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A novel method is introduced for the measurement of a 3D strain field by exploiting the interaction between ultrasound waves and geometrical characteristics of the insonified specimen. First, the response of obliquely incident harmonic waves to a deterministic surface roughness is utilized. Analysis of backscattered amplitudes in Bragg diffraction geometry then yields a measure for the in-plane strain field by mapping any shift in angular dependency. Secondly, the analysis of the reflection characteristics of normal incident pulsed waves in frequency domain provides a measure of the out-of-plane normal strain field component, simply by tracking any change in the stimulation condition for a thickness resonance. As such, the developed ultrasonic strain gauge yields an absolute, contactless and single-sided mapping of a local 3D strain field, in which both sample preparation and alignment procedure are needless. Results are presented for cold-rolled DC06 steel samples onto which skin passing of the work rolls is applied. The samples have been mechanically loaded, introducing plastic strain levels ranging from 2 % up to 35 %. The ultrasonically measured strains have been validated with various other strain measurement techniques, including manual micrometer, longitudinal and transverse mechanical extensometer and optical mono- and stereovision digital image correlation. Good agreement has been obtained between the ultrasonically determined strain values and the results of the conventional methods. As the ultrasonic strain gauge provides all three normal strain field components, it has been employed for the extraction of Lankford ratios at different applied longitudinal plastic strain levels, revealing a strain dependent plastic anisotropy of the investigated DC06 steel sheet.

Already in the early 1980's, it has been conjectured that the pulsed ultrasonic polar scan (P-UPS) provides a unique fingerprint of the underlying mechanical elasticity tensor at the insonified material spot. Until now, that premise has not been thoroughly investigated, nor validated, despite the opportunities this would create for NDT and materials science in general. In this paper, we report on the first-ever implementation of an inverse modeling technique on the basis of a genetic optimization scheme in order to extract quantita- tive information from a P-UPS. We validate the optimization approach for synthetic data, and apply it to experimentally obtained polar scans for annealed aluminum, cold rolled DC-06 steel as well as for carbon fiber reinforced plastics. The investigated samples are plate-like and do not require specific preparation. The inverted material characteristics show good agreement with literature, micro-mechanical models as well as with results obtained through conventional testing procedures.

This article describes an inverse method for the identification of the plastic behavior of aluminum plates subjected to sudden blast loads. The method uses full-field optical measurements taken during the first milliseconds of a free air explosion and the finite element method for the numerical prediction of the blast response. The identification is based on a damped least-squares solution according to the Levenberg–Marquardt formulation. Three different rate-dependent plasticity models are examined. First, a combined model based on linear strain hardening and the strain rate term of the Cowper–Symonds model, secondly, the Johnson–Cook model and finally, a combined model based on a bi-exponential relation for the strain hardening term and the strain rate term of the Cowper–Symonds model. A validation of the method and its sensitivity to measurement uncertainties is first provided according to virtual measurements generated with the finite element method. Next, the plastic behavior of aluminum is identified using measurements from real free air explosions obtained from a controlled detonation of C4. The results show that inverse methods can be successfully applied for the identification of the plastic behavior of metals subjected to blast waves. In addition, the material parameters identified with inverse methods enable the numerical prediction of the material’s response with increased accuracy.

Local stiffness of Euler–Bernoulli beams can be identified by dividing the bending moment of a deformed beam by the local curvature. Curvature and moment distributions can be derived from the modal shape of a beam vibrating at resonance. In this article, the modal shape of test beams is measured by both scanning laser vibrometry (SLV) and shearography. Shearography is an interferometric optical method that produces full-field displacement gradients of the inspected surface. Curvature can be obtained by two steps of derivation of the modal amplitude (in the case of SLV) or one step of derivation of the modal shape slope (in the case of shearography). Three specially prepared aluminium beams with a known stiffness distribution are used for the validation of both techniques. The uncertainty of the identified stiffness distributions with both techniques is compared and related to their signal-to-noise ratios. A strength and weakness overview at the end of the article reveals that the shearography is the technique that shows the most advantages.

In this international permeability benchmark exercise, in-plane permeability data for two reinforcement fabrics, obtained using a total of 16 different experimental procedures, were compared. Although, for each procedure, the results appear consistent, different procedures result in a scatter of up to one order of magnitude in principal permeability values for each fabric at any given fibre volume fraction. The ratio of the principal permeability values varies by factors of up to 2. While experimental uncertainties and variability of the specimens affect the scatter in results for any single series of experiments, it is suspected that the main source of scatter in results from different procedures is related to human factors. Aiming at standardisation of measurement methods and interchangeability of results, "good practice" guidelines will be formulated in order to eliminate sources of scatter. (C) 2011 Elsevier Ltd. All rights reserved.

Single Point Incremental Forming (SPIF) is a modern and flexible alternative to traditional forming techniques. It thanks its flexibility to the fact that it does not require a dedicated tool set to operate. Numerical simulation of the SPIF process requires an accurate FE model. In the past several attempts have been undertaken to use inverse methods for sheet metal SPIF material model identification based on shearing, tensile and indenting tests. The basic idea of this paper is that the results of inverse methods can be improved by using the SPIF process itself as experimental data source. A SPIF experiment dedicated for material identification on a simple geometry using large step sizes is presented and compared with the FE simulation of the forming process based on an initial guess for the material behavior.

Clinching is a mechanical joining technique which involves severe local plastic deformation of two or more sheet metal parts resulting in a permanent mechanical interlock or joint. The required forming load and energy can be determined with the aid of the finite element method. However, a good knowledge of the elasto-plastic properties is of utmost importance to perform a sufficiently accurate simulation. This paper presents two alternative material tests to identify the hardening behaviour of sheet metal beyond the point of maximum uniform elongation. In addition, the material tests were applied to DC05 and the identified material behaviour is evaluated through the prediction of the forming load during clinching.

The resonant-based identification of the in-plane elastic properties of orthotropic materials implies the estimation of four principal elastic parameters: E 1 , E 2 , G 12 , and ν 12 . The two elastic moduli and the shear modulus can easily be derived from the resonant frequencies of the flexural and torsional vibration modes, respectively. The identification of the Poisson’s ratio, however, is much more challenging, since most frequencies are not sufficiently sensitive to it. The present work addresses this problem by determining the test specimen specifications that create the optimal conditions for the identification of the Poisson’s ratio. Two methods are suggested for the determination of the Poisson’s ratio of orthotropic materials: the first employs the resonant frequencies of a plate-shaped specimen, while the second uses the resonant frequencies of a set of beam-shaped specimens. Both methods are experimentally validated using a stainless steel sheet.

The capability to simulate the flow of resin through a porous reinforcement by FE modelling has become very important for designing RTM production processes for high-performance composite parts. The key parameter in RTM flow simulations is the fibre reinforcement permeability. The measurement of this material parameter is still not standardized and many different set-ups have been proposed. Recently, a stereolithography technique was used to produce a textile-like solid specimen with anisotropic permeability, designed as a reference for calibration and comparison of permeability measurement set-ups and for validation of numerical permeability computation software. Unlike real textiles, the permeability properties of such reference specimens do not vary from test to test. Excellent repeatability of the experiments is achieved. When used for benchmarking, any discrepancy between different measurements on this specimen must be attributed to the set-up and data processing. This paper presents the first experimental measurements of the permeability of such reference specimens, obtained with a 2D central injection rig. The measured values, with principal components of the 2D permeability tensor of 2.47 ± 0.09 × 10−9 m2 and 5.44 ± 0.22 × 10−9 m2, are in good agreement with the values predicted using numerical permeability computation software. Statistics from a series of measurements using the same set-up show that the precision of the permeability identification depends on the data processing procedure. An approach which incorporates a numerical model that is also valid after the fluid reached an edge of the reinforcement performs significantly better than the approach, based on an analytical approximation, which was used before.

Single point incremental forming (SPIF) is a promising new production technique in which a metal sheet is formed stepwise by a spherical tool. However, the technique still shows some particularities. It is observed that the final geometry of a SPIF part can deviate significantly from the programmed tool path. As illustrated in this paper, elastic springback is only to a minor extent responsible for this phenomenon. The goal of the presented paper is to illustrate the gradual emergence of unintended deviations as measured by means of a Digital Image Correlation (DIC) technique. Two CCD cameras were used to take the necessary in-process images. The mechanism of deformation in function of the forming depth is documented and discussed.

A simplified method to determine the strain distribution during incremental forming of a cone is proposed in this paper. Because of the symmetry of the deformed part, the strain can be derived using the results obtained from a limited number of consecutive tool contours instead of going through the whole process. Comparisons made between the measured and simulated results show that the proposed method can be applied to determine the strain encountered in such kind of incremental forming process where axi-symmetric parts are formed.

Inverse methods offer a powerful tool for the identification of elasto-plastic material properties of metals. The basic principle of the inverse method we are studying, is to compare an experimentally measured strain field with a strain field computed by a finite element (FE) model. The material parameters in the FE model are iteratively tuned in such a way that the numerically computed strain field matches the experimentally measured field as closely as possible. One of the building blocks in this identification procedure is the optimization algorithm for the material parameters in the numerical model. The key problem of this optimization algorithm is the determination of a sensitivity matrix, which expresses the sensitivities of the strains with respect to the material parameters. This paper presents an analytical method for the calculation of this sensitivity matrix in the case of a tensile test with non-rotating principal axes of strain.

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.

Based on the well-known pin-on-disc test rig, a new test setup for online measuring of wear and friction behaviour of polymer matrix composites has been developed. In contrast to a traditional friction-and-wear test rig, a steel pin and composite disc are used for studying the influence of wear debris and fibre orientation. During sliding, a thin adhesive film is possibly formed on the wear track of a composite disc, consisting of wear debris that is squeezed under the steel pin and that finally smoothens onto the composite surface. By optical microscopy, it was observed that most of the debris particles originate from the edges of the wear track. The thin film deforms continuously, with large and dark wear particles observed at the edge of the wear track. A lower coefficient of friction is achieved when the particles are re-adhered to the mating surface. The film formation mechanism depends on the normal force, sliding velocity, and bulk composite structure: because pultruded composite profiles are prese...

Numerical models of a railway track rarely take the nonlinear dynamic component behaviour of the railpad into account due to three important problems: first, the considerable amount of calculation time consumed by nonlinear numerical models; second, the lack of validation tools for nonlinear numerical models; third, the lack of data on the nonlinear properties of those components. The ever-increasing power of computers will solve the first problem. Scale models can be a solution for the validation problem. This paper discusses a practical solution for the third problem. The paper will present an alternative set-up for railpad testing allowing for the measurement of stiffness and damping values between 20 and 2500 Hz with variable preload. It shows the important variation of the dynamic stiffness and the loss factor throughout the chosen frequency range. It is also found that the nonlinear dynamic behaviour of this railway track component certainly affects the dynamic behaviour of the complete track.

Mixed numerical-experimental techniques (MNETs) combine experimental test results and numerical modelling techniques with the goal of identifying physical properties. Experimental results always come with a level of uncertainty. This input uncertainty will migrate through the MNET routine, and will result in an uncertainty on the identified parameters. Therefore, MNET procedures should not only provide an estimated value for the physical properties, they should also provide additional information about the reliability of the results obtained. This paper presents a routine that is able to transform the uncertainty on the input parameters of a MNET into the uncertainty on the output parameters. The approach does not require any change of the initial MNET routine, it is just an additional computational step that has to be performed after the MNET has identified the deterministic values of the unknown physical properties. The routine is demonstrated on a vibration based MNET used to identify elastic material properties.

Sandwich structures are extensively used in engineering because of their high specific stiffness and strength. The modelling of sandwich structures has been studied extensively, but less attention has been paid to their material identification. This paper proposes an inverse method for the material identification of sandwich beams by measured flexural resonance frequencies. The procedure is illustrated with numerically generated test data and also applied on experimentally measured data taken out of literature. An error estimation procedure is conducted to discover and discuss the main error sources.

Many papers have already been presented about identification of 2D in plane elastic engineering constants E1, E2, v12 and G12 by inverse methods. Most of the described methods are based on measured resonance frequencies on plate specimens. Less attention has been paid to the identification of transverse shear moduli. Especially, validation of the obtained results and error bound estimations are often lacking. This paper presents an inverse method for the identification of the transverse moduli of test beams by measured flexural resonance frequencies. The procedure is first illustrated with numerically generated test data and next applied on experimentally measured results. The sensitivity of the flexural resonance frequencies for variations of the shear modulus is discussed as well as an estimation of the uncertainty intervals on the obtained moduli. The results are validated by using the obtained shear moduli for the prediction of torsional resonance frequencies.

Time consumption is the major drawback of many existing set-ups for permeability measurement. This drawback has prevented many researchers from studying the statistical distribution of experimentally obtained permeability values. To overcome this problem—while maintaining the necessary accuracy—an automated central injection rig for permeability identification called ‘PIERS set-up’ (permeability identification using electrical resistance sensors) was developed. The PIERS set-up was used to characterize two typical glass fiber reinforcements. The test results demonstrated the presence of large scatter in the identified permeability values and hence the necessity to consider a statistical distribution of permeability values. The existence of a permeability distribution implies that a small number of measurements will not be sufficient to fully characterize the material. This paper discusses the necessary number of measurements to adequately characterize the statistical distribution and investigates the origins of the observed scatter. The paper also shows that the nesting of layers during stacking and mold closing is a major source of the observed variations in permeability values.

Vibration control of structures is confronted with many problems like the proper selection of modelling methods, controllability and observability of models, model size and model reduction methods. In this paper a practical procedure is proposed to overcome technical problems of structure control due to a large model size. Firstly, an accurate numerical model is derived by using the finite element method. This model is verified by modal analysis experiments. Secondly, a new model reduction procedure is proposed to reduce considerably the full order model. This reduction makes the reduced order model controllable and observable. In a further step, a controller is designed based on the verified reduced order model. Finally, a real-time control system is set up. The controlled and uncontrolled impulse responses at the free tip of the cantilever beam with active constrained layer damping treatments are compared both in time domain and frequency domain. The results clearly show the efficiency of the proposed procedure. The procedure proposed in this paper can be extended towards more complex structures.

Railway-induced vibrations are a growing matter of environmental concern. The rapid development of transportation, the increase of vehicle speeds and vehicle weights have resulted in higher vibration levels. In the meantime vibrations that were tolerated in the past are now considered to be a nuisance. Numerous solutions have been proposed to remedy these problems. The majority only acts on a specific part of the dynamic behaviour of the track. This paper presents a possible solution to reduce the noise generated by the ‘pinned–pinned’ frequencies. Pinned–pinned frequencies correspond with standing waves whose nodes are positioned exactly at the sleeper supports. The two first pinned–pinned frequencies are situated approximately at 950 and 2200 Hz (UIC60-rail and sleeper spacing of 0.60 m). To attenuate these vibrations, the Department of MEMC at the VUB has developed a dynamic vibration absorber called the Double Tuned Rail Damper (DTRD). The DTRD is mounted between two sleepers on the rail and is powered by the motion of the rail. The DTRD consists of two major parts: a steel plate which is connected to the rail with an interface of an elastic layer, and a rubber mass. The two first resonance frequencies of the steel plate coincide with the targeted pinned–pinned frequencies of the rail. The rubber mass acts as a motion controller and energy absorber. Measurements at a test track of the French railway company (SNCF) have shown considerable attenuation of the envisaged pinned–pinned frequencies. The attenuation rate surpasses 5 dB/m at certain frequency bands.

Resin transfer molding (RTM) is becoming increasingly important as a production technique for FRPs. However, the design of molds that assures the production of parts with acceptable quality remains a difficult task. Simulation codes developed for design need reliable input data such as reinforcement permeability. The measurement of this material parameter is still not standardized and thus many different set-ups have been proposed. In this paper a new method will be presented that is much faster and much less operator-dependant than other set-ups. It is a 2D central injection set-up, based on the automatic detection of the flow front position as a function of time. For this purpose, simple electrical sensors were designed and an automated calculation procedure was programmed on a PC-based system. As will be shown, the elements of the permeability tensor are not single valued at a particular fiber volume fraction. Rather, each element displays a broad distribution. More importantly, the variations in the principal permeability values are not correlated since their ratio, the anisotropy, also displays a broad distribution.

In this paper, the hybrid compliance-stiffness matrix method for simulating wave propagation in (delaminated) multilayered media with viscoelastic anisotropy has been confronted with high-quality amplitude and phase experiments on delaminated composites, obtained using the ultrasonic polar scan setup (UPS) in transmission by considering harmonic as well as pulsed ultrasound. Results are presented for multiple thin carbon/epoxy laminates with an artificial edge delamination induced by a foil insert, showing a good agreement between experimental recording and numerical modeling. The obtained results further reveal the feasibility of the harmonic UPS to detect and even locate the depth-position of multiple delaminations in fiber reinforced composites. Considering that the harmonic UPS method does not rely on the detection of different echoes like the classical C-scan, but rather expounds the conditions for efficient stimulation of guided waves in the solid, the method is found to be highly suited for inspecting thin composite materials for the presence of delaminations.

This study investigates the use of both the amplitude and time-of-flight based pulsed ultrasonic polar scan (P-UPS) for the nondestructive detection and evaluation of fatigue damage in fabric reinforced composites. Several thermoplastic carbon fabric reinforced PPS specimens (CETEX), loaded under various fatigue conditions, have been scanned at multiple material spots according to the P-UPS technique in order to extract material degradation in a quantitative way. The P-UPS results indicate that shear dominated fatigued carbon/PPS goes with a reduction of shear properties combined with large fiber distortions. The P-UPS results of the tension-tension fatigued carbon/PPS samples on the other hand reveal a directional degradation of the stiffness properties, reaching a maximum reduction of −12.8 % along the loading direction. The P-UPS extracted damage characteristics are fully supported by simulations, conventional destructive tests as well as visual inspection. The results demonstrate the excellent capability of the P-UPS method for nondestructively assessing and quantifying both shear-dominated and tension-tension fatigue damage in fabric reinforced plastics.

In liquid composite moulding (LCM) techniques, the liquid resin has to flow a long distance to impregnate the dry fibres. The measure for the resistance of the fibre preform to the resin flow is the permeability of the fibre preform. Because of the dual-scale porous structure of the textile preforms, test fluid can influence the unsaturated permeability values through the interaction of the fluid and fibres. In this study, the influence of test fluid on the permeability measurement of several types of textile reinforcements is investigated. First the contact angle of various fluids and fibres was measured. Then the permeability measurement of the textile reinforcements was carried out. The results showed that the influence of test fluid is small under the test conditions.

In a conventional ultrasonic polar scan (UPS) experiment, the amplitude or time-of-flight-diffraction (TOFD) values of the transmitted and/or reflected acoustic pulse are recorded for a wide range of incidence angles, in view of gaining knowledge about the elastic properties at the insonified material spot. Here we apply the pulsed UPS technique and investigate the backscattered signal, resulting in the ultrasonic backscatter polar scan (UBPS). It is shown that a UPBS contains a blueprint of geometrically related features of the insonified material spot which can be of particular interest for various industrial applications. We applied the UBPS for (i) the determination of the stacking sequence of a cross-ply composite laminate, (ii) the semi-quantification of a multidirectional microscopic surface corrugation, (iii) the detection of corrosion in an early stage as well as (iv) the detection and the localization of a closed surface breaking crack.

The ultrasonic backscattering technique is employed for the characterization of a 2D surface corrugation which is superposed on or hidden on the backside of a polycarbonate sample. In contrast to previous studies where the incident angle at well-defined and a-priori known symmetry orientations of the surface structure is varied in order to extract the characteristic periodicities, the backscatter polar scan method incorporates an additional variation of the orientation of the vertical insonification plane within the experimental measurement protocol. As such, the characteristic periodicities as well as the surface symmetries can be extracted without any prior knowledge of the surface structure. As a benefit compared to optical methods, we have also validated this extended methodology for the investigation of a 2D subsurface corrugation. Although the diffraction conditions do not change in comparison with a visible 2D surface corrugation, we remark that additional attention is required in the sense that the elastic properties of the substrate material put further restrictions to the range of applicable ultrasonic frequencies. The characterized periodicities and symmetries are in excellent agreement with the design parameters of the (hidden) 2D surface grating.

Protection of buildings against explosions due to terrorism actions or accidents is a growing concern in civil engineering. Full-field measuring techniques as well as finite element simulations are two valuable tools in the hands of engineers to understand the structural mechanisms during blast load events. The research leading to this article is motivated by the fact that only limited knowledge about finite element simulations and experimental validation of structures under free air explosions seems to be available. This article investigates the benefits and accuracy of a finite element simulation of a blast loaded thin aluminum plate by validating the results with small-scale blast loading experiments. Experimental data obtained from 3D high-speed digital image correlation, during the first 7 ms with a frame rate of 25,000 frames per second, is compared with results obtained from the finite element analysis. The influence of different parameters (amongst others: the element type, element size and integration method) with respect to the accuracy of the finite element results is investigated. It is shown that for the modeling of the deformation of the investigated thin plate, the use of shell elements is allowed as the transverse shear strains appear to be sufficiently small. Furthermore, it is concluded that the use of an explicit integration scheme instead of an implicit scheme dramatically reduces the computational effort without significant loss of accuracy.

Assessment of the structural dynamic response caused by an explosion is complex due to the high velocity impact, the transient nature of the deformation and the interactions between the structure and the pressure wave. This paper deals with full-field measurements of aluminum plates under free air blast loading conditions. Forty grams of explosive material C4 is detonated at a stand-off-distance of 250 mm and two synchronized high-speed cameras in a stereoscopic setup are used to capture the plate response with an inter frame rate of 6,000 fps. The transient deformation fields are calculated using a three-dimensional digital image correlation technique. The observations appeared to be interesting and somewhat counter intuitively. Results show that a free air blast load induces a highly localized, rapid material response which can be essentially divided in two different stadia. First, when the shock impulse occurs, all particles are forced to move out-of-plane and provided with initial velocities. Secondly, when the pressure wave has vanished, the deformation is further driven by this imparted momentum. This paper shows that a 3D high-speed DIC system is a powerful tool for the assessment of the dynamic response of a structure subjected to extreme loading conditions such as explosions and that this system is capable of accurately measuring surface displacement and deformation data at high rates. Moreover, a free air blast load makes it possible to load a plate specimen at different strain rates in different zones. This makes the test suitable for future material identification using inverse methods, which profit from heterogeneous displacement and strain fields.

A fast and robust mixed numerical/experimental technique is presented, that allows with a single experiment to determine all components of the in-plane permeability tensor, needed for process simulation of resin transfer molding. This technique combines the highly automated “PIERS” (permeability identification using electrical resistance sensors) central injection rig with a customized numerical simulation of the experiment, and uses an iterative inverse method to identify permeability values for which the simulation agrees with the experiment. It is shown that, for reinforcements that are not approximately isotropic, the numerical simulation in the inverse method significantly improves the precision of the parameter identification, compared to inverse methods with models that are valid only until the injected fluid reaches an edge of the reinforcement.

The Laboratory Soete developed a new test setup, based on the well-known pin-on-disc test rig. Instead of the standard composite specimen and steel disc, a rotating composite disc and a steel pin is presently used to have a visible wear track. Other measurement techniques (Acoustic Emission, vibrations, temperature) can be used on the test rig. Continuous monitoring of the wear track combined with standard wear and friction measurements, give results of the current state of the wear track. Fourier frequency analysis (FFT) of these signals gives an indication of the change in condition and contact geometry of the resulting pin-disc combination. A high-speed camera will be used to acquire digital images of the worn composite surface. These online measurements yield to the gradual evolution in damage of the composite specimens.

The resonalyser method is a material identification technique which is based on the measurement of resonance frequencies of freely suspended rectangular test plates, combined with numerical simulations. By adjusting the ratio of the width to the length of the test plate, the resonance frequencies can be made very sensitive for small variations of Poisson’s ratio. This study examines a fabric-reinforced composite material with a very small value of Poisson’s ratio. The material on which the experiments are performed is a carbon fabric-reinforced polyphenylene sulphide. The accurateness of the determined values of the in-plane elastic properties of the test plates is validated with static tensile tests. First, the four orthotropic elastic properties, Young’s moduli E11 and E22, the in-plane shear modulus G12 and Poisson’s ratio m12, are identified using the resonalyser technique. Next, the obtained values for Young’s moduli and Poisson’s ratio are validated with static uni-axial tests. It can be concluded that the results derived from both measurement methods corresponded very well. � 2007 Elsevier Ltd. All rights reserved.