for palatine tonsil tissue samples while measured Young's moduli of other upper airway tissues were obtained for the first time using fresh human tissue samples.