Force-deflection Data Research Articles

Comparison of small female PMHS thoracic responses to scaled response corridors in a frontal hub impact

Objective The purpose of this study was to generate biomechanical response corridors of the small female thorax during a frontal hub impact and evaluate scaled corridors that have been used to assess biofidelity of small female anthropomorphic test devices (ATDs) and human body models (HBMs). Methods Three small female postmortem human subjects (PMHS) were tested under identical conditions, in which the thorax was impacted using a 14.0 kg pneumatic impactor at an impact velocity of 4.3 m/s. Impact forces to PMHS thoraces were measured using a load cell installed behind a circular impactor face with a 15.2 cm diameter. Thoracic deflections were quantified using a chestband positioned at mid-sternum. Strain gages installed on the ribs and sternum identified fracture timing. Biomechanical response corridors (force-deflection) were generated and compared to scaled small female thoracic corridors using a traditional scaling method (TSM) and rib response-based scaling method (RRSM). A BioRank System Score (BRSS) was used to quantify differences between the small female PMHS data and both scaled corridors. Results Coefficients of variation from the three small female PMHS responses were less than 2% for peak force and 7% for peak deflection. Overall, the scaled corridor means determined from the TSM and RRSM were less than two standard deviations away from the mean small female PMHS corridors (BRSS < 2.0). The RRSM resulted in smaller deviation (BRSS = 1.1) from the PMHS corridors than the TSM (BRSS = 1.7), suggesting the RRSM is an appropriate scaling method. Conclusions New small female PMHS force-deflection data are provided in this study. Scaled corridors from the TSM, which have been used to optimize current safety tools, were comparable to the small female PMHS corridors. The RRSM, which has the great benefit of using rib structural properties instead of requiring whole PMHS data, resulted in better agreement with the small female PMHS data than the TSM and deserves further investigation to identify scaling factors for other population demographics.

Thermally modified (TM) beech wood: compression properties, fracture toughness and cohesive law in mode II obtained from the three-point end-notched flexure (3ENF) test

Abstract The fracture properties of thermally modified beech (Fagus sylvatica) wood (TMW) at 180° and 200°C were evaluated in mode II using the three-point end-notched flexure (3ENF) scheme assisted by three-dimensional (3D) stereovision equipment for obtaining displacements and strains. The compliance-based beam method (CBBM) provided the strain energy release rates (G II) of TMW and cohesive laws for both native wood (W) and TMW. Based on the CBBM and equivalent crack length approach (ECLA), G II was obtained directly from the force-deflection data. The thermal modification (TM) process reduced the compressive strength by 4.4% and increased the compressive elastic modulus by 38.3%, whereas G II was reduced substantially by 40.8% and 67.9% at TM180°C and TM200°C, respectively. TM also increased wood brittleness that was visible on the displacement slip reduction. The resulting mean cohesive models can be used for numerical analyses. The fracture properties of TMW have to be taken into consideration for constructional wood application, when cyclic loading may lead to microcracking and material fatigue.

Initial estimation of the in vivo material properties of the seated human buttocks and thighs

On average, people are sedentary for 70% of the day, either seated or lying down. Of particular interest for this work is the seated posture; while seated the buttocks and thigh tissues experience loading for prolonged periods of time. When modeling human body interactions with seating devices and in the design of these devices, it is necessary to appropriately model the material characteristics of the soft tissue in the thigh and buttock areas. Thus, there is a pressing need for in vivo, experimentally measured data that describe the mechanical behavior of the soft tissue within the buttocks and thigh regions of humans in the seated posture. We developed an innovative experimental set-up to gather in vivo force–deflection data for both men and women in six regions located along the buttocks and thighs. Then, using anatomical measures, cadaver measures, and reported literature on regional tissue thickness, the data were converted to normal stress and strain curves. Next, these curves were described using the Mooney–Rivlin material model. Finally, best-fit mechanical parameters were reported, along with the original force–deflection data. Results indicated that, in general, the male tissue differed from female tissue, and that the mechanical properties differed between regions. Thus, when developing computer models that represent the human body, different material properties should be considered for men and women. Furthermore, appropriate properties should be used for the body region being evaluated. These data are unique in that they are quantified in vivo, represent the seated body position, and include multiple regions for both men and women. The material properties presented in this work will lead to improved numerical models, and consequently improved device design.

A procedure for determining parameters of a simplified ligament model

A previous mathematical model of ligament force-generation treated their behavior as a population of collagen fibres arranged in parallel. When damage was ignored in this model, an expression for ligament force in terms of the deflection, x, effective stiffness, k, mean collagen slack length, μ, and the standard deviation of slack lengths, σ, was obtained. We present a simple three-step method for determining the three model parameters (k, μ, and σ) from force-deflection data: (1) determine the equation of the line in the linear region of this curve, its slope is k and its x -intercept is -μ; (2) interpolate the force-deflection data when x is -μ to obtain F0; (3) calculate σ with the equation σ=2πF0/k.Results from this method were in good agreement to those obtained from a least-squares procedure on experimental data – all falling within 6%. Therefore, parameters obtained using the proposed method provide a systematic way of reporting ligament parameters, or for obtaining an initial guess for nonlinear least-squares.

On the determination of the ductile to brittle transition temperature from small punch tests on Grade 91 ferritic-martensitic steel

The exposure of structural materials to the environment in nuclear power plants leads to aging through thermal and/or irradiation effects. One of the consequences of this aging is the shift of the ductile to brittle transition temperature (DBTT) towards higher temperatures. Characterising the aging of structural materials is therefore a safety relevant topic especially in the context of long term operation of nuclear plants.For testing in service materials and to reduce the health risks and costs associated with handling of irradiated materials miniature testing techniques are being developed. The small punch (SP) technique is one of these methods. In a tensile/fracture SP test, a punch with a hemispherical tip is pushed with a constant displacement rate through the center of a small cylindrical disk specimen.A series of tensile SP tests on the ferritic/martensitic steel Gr. 91 at two different displacement rates show no impact of the displacement rate on the DBTT. A new method using fracture energies normalized to the maximum force for deriving the DBTT from force-deflection data is presented.Post-test analysis by means of X-ray computed tomography is used for deriving the DBTT from fracture strains. Both methods give consistent values for the transition temperature. However, the DBTT determined in this study is higher than what can be found in the literature. Supplementary tests indicate that the punch diameter has an effect on the SP defined DBTT.

Comparison of Q3s ATD Biomechanical Responses to Pediatric Volunteers

Objective: The biofidelity of pediatric anthropomorphic test devices (ATDs) continues to be evaluated with scaled-down adult data, a methodology that requires inaccurate assumptions about the likeness of biomechanical properties of children and adults. Recently, evaluation of pediatric ATDs by comparison of pediatric volunteer (PV) data has emerged as a valuable and practical alternative to the use of scaled adult data. This study utilized existing PV data to evaluate a 3-year-old side impact ATD, the Q3s. Though ATDs have been compared to volunteer responses in frontal impacts, this study is the first to extend ATD-PV comparison methods to the Q3s ATD and among the first to extend these methods to side impacts.Methods: Previously conducted experiments were replicated in order to make a direct comparison between the Q3s and PVs. PV data were used from 4- to 7-year-olds (shoulder tests, n = 14) and 6- to 8-year-olds (sled tests, n = 7). Force–deflection data were captured during quasistatic shoulder tests through manual displacement of the shoulder joint. Resulting shoulder stiffness was compared between the Q3s and PVs. Low-speed far-side sled tests were conducted with the Q3s at lateral (90°) and oblique (60°) impacts. Primary outcomes of interest included (1) lateral displacement of the torso, (2) torso rollout angle, and (3) kinematic trajectories of the head and neck.Results: The Q3s exhibited shoulder stiffness values at least 32 N/mm greater than the PVs for all conditions (PV muscle tensed and relaxed, deflection calculated for full- and half-thoracic). In lateral sled tests, the Q3s demonstrated increased coronal torso rollout (Q3s: 49.2°; PVs: 35.7° ± 12.4°) and lateral (ΔY) movement of the top of the head (Q3s: −389 mm; PVs: −320 ± 23 mm) compared to PVs. In oblique trials, the Q3s achieved significantly decreased lateral torso displacement (Q3s: 153.3 mm; PVs: 193.6 ± 25.6 mm) and top of the head forward (ΔX) motion (Q3s: 68 mm; PVs: 133 ± 20 mm) compared to PVs. In all tests, greater downward (ΔZ) excursions of C4 and T1 were observed in the Q3s relative to PVs.Conclusions: Increased Q3s shoulder stiffness could affect head–neck kinematics as well as thorax responses because unrealistic force can be transmitted to the spine from the shoulder. Q3s and PV trajectories were of similar shape, although Q3s head kinematics displayed rigid body motion followed by independent lateral bending of the head, suggesting cervical and thoracic spine rigidity compared to PVs.

Experimental study of the impact behavior of laminated composites stricken by sharp impactors

AbstractIn this study, the influence of the impactor shape on the dynamic response of E-glass/epoxy laminates was investigated. Composite samples were impacted using steel 90° and 120° conical, 24 mm and 12 mm in diameter hemispherical, pyramidal impactors via a specially developed drop weight test machine. The impact tests were performed at impactor mass (20 kg) for impact velocity (2.5 m/s). Plate specimens consisting of 18 plies for tests (180×50 mm) with a nominal thickness (7 mm) were used. Contact force-time and contact force-deflection data obtained from the experiments were interpreted. It was found that the contact force was smaller in the 90° conical impactor while it was bigger in the 24 mm hemispherical one. Absorbed energies were also investigated. The absorbed energy obtained for pyramidal impactor was greater than that of the others. Furthermore, overall damage areas caused by the impactor were evaluated.

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

Identifying the properties of ultra-soft materials using a new methodology of combined specimen-specific finite element model and optimization techniques

Development of novel protective helmets requires a better understanding of the mechanical properties of brain tissues. In this paper, a new methodology was developed using a reverse engineering (RE) based approach to identify the material properties for ultra-soft materials, such as human brain tissues, that are very difficult to cut into an accurate geometric shape necessary for engineering measurements. The basic idea behind this method is to include geometric effects by using a sample-specific finite element model in conjunction with a set of optimization procedures that allows systematic adjustments of material parameters until the calculated responses matched the measured ones. The experimental component consists of conducting simple uniaxial compression tests at two different loading rates to obtain force–displacement relationships, instead of the less accurate stress–strain curves, that could be used directly to minimize an objective function. The Shepard-k-Nearest method was employed to establish an approximated model (i.e. a response surface) and a genetic algorithm was used to search the optimal design variables (i.e. material parameters) in the design space. The optimized parameters were then used to describe the material behavior in a third sample-specific FE model and the model-predicted force–deflection data were compared with experimental data at a third loading rate that were not used for optimizing material parameters. This new approach makes it possible to identify material constants of ultra-soft biological tissues and engineering materials (e.g. silicone gels and rubbers) without using a large number of test samples.

Age-Dependent Regional Mechanical Properties of the Rat Hippocampus and Cortex

Age-dependent outcomes following traumatic brain injury motivate the study of brain injury biomechanics in experimental animal models at different stages of development. Finite element models of the rat brain are used to better understand the mechanical mechanisms behind these age-dependent outcomes; however, age- and region-specific rat brain tissue mechanical properties are required for biofidelity in modeling. Here, we have used the atomic force microscope (AFM) to measure region-dependent mechanical properties for subregions of the cortex and hippocampus in P10, P17, and adult rats. Apparent elastic modulus increased nonlinearly with indentation strain, and a nonlinear Ogden hyperelastic model was used to fit the force-deflection data. Subregional heterogeneous distributions of mechanical properties changed significantly with age. Apparent elastic modulus was also found to increase overall with age, increasing by >100% between P10 and adult rats. Unconfined compression tests (epsilon=-0.3) were performed on whole slices of the hippocampus and cortex of P10, P17, and adult rats to verify the mechanical properties measured with the AFM. Mean apparent elastic modulus at an indentation strain of 30% from AFM measurements for each region and age correlated well with the long-term elastic modulus measured from 30% unconfined compression tests (slope not significantly different from 1, p>0.05). Protein, lipid, and sulfated glycosaminoglycan content of the brain increased with age and were positively correlated with tissue stiffness, whereas water content decreased with age and was negatively correlated with tissue stiffness. These correlations can be used to hypothesize mechanistic models for describing the mechanical behavior of brain tissue as well as to predict relative differences between brain tissue mechanical properties of other species, at different ages, and for different regions based on differences in tissue composition.

Experimental and simulated flexion tests of humerus

To enhance car occupant protection during lateral impacts, experimental shoulder impacts have been realised. The simulation of these tests with a finite element method allows a better understanding of the shoulder response. Nevertheless, to simulate shoulder impacts, shoulder bone models have to be validated first. Thus, the aims of this study were firstly, to perform experimental dynamic tests on humerus, and then, to reproduce these tests by simulation in order to assess humerus models. Twelve humerus bones from six subjects (four males, two females, average age = 76) were submitted to flexion tests until failure. Drop tests were carried out with a 6 kg-mass at velocities from 1 to 2 m/s. Impact forces were recorded, and displacements were calculated through video analysis. Then, simulations were performed to compare humerus model responses under loading and experimental force–deflection data. Thus, this work provides experimental results that are used for the assessment of humerus models. The validated humerus bones could be integrated into global shoulder models for further applications such as simulation of car lateral impacts.

Design of an Endoscopic Biopsy Needle With Flexural Members

As a minimally invasive means of extracting a tissue sample from a patient, current endoscopic biopsy needles generally do not preserve tissue histology and often require multiple attempts to obtain a tissue sample. This paper presents an endoscopic biopsy needle with internal flexures that enables tissue to enter the hollow needle and then be severed from the surrounding tissue when the needle is withdrawn. Using force-deflection and sample weight data from 10× scaled prototypes, variations of a flexural design captured 1.1grams of a tissue phantom on average, as compared to wedge-type designs that averaged 0.7-0.8grams. Sample mass exhibited an increase in mass as the feature angle decreased. Peak entrance forces (P2) for the flexure design were lower than for both wedge and extended wedge designs, and resistance forces (S2) were higher upon needle extraction. A low-angle (15 and 30deg) feature also produced a lower entrance friction (S1) and higher exit resistance (S2) compared with 45 and 60deg features. These results suggest that a biopsy needle with 15deg flexures could increase sample length and mass as well as sampling success rates for core biopsy procedures. Future tests of the flexural biopsy needle design will use this information to determine dimensions for laser cut features of 1× scale needles.

Dynamics of basketball-rim interactions

A dynamic model for motion of a basketball on the rim is derived. The model is used to investigate shot success sensitivity to initial conditions and to search for initial conditions that lead to long rim contact times. Nonlinear ordinary differential equations describe three components of ball angular velocity and contact point position on the toroidal rim. The model includes radial ball compliance and dissipation and contains three sub-models describing slipping contact, nonslipping contact and purely gravitational flight. Switching between the three sub-models depends on contact point velocity and friction forces. Equivalent radial stiffness and damping constants are estimated using experimental ball force-deflection hysteresis data. General initial conditions almost always involve slip of the ball on the rim. Bouncing on the rim can also occur. After contact it is possible for the ball to enter the rim with its centre passing significantly below the rim plane before rising and ultimately escaping. Exotic quasi-equilibrium periodic circular trajectories exist inside but below the rim plane, relying for their existence on a combination of centripetal force, friction and gyroscopic precession of radial spin about the contact point. Trajectories, and consequent ball capture or escape, are extremely sensitive to initial conditions, especially rim contact position and backspin angular velocity. Backspin aids capture on longrolling trajectories.

Heel–shoe interactions and the durability of EVA foam running-shoe midsoles

A finite element analysis (FEA) was made of the stress distribution in the heelpad and a running shoe midsole, using heelpad properties deduced from published force-deflection data, and measured foam properties. The heelpad has a lower initial shear modulus than the foam (100 vs. 1050 kPa), but a higher bulk modulus. The heelpad is more non-linear, with a higher Ogden strain energy function exponent than the foam (30 vs. 4). Measurements of plantar pressure distribution in running shoes confirmed the FEA. The peak plantar pressure increased on average by 100% after 500 km run. Scanning electron microscopy shows that structural damage (wrinkling of faces and some holes) occurred in the foam after 750 km run. Fatigue of the foam reduces heelstrike cushioning, and is a possible cause of running injuries.

Geometric and mechanical properties of human cervical spine ligaments.

This study characterized the geometry and mechanical properties of the cervical ligaments from C2-T1 levels. The lengths and cross-sectional areas of the anterior longitudinal ligament, posterior longitudinal ligament, joint capsules, ligamentum flavum, and interspinous ligament were determined from eight human cadavers using cryomicrotomy images. The geometry was defined based on spinal anatomy and its potential use in complex mathematical models. The biomechanical force-deflection, stiffness, energy, stress, and strain data were obtained from 25 cadavers using in situ axial tensile tests. Data were grouped into middle (C2-C5) and lower (C5-T1) cervical levels. Both the geometric length and area of cross section, and the biomechanical properties including the stiffness, stress, strain, energy, and Young's modulus, were presented for each of the five ligaments. In both groups, joint capsules and ligamentum flavum exhibited the highest cross-sectional area (p < 0.005), while the longitudinal ligaments had the highest length measurements. Although not reaching statistical significance, for all ligaments, cross-sectional areas were higher in the C5-T1 than in the C2-C5 group; and lengths were higher in the C2-C5 than in the C5-T1 group with the exception of the flavum (Table 1 in the main text). Force-deflection characteristics (plots) are provided for all ligaments in both groups. Failure strains were higher for the ligaments of the posterior (interspinous ligament, joint capsules, and ligamentum flavum) than the anterior complex (anterior and posterior longitudinal ligaments) in both groups. In contrast, the failure stress and Young's modulus were higher for the anterior and posterior longitudinal ligaments compared to the ligaments of the posterior complex in the two groups. However, similar tendencies in the structural responses (stiffness, energy) were not found in both groups. Researchers attempting to incorporate these data into stress-analysis models can choose the specific parameter(s) based on the complexity of the model used to study the biomechanical behavior of the human cervical spine.

A method of calculating the mechanical properties of nanoscopic plant cell wall components from tissue properties

Biological tissues are made from nano-composite materials and given the recent interest in manufacturing synthetic nano-composites an analysis of natural nano-composites seems a worthwhile exercise. There is also potential for extracting natural nano-fibres and using them as reinforcements in other materials. In this paper a hierarchical mechanical model is formulated to describe potato tuber tissue and the model is used to back calculate the properties of cell wall nano-fibres. The model contains two structural levels, the cell structure and the cell wall structure. Material properties are assigned at the level of cell wall microfibrils (nano-composite fibres). Force deflection data from the compression of cubes of potato tissue were fed into the model and the properties of the cell wall microfibrils predicted. The modulus was found to vary with strain, but had a maximum value of 130 GPa, which is close to predictions from theoretical chemistry for the stiffness of cellulose microfibrils. At 8% wall strain (the value at which failures were suspected to begin), the stress was predicted to be 7.5 GPa which is also close to theoretical chemistry predictions for the strength of cellulose microfibrils. The large strains and decreasing stiffness indicate the influence of polymers other than cellulose.

Uniaxial Deformation of Rubber Cylinders

Abstract Stress, strain and optical birefringence measurements were made on elastomeric cylinders deformed in tension and compression. The birefringence data enables the actual stress to be determined even when the deformation is not homogeneous. In the absence of lubricant, uniaxially loaded rubber cylinders deviate from homogeneous deformation due to bonding of the cylinder ends. The existing analysis to correct the force-deflection curve for the effect of this sticking, strictly valid for infinitesimal strains, is premised on the idea that the deformed cylinder has a parabolic profile. Experimentally, however, it was found that slender rubber cylinders assume a much flatter profile, while maintaining constant volume, when deformed. Nevertheless, the accuracy of the stress-strain curve when the standard correction is applied turns out to be quite good, partially a result of cancellation of two, relatively small, errors. This accuracy was assessed by comparison of force-deflection data from bonded cylinders both to stress-strain data obtained on lubricated cylinders and to the stresses deduced from the measured birefringence.

Measuring stiffnesses and residual stresses of silicon nitride thin films

The mechanical deflection of circular membranes of SiN x is presented as a technique for measuring the stiffness and residual stress of very thin, single-layer films. The dimensions of the membranes are controlled precisely using standard photolithography, dry etching and wet etching techniques. Thicknesses vary between 0.09 μm and 0.27 μm and average diameters range between 1100 μm and 4100 μm. A Nanoindenter is used to deflect the membranes with a point force at their centers, and to continuously record the applied forces and the resulting deflections. The analysis of the force-deflection data yields the values of Young’s moduli and residual stresses for the films.

Interaction of contact velocity and cord compression in determining the severity of spinal cord injury.

Rate, depth, and duration of compression are the principal determinants of experimental spinal cord injury (SCI) severity. Since existing models do not allow independent control of these variables, the interaction of these factors has not been fully elucidated. The purpose of this study was to define the interactive relation of velocity (V) and compression (C) in SCI using a constrained stroke pneumatic impactor that allowed independent control of these variables. Computer simulation of previous weight-drop experiments using a lumped-mass model were compared with this series of impacts. After rigid stabilization of adjacent cervical vertebrae, the spinal cord (SC) in 48 male ferrets was compressed through the C6-C7 interspace. Maximum compression was 25%, 35%, 50%, or 65% of the SC diameter. Impacts were delivered at five velocities from 1.5 m/s to 6 m/s. Severity of injury was determined by pre and postinjury measurement of somatosensory evoked potentials (SEP) and blinded quantitation of histopathologic findings. Twenty-three of 48 animals (48%) had measurable SEP at 4 hs. No animal recovered SEP at 65% compression at any velocity, or at a velocity of 6 m/s for any level of compression. Recovery of SEP and histologic severity score correlated better with velocity-compression product, or maximum viscous response (VC) than with either V or C alone. The mean histologic severity score was higher in animals exhibiting no recovery of SEP. Modeling the viscoelastic elements of the SC using existing force-time and force-deflection data suggests that estimates of compression from current weight-drop techniques may be inaccurate. At low contact velocity, functional and anatomic damage is best predicted by maximum SC compression. However, as velocity increases, SCI severity becomes a function of the viscous response (VC), demonstrating the rate sensitivity of spinal cord tissue. Tolerance to SC compression decreases as the rate of deformation increases. This helps to explain apparent discrepancies between compression and severity of experimental SCI.

Holographic and analytic study of a semiclamped rectangular plate supported by struts

The purpose of this paper is to present a comparison of holographically, mechanically and analytically determined deflection of a uniformly loaded semiclamped rectangular plate supported by struts. Double-exposure holographic interferometry provides experimental static deflection as well as force-deflection hysteresis data. The experimental holographic technique is discussed. The analytic solution by method of superposition is also presented.