Direct Strain Measurement Research Articles

Crack Propagation Tests for Load Sequences Developed Using Different Flight Parameters of a Trainer Aircraft

Abstract Military aircraft are subjected to highly variable and unpredictable loads due to diverse mission profiles, armament configurations, and individual piloting styles. This variability complicates the definition of precise load spectra, particularly in cases where data loss occurs due to Flight Data Recorder (FDR) malfunctions or data mishandling. This paper investigates the use of different flight parameters, such as load factor (nz ), barometric height (Hb ), and horizontal velocity (Vp ), to define load sequences for the PZL-130 “Orlik” TC-II military trainer aircraft. These sequences were then used to evaluate crack propagation using Compact Tension (CT) specimens. The results show that the incorporation of additional flight parameters improves the accuracy of crack propagation predictions when compared to direct strain measurements. This study highlights the potential of using available flight data to develop reliable load spectra for fatigue life estimation in military aircraft, even when direct load measurements are not financially feasible.

ZnO modified carbon fiber-matrix interfacial evaluation via nanoscale digital image correlation and nanoindentation

Improving the adherence of the fiber-matrix interface is an important step for enhancing the capabilities of polymer composites. In this study, carbon fibers were modified by growing zinc oxide (ZnO) nanorods on the fiber surface using a hydrothermal approach, with the aim of increasing the interfacial area and enhancing the friction between the fiber and the matrix. To fully understand the deformation mechanisms at the interface, a microscale evaluation combining nanoindentation with digital image correlation (DIC) for mapping the deformations by using nanoscale speckles is developed in this work. The main objective of this research was to develop a protocol for speckling the modified single fiber composite and show that DIC can be used in microscopic level and to evaluate the fiber-matrix interface by means of nano indentation. The speckle pattern was created using Ti nano powder and used to generate the strain maps in the fiber-matrix interface region. A comparative analysis of DIC results from ZnO modified carbon fibers has shown that shear strains around the interfacial boundary are 60 % reduced on average, as compared to neat carbon fibers, across all nano indentations from 8mN to 65mN of peak load. Results used direct strain measurements to confirm that modification by ZnO growth on the surface of individual fibers has a significant benefit to the interfacial mechanical properties of fiber-matrix composites.

Development of Tools for the Direct Measurement of Shear Stress and Shear Strain within a Soil Mass

Abstract This article describes the development of sensing tools designed and applied to the direct measurement of shear stresses and shear strain within a soil mass. The importance in the development of these tools is in their ability to measure shear stresses and shear distortions within soil without any a priori information of the stress and strains applied at the boundaries of the system. These tools may be applied to element testing, testing of physical models, and field applications. The sensors were used in the testing of a sand in a large simple shear apparatus, under both constant height and constant vertical pressure conditions. Testing demonstrated that shear stresses smaller than 0.1 kPa are easily resolved. Shear strains smaller than 10−5 (abs) were reliably measured. Measurement of shear stress and shear distortion within the soil mass allows for direct determination of the shear stiffness of the soil. Shear stiffness measured in this fashion is significantly greater than that determined from the globally measured shear stress and shear strain. The stiffness degradation curve illustrates a constant shear stiffness over the range of 10−5 through 5·10−4.

Real-time forecasting of COVID-19-related hospital strain in France using a non-Markovian mechanistic model.

Projects such as the European Covid-19 Forecast Hub publish forecasts on the national level for new deaths, new cases, and hospital admissions, but not direct measurements of hospital strain like critical care bed occupancy at the sub-national level, which is of particular interest to health professionals for planning purposes. We present a sub-national French framework for forecasting hospital strain based on a non-Markovian compartmental model, its associated online visualisation tool and a retrospective evaluation of the real-time forecasts it provided from January to December 2021 by comparing to three baselines derived from standard statistical forecasting methods (a naive model, auto-regression, and an ensemble of exponential smoothing and ARIMA). In terms of median absolute error for forecasting critical care unit occupancy at the two-week horizon, our model only outperformed the naive baseline for 4 out of 14 geographical units and underperformed compared to the ensemble baseline for 5 of them at the 90% confidence level (n = 38). However, for the same level at the 4 week horizon, our model was never statistically outperformed for any unit despite outperforming the baselines 10 times spanning 7 out of 14 geographical units. This implies modest forecasting utility for longer horizons which may justify the application of non-Markovian compartmental models in the context of hospital-strain surveillance for future pandemics.

High‐speed fatigue testing of high‐performance concretes and parallel frequency sweep characterization

AbstractCycling loading of brittle materials like ultra‐high‐performance concrete (UHPC), which is often used in marine and civil structures, results in unexpected failures. When a material is subjected to cyclic loading, its mechanical properties change due to the evolution of (micro‐)fractures often denoted as damage. To better understand the effective material's properties under such kind of fatigue load and to relate the material's properties to the specific time‐dependent loading characteristics, the mechanical response of the material shall be characterized at characteristic harmonic excitations.Therefore, cyclic loading experiments are conducted to determine how the evolution of microfractures, that is, fatigue, affects the material's effective mechanical properties and after how many cycles microfractures further evolve towards meso‐ and macrofractures leading finally to a critical number of cycles to material's failure. The problem with such cyclic fatigue tests is that they are potentially “expensive” to conduct as the number of loading cycles at failure can be extremely high. Moreover, it is not possible to observe and characterize further the evolution of (micro‐)fractures within the different damage phases of the cycling experiment. Further, it is challenging to characterize the material's small‐strain stiffness evolution.In this investigation, a combination of a (high‐amplitude) high‐frequency excitation and a high‐speed fatigue testing approach is used for the high cycle fatigue experiment along with a characterization approach of the material properties using a (low‐amplitude) dynamic mechanical analysis (DMA). The test setup applies harmonic excitations for high and low amplitudes using a high‐voltage piezoelectric actuators. Furthermore, the failure modes of the material will be examined.The excitation frequency f for the fatigue test is significantly higher than in classical low‐ and high‐cyclic fatigue approaches, that is, Hz, allowing to reduce the overall time of the experimental investigation time to failure. Further, the frequency‐dependent number of cycles to failure is studied. Similar to standard DMA, effective complex mechanical properties of the material in tangential space are obtained in frequencies between 0.01 and 1000 Hz; while the observed mechanical properties of these materials change with increasing frequency. In the case of materials' behavior, by increasing the frequency, Young's modulus increases and Poisson's ratio decreases. Experimental fatigue results will be presented for UHPC samples. Harmonic experimental data include (direct) strain measurements in axial and circumferential directions as well as forces in axial directions. In addition, the resulting complex Young's modulus and evolving damage‐like “history” of UHPC will be shown.

Wave–current-structure blockage: Validation of one-way hydro-structural coupling with large-scale model tests of a stiffness-similar jack-up in elevated condition

This paper documents extensive comparison between one-way hydro-structural coupling model (OF-ABAQUS) and key findings from the physical model tests of a jack-up performed in TCOMS Ocean Basin. A generic jack-up model in elevated condition is considered at 1:30 scale. A series of model tests involving waves and current is performed on one of the jack-up legs for calibration of hydrodynamic coefficients, as well as on the whole jack-up for characterisation of its dynamic response. With the novel use of polycarbonate rods for the jack-up legs, stiffness similarity can be maintained at model-scale which allows direct strain measurements on the legs and meaningful connection force measurements at the spudcan modules and leg-to-hull connection modules. Using the OF-ABAQUS coupling model, the jack-up legs are first numerically represented as porous blocks and simulated in OpenFOAM to derive the hydrodynamic forces and additional fluid damping following Santo et al. (2018a), where static simulations are performed. The forces and damping are subsequently mapped into a Finite Element (FE) model of the jack-up in ABAQUS as a one-way transfer to derive its dynamic response following Li et al. (2022), where dynamic simulations are performed. The novelty of this paper is on the demonstration of the coupling model in capturing dynamic structural modes and responses in multiple degree-of-freedoms (DOFs) which is more realistic, unlike the earlier work by Santo et al. (2018a) who demonstrated the coupling model for an idealised single DOF system.Comparisons with model test results yield reasonably good agreement for all the cases considered, covering not just bending moment at one of the spudcan modules but also strain and leg-to-hull connection force of one of the legs. From the dynamic response spectra, the total system damping at the surge resonance frequency is adequately represented using the coupling model, which accounts for the additional fluid damping contributed by the effect of wave–current-structure blockage, or more precisely by the relative velocity. Most importantly, the use of single and consistent set of hydrodynamic coefficients for the derivation of hydrodynamic forces and additional fluid damping is demonstrated throughout all the cases. In contrast, the use of standard Morison equation will require tuning of the hydrodynamic coefficients and arbitrary increase in the hydrodynamic damping to match the measured peak response of each wave condition, resulting in huge uncertainties when evaluating the structural reliability in larger and unseen sea-states. This paper demonstrates that, once the hydrodynamic inputs are adequately represented, the corresponding dynamic structural responses can be derived accurately for any sea-states. The proposed approach can be regarded as a step improvement in accurate prediction of hydrodynamic forces and dynamic responses of space-frame structures, which has its important applications covering new-builds, re-assessment of old platforms, and structural health monitoring or digital twinning of offshore assets.

Structural condition assessment based strain-stress behaviour for railway welded rail joint using rosette fibre Bragg grating optical sensor

The rail provides a medium for trains to operate along and a support system for the cargo trains to carry. Proper caution should be exercised when handling the thermite welded rail, as it can be vulnerable to damage and failure if not properly maintained. The thermite welded rail joint experiences the greatest amount of train impact and has the least material rigidity. However, measuring the deformation or strain that occurs on a rail is difficult as limitation of the strain gauge itself and challenges to perform the measurement on site due to surroundings. A rectangular rosette Fibre Bragg Grating (FBG) sensor setup was mounted on the web surface of the rail to obtain three distinct strain directions, in order to measure and monitor the direct strain on the thermite welded rail joint. The location for the FBG sensor setup is determined by the presence of visible defects and the production of load sounds when the railway passes through specific locations on the rail track. The FBG sensor's wavelength signal displays three distinct patterns for each strain direction and is used to compare the results between the thermite welded joint and the smooth base rail structure. The wavelength signal exhibits tensional strain, compressional strain and tensional and compressional strain in combination. The principal strain and principal stress are examined between four different locations. The strain value obtained from FBG sensors show instability and variations, which can be attributed to factors such as the dynamic wheel-rail interaction and the condition of the rail structure. Therefore, the FBG sensors are proven to be acceptable in rail track condition assessment based on direct strain measurement for running rail track applications.

Auto left atrial strain by speckle tracking echocardiography and auto left atrial volumes by 3D transthoracic echocardiography after electrical cardioversion for atrial fibrillation

Abstract Funding Acknowledgements Type of funding sources: None. Introduction We have evidence that left atrial dysfunction and stunning occur after electric cardioversion for atrial fibrillation (CAF). Additionally, after successful cardioversion to sinus rhythm, a dissociation between electrical and mechanical recovery may be observed. Traditional pulsed Doppler and tissue Doppler imaging parameters demonstrate reduced atrial contractility immediately after cardioversion. Improvement in atrial function occurs within the first 4 weeks after sinus rhythm is restored. Recent advances in the assessment of myocardial function have facilitated the direct measurement of auto left atrial strain using speckle tracking echocardiography, and auto left atrial volumes measurements using dynamic heart model modern 3D transthoracic echo logistics. Purpose Aim of this study was to determine whether auto left atrial strain (auto LAs) by speckle tracking echocardiography, and auto left atrial volumes measurements, auto left atrial volume indices calculations (auto LAVI), could be used to evaluate global left atrial function and when a main improvement occurs after electrical cardioversion for CAF. Methods Auto LAs was measured from transthoracic echocardiography in 25 patients with CAF who had been cardioverted to sinus rhythm and followed up for 4 weeks, and in a cohort of 25 healthy individuals. Left atrial contractile strain (LACTS), conduit strain (LACDS) and reservoir strain (LARSS) were measured. Conventional measures of atrial function derived from transmitral pulsed wave doppler (PW) and tissue doppler imaging (TDI) of lateral mitral annulus were included, such as A wave velocity, A wave velocity time integral, A' wave velocity and A' velocity time integral. Results Immediately after cardioversion all PW, TDI and all three auto LAs parameters were significantly lower than in controls. On the other hand, auto LAVI was significantly higher in patients compared to controls immediately after cardioversion Atrial function was improved over time with maximal change observed 4 weeks after cardioversion and restoration to sinus rhythm. Auto LAs parameters were significantly higher in the group of patients. Auto LA volumes and auto LAVI with dynamic heart model logistics were lower in the same group, but with no statistical significance. Three patients with the lowest auto LAs values immediately after cardioversion, suffered recurrence of atrial fibrillation during the 4 weeks follow up. Conclusions Although left atrial electrical function is immediately restored after cardioversion in CAF patients, a persistent degree of atrial dysfunction remains for up to 4 weeks. This difference could explain the increased propensity for these patients to develop recurrent atrial fibrillation. Additional this dysfunction could indicate the longer-term use of antiarrhythmic and antithrombotic medication in the CAF cohort.

Using the method of correlation of digital images for plotting stress–strain curves in true coordinates

This article describes the features of determining strain curves in true stress–true strain coordinates, using samples of circular cross section from Al–Cu–Mg–Zn aluminum alloy. The calculation and experimental methods of determining true stresses and strains were compared Calculation methods based on the condition of volume constancy may not reflect actual regularities of deformation at the stage of strain localization in the considered material. Nevertheless, the use of systems of digital image correlation (DIC) allows measurements of both the geometrical sizes of deformed sample and strain fields on its surface to be performed, including on the sample neck. It was demonstrated that the measurement error of the sample diameter by the coordinate field was 0.02 mm at the instance of destruction. In order to improve the measurement precision, an increase in the recording frequency in proportion to increase in strain rate was proposed, as well as measuring the surface coordinates from both sides of the sample. It is also possible to supplement the strain curves obtained by DIC optical systems with the measurements of true fracture stress, and the true fracture strain determined by calculations on the destructed sample. The presented methods of analysis of plastic flow by direct measurement of field displacements and strains allow actual regularities between true stresses and strains at the interval of irregular plastic strain to be established. This cannot be achieved by analytical conversion of conventional curve. The obtained hardening coefficients and strain curves can be used for simulation and design of machinery structures and parts.

A local response function approach for the stress investigation of a centenarian steel railway bridge

Local stress concentrations in some specific geometric details often play an essential role in time-dependent damage propagation. However, measured strain or stress data are generally available in locations that are not the most critical ones. Proper numerical models are thus required to aid the damage severity assessment. In this paper, a surrogate model procedure based on the local response function method is proposed to accurately predict stress time histories in particular regions of bridges through a multiscale numerical analysis. The methodology is calibrated on the basis of direct strain measurements on a railway bridge in Vänersborg, Sweden. The bridge is currently monitored with a set of strain gauges, accelerometers, and an inclinometer allowing the investigation of its in-service conditions during the train passages and the lifting of the bascule truss. The results show the reliability of the method for stress prediction in specific regions of the bridge without the availability of directly measured data together with more detailed knowledge about the stress histories that could lead to fatigue or corrosion damage.

Experimental evaluation of strategies for wind turbine farm-wide fatigue damage estimation

A significant percentage of the existing wind turbines are reaching their theoretical design life. Therefore, important decisions about decommissioning or life extension will have to be made soon. Direct measurement of strains allows estimating the accumulated fatigue damage with good accuracy over the monitoring period, but these are still rare in this industry. As this paper demonstrates, this can be used for estimation of the damage prior to and after the measurement period. Furthermore, considering that similar wind turbines of the same wind farm have similar behaviour, the damage results can be extrapolated to the entire wind farm. In this work, the strain measurements on an onshore wind turbine over two years are used to evaluate the fatigue progression over time. The experimentally evaluated fatigue damage is analyzed against operational and environmental conditions and clustered into several load cases. Then, the damage values are stored in a database according to the corresponding environmental conditions. Based on this and on the variables that characterize operating conditions recorded since the wind farm installation, it is possible to probabilistically predict the fatigue consumption in the entire wind farm. Alternative approaches to estimate fatigue damage for non-monitored operating conditions are proposed and evaluated. The obtained results are an important step to demonstrated the feasibility of farm-wide fatigue assessment with limited additional instrumentation.

The high cycle fatigue testing of High‐Performance Concretes using high frequency excitation

AbstractThe effect of fatigue failure in brittle materials like (ultra) High Performance Concrete (UHPC) due to cyclic loading causes unexpected failure that consequently results in heavy costs in marine and civil structures. To characterize the effect of fatigue, cyclic loading tests are performed, and “the number of cycles to failure” are experimentally determined. One problem with these kinds of tests is that such experimental investigations are potentially expensive, i.e., time‐consuming process since the number of loading cycles could be extremely high. Further, within the different damage phases of the cycling tests, one has no access to the small‐scale, i.e., microscopical evolution of (micro‐)cracks. Additionally, a full characterization of the small‐strain stiffness evolution of the material is challenging. The goal of the research investigation is to combine a (large amplitude) High Cycle Fatigue experiment with a (low amplitude) Dynamic Mechanical Analysis (DMA). Using a setup based on the piezoelectric actuator, the (rate‐dependent) mechanical properties of the material in tangential space, and the failure modes of the material will be examined accurately. The excitation frequency is between 0.01 Hz to 1000 Hz which allows for reducing the experimental investigation time to failure. Further, it allows investigating the effect of frequency on the number of cycles to failure. Firstly, experimental results for HPC and berea sandstone samples will be presented. Harmonic experimental data include (direct) strain measurements in axial and circumferential directions as well as forces in axial directions. In addition, the resulting complex Young's modulus and evolving damage‐like “history” of HPC and berea sandstone specimens will be shown.

Direct Measurement of the Thermomechanical Properties of Poly(3-hexylthiophene) Thin Films on Ionic Liquid Surfaces

Thermomechanical properties of conjugated polymers (CPs) have emerged as critical factors for the long-term stability of CP-based electronics. However, very little is known about the thermomechanical properties of CP thin films (thickness ≤100 nm) without constraints from a supporting substrate. Herein, we investigate the intrinsic thermomechanical properties of CP thin films by direct measurement of thermal strains of thin films floating on an ionic liquid (IL). The IL surface provides almost frictionless gliding and thermal expansion of the pseudo-free-standing CP thin films for a wide range of temperatures up to 250 °C. We apply the method to examine the thermomechanical properties of poly(3-hexylthiophene)s (P3HTs) with different regioregularities (RRs). With increasing IL temperature, the P3HT thin film exhibits a linear in-plane thermal expansion, followed by a rapid increase in thermal strain above the melting temperature (Tm). When RR decreases from 95 to 60%, we observe a higher coefficient of thermal expansion (CTE) (from 164 to 395 ppm K–1) and a lower Tm (from 189 to 57 °C) due to the reduced crystallinity and crystal size. At the same RR, both CTE and Tm values decrease as the film becomes thinner. When the thickness of 82% RR P3HT film decreases from 550 to 45 nm, CTE and Tm values reduce from 294 to 201 ppm K–1 and from 160 to 128 °C, respectively. The in-plane hardening of the amorphous phase decreases the CTE, while the smaller crystal size from the thickness limitation reduces Tm. Our methods enable the direct measurements of thermomechanical properties of the CP thin films over a wide temperature range.

Direct Measurement of Atomic Reconstruction, Strain, and Disorder in Moiré Materials using 4D-STEM

Direct Measurement of Atomic Reconstruction, Strain, and Disorder in Moiré Materials using 4D-STEM

Molecular‐Level Methylcellulose/MXene Hybrids with Greatly Enhanced Electrochemical Actuation

Ti3 C2 Tx MXene film is promising for electrochemical actuators due to its high electrical conductivity and volumetric capacitance. However, its actuation performance is limited by the slow ion diffusion through the film and poor mechanical property in aqueous electrolytes. Here, molecular-level methylcellulose (MC)/MXene hybrid films are assembled with obviously enlarged layer distance, improved wet strength, and ambient stability. The hybrid films show significantly higher in-plane actuation strain in a liquid electrolyte. Based on direct strain measurements, insitu X-ray diffraction (XRD) and exsitu X-ray photoelectron spectroscopy (XPS) analyses, the actuation enhancement can be ascribed to the enlarged layer distance allowing more water and ions to be intercalated/de-intercalated and MC-induced sliding of MXene sheets. The assembled soft actuator has a high Young's modulus of 1.93GPa and can be operated in air, generating a peak-to-peak strain difference up to 0.541% under a triangular wave voltage of ±1Vand a blocking force of 4.7times its own weight.

Investigation on Temperature-Dependent Multiaxial Ratchetting of Polycarbonate by a Novel Experimental Method

A novel method to heat the multiaxial hollow thin-wall specimen was proposed, where its gauge length section can be heated by the liquid (i.e., water) filled inside the specimen instead of the closed furnace. This method realizes the direct measurement of multiaxial strain on the surface of specimen at different temperatures by the noncontact digital image correlation. By utilizing the proposed method, the multiaxial stress-control cyclic tests were performed to investigate the multiaxial ratchetting of polycarbonate (PC) at different temperatures. It is found that the multiaxial ratchetting of PC depends greatly on the test temperatures and the multiaxial ratchetting strain increases with increasing the test temperature. The temperature-dependent multiaxial ratchetting is also influenced by valley stresses. The unrecoverable part of deformation in the multiaxial ratchetting strain increases with increasing temperature.

State observer for the deformation state of wind turbine blades based on inertial measurements

The design of wind turbines is based on conservative load assumptions compared to the actual load conditions at the designated erection site. As a consequence, structural reserves are very likely at the end of the turbine’s approved life time. To safely exploit these structural reserves, a continuous, model-based fatigue monitoring of the individual wind turbine is necessary. Direct strain measurements are possible at accessible locations only and, moreover, have limited long-term stability. Therefore, an indirect, model-based estimation of structural deformations is proposed that relies on integrated motion measurement with only a minimal number of robust inertial sensors. Tests on a small-scale structural test rig of a wind turbine prove the feasibility of the concept.

Fatigue Crack Propagation Estimation Based on Direct Strain Measurement during a Full-Scale Fatigue Test.

Military aircraft are subjected to variable loads, which are the main cause of initiation and propagation of cracks in the most stressed locations of the airframe. The aim of a Full-Scale Fatigue Test (FSFT) is to represent actual load conditions in such a way that the results obtained are a good representation of the actual loads and may be used as data that give insight into the development of real fatigue damage in critical locations. The FSFT load spectrum is a generalized depiction of the expected service loads and is designed to give an overall good representation of loads exerted on the airframe’s structural elements during operation. Moreover, the discrete method of load application on the structure (exerting loads with hydraulic actuators rather than pressure fields or inertia loads expected in actual operation) may cause some local effects, which may not be present in operation. The proposed usage of direct strain data from the test include such local effects. Moreover, operational loads may vary between individual aircraft, therefore it is crucial to understand the whole process of fatigue crack onset and development in order to determine safe inspection intervals and thereby mitigate risk. This paper presents crack propagation calculations regarding the development of a crack in a critical location of the PZL-130 “Orlik” TC-II aircraft, discovered during FSFT. The discussed crack was found already developed, hence the information about nucleation and initial propagation of the crack was not available. Therefore, there was a need to recreate the whole propagation process by means of numerical estimations using the FSFT results like location of the crack and total life for model validation. Moreover, in order to gather real load data for calculations a dedicated stain gage was installed on the damaged load path to monitor the actual remote strain in the element during the FSFT. This allowed for the definition of load sequence exerted on the damaged element directly during the test rather than estimating it from the general load conditions of the wing. The calculations allowed for the estimation of crack propagation curves from initiation to critical crack length causing fatal damage. The obtained curves allowed to visualize the crack behavior due to applied load and furthermore define initial and recurring inspection intervals for the entire fleet during operation, which allowed to define which cracks could be found before they reach critical size in order to carry out mitigation actions like repair or replacement of the damaged part. The authors present the methodology for load spectrum development based on direct strain measurements and furthermore crack propagation curves estimation, validated with the actual FSFT results, which allowed to propose nondestructive inspection intervals for future operation.

METHOD TO GENERATE ACCURATE ELASTIC AND HYPERELASTIC UNIAXIAL TENSION STRESS–STRAIN DATA WITHOUT AN EXTENSOMETER

ABSTRACT Uniaxial tension tests on dumbbells are routinely used to determine the stress–strain response of engineering materials. The simplest way to calculate strain is from grip displacement during extension, but this introduces significant error when dumbbells are gripped at the wider end sections to avoid the sample breaking prematurely in the grips. Mechanical and optical extensometers alleviate this problem by directly measuring strain in the gauge section. However, the equipment introduces significant additional hardware and software costs, and some experimental setups obstruct or prevent direct measurement of strain. The strain following systems also struggle both with the loss in mark intensity and changes of the shape of the marked point as the strain level is increased. To address these shortcomings, a novel analytical model to correct stress–strain data based on grip displacement is proposed. The model is implemented in Fortran and applied to hyperelastic materials which are assumed isotropic, but in principle the method is not restricted to elastomers. The model is validated with three studies on dumbbells: (i) a finite-element analysis for strains up to 660%; (ii) an experimental test with unfilled natural rubber up to 300% strain using a video extensometer; and (iii) a high temperature experimental test to fracture where the strain is corrected for a filled rubber. The model errors range from 2.2% to 3.1%, which is well within material and experimental uncertainties; hence, the model provides an accurate, inexpensive means of determining stress–strain behavior from grip displacement.

Direct measurement of geomembrane strain from aggregate indentations

High localized strain in geomembranes caused by indentations from coarse, uniform drainage aggregate is associated with long-term stress cracking and has been widely studied. A number of large-scale lab tests were carried out with direct measurement of the distribution of the major and minor principal (engineering) strain across the area of a large laboratory sample of geomembrane. This ‘grid-point’ method of strain estimation is compared to the method developed by Tognon et al. which has been recommended as the best available approach at this time. It has been found that the method by Tognon et al. tends to over- and under-predict geomembrane strain depending on the aggregate and protection layers used. Indentations with higher smaller ratios of membrane to bending strains tend to be underestimated. A correction factor is proposed based on the ratio of membrane to bending strains and fits the measured grid strain method used in this study well.