Fabrice Pierron

The Virtual Fields Method

The Virtual Fields Method (VFM) is one of the techniques developed to identify the parameters governing constitutive equations, the experimental data processed for this purpose being displacement or strain fields. It will be shown in this chapter that one of its main advantages is the fact that, in several cases, the sought parameters can be directly found from the measurements, without the need of calculating the stress with a numerical tool such as a finite element programme.

Special virtual fields for the direct determination of material parameters with the virtual fields method. 1–Principle and definition

This paper deals with the direct and simultaneous estimation of parameters used in some constitutive laws. Whole-field data captured in mechanical configurations which give rise to heterogeneous stress fields are processed. Since no analytical relationship is available between measured data and unknown parameters, a specific procedure based on a relevant use of the principle of virtual work is proposed. The main advantage is to provide directly the unknown parameters. The main features of the method are described in the paper.

A Numerical and Experimental Study of Woven Composite Pin-Joints

A numerical and experimental study was carried out to determine the stiffness and the bearing strength of bolted woven composite joints. The main objective was to investigate the possibility of predicting the properties of the joint from the properties of the material measured with standard tests. A refined finite element model was developed in which the nonlinearities due to both the material and the contact angle between the pin and the hole were taken into account. Particular attention was paid to account for the influence of the clearance which has been shown to be very significant. In conclusion, good agreement between experimental results and numerical predictions has been obtained.

Special virtual fields for the direct determination of material parameters with the virtual fields method. 2-Application to in-plane properties

This paper deals with the direct identification of mechanical parameters that govern the in-plane constitutive law of orthotropic materials. Those parameters are extracted from heterogeneous strain fields that occur in a short beam specimen tested in a Iosipescu fixture. The procedure used is the virtual fields method with special virtual fields. The case of linear elasticity is first addressed. It is shown that the parameters are directly extracted with this method: no iterative calculations are required. The stability is also discussed in different cases. A non-linear shear response is then considered. The parameter that governs this non-linearity is also directly identified with the special virtual fields.

Measurement of the in-plane shear strengths of unidirectional composites with the Iosipescu test

This paper addresses the issue of the measurement of the in-plane shear strengths of unidirectional carbon/epoxy composites from Iosipescu specimens. A description of the failure of the samples is presented together with finite-element calculations that confirm the observations. This leads to a discussion of the influence of the boundary conditions on failure, supported by both experimental and finite-element analyses. Eventually, it is shown that failure under a homogeneous stress state is achieved, although the presence of parasitic transverse compressive stress complicates the interpretation in terms of in-plane shear strength. It is shown that the use of a quadratic failure criterion leads to the determination of the in-plane shear strength.

Beyond Hopkinson's bar

In order to perform experimental identification of high strain rate material models, engineers have only a very limited toolbox based on test procedures developed decades ago. The best example is the so-called split Hopkinson pressure bar based on the bar concept introduced 100 years ago by Bertram Hopkinson to measure blast pulses. The recent advent of full-field deformation measurements using imaging techniques has allowed novel approaches to be developed and exciting new testing procedures to be imagined for the first time. One can use this full-field information in conjunction with efficient numerical inverse identification tools such as the virtual fields method (VFM) to identify material parameters at high rates. The underpinning novelty is to exploit the inertial effects developed in high strain rate loading. This paper presents results from a new inertial impact test to obtain stress–strain curves at high strain rates (here, up to 3000 s−1). A quasi-isotropic composite specimen is equipped with a grid and images are recorded with the new HPV-X camera from Shimadzu at 5 Mfps and the SIMX16 camera from Specialised Imaging at 1 Mfps. Deformation, strain and acceleration fields are then input into the VFM to identify the stiffness parameters with unprecedented quality.

The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression

Digital Volume Correlation (DVC) has been emerged recently as an innovative approach to full volume (i.e. internal) displacement and strain field measurement in materials and structures, particularly in conjunction with high resolution X-ray computed tomography (CT). As a relatively novel technique certain aspects of precision, accuracy and the breadth of application are yet to be fully established. This study has applied DVC to volume images of porcine trabecular bone assessing the effect of noise and sub-volume size on strain measurement. Strain resolutions ranging between 70 and 800με were obtained for the optimum sub-volume size of 64 voxels with a 50% overlap for metrological studies conducted. These values allowed the mechanical behaviour of porcine trabecular bone during compression to be investigated. During compression a crushed layer formed adjacent to the boundary plate which increased in thickness as the specimen was further deformed. The structure of the crushed layer was altered to such an extent that it confounded the correlation method. While investigating this factor, it was found that for reliable strain calculations a correlation coefficient of 0.90 or above was required between the sub-volumes in the reference and the deformed volumes. Good agreements between the results and published bone strain failures were obtained. Using the full field strain measurements, Poissons ratio was identified for each compression step using a dedicated inverse method called the virtual fields method (VFM). It was found that for a given region outside of the crushed zone the Poisson ratio decreased from 0.32 to 0.21 between the first and the final compression steps, which was hypothesised to be due to the bone geometry and its resulting deformation behaviour. This study demonstrates that volumetric strain measurement can be obtained successfully using DVC, making it a useful tool for quantitatively investigating the micro-mechanical behaviour of macroscale bone specimens.

Novel experimental approach for longitudinal-radial stiffness characterisation of clear wood by a single test

Abstract Experimental results obtained from maritime pine (Pinus pinaster Ait.) wood are presented for the characterisation of all LR=(1,2) orthotropic stiffness parameters of clear wood specimens by a single test. The approach relies on application of the virtual field method (VFM) to a rectangular specimen loaded in the Iosipescu fixture. The displacement field over the gauge surface of the specimen is measured by the grid method. Two configurations are investigated: (1) with grain aligned along the specimen length (0° configuration) and (2) with grain at 45°. For the 0° configuration, only the parameters Q 11 and Q 66 are correctly identified, with coefficients of variation of the same order of magnitude as those obtained from reference tensile and shear tests. Better identification is obtained for the 45° configuration, for which only the parameter Q 12 exhibits large scatter. This improvement results from a more balanced influence of all stiffness parameters on the response of the 45° specimen. However, all stiffness parameters identified were systematically underestimated by approximately 30% in comparison to reference values. This deviation is due to the vertical spatial variation of the mechanical properties of wood within the stem. Literature data confirm this interpretation.

Novel procedure for complete in-plane composite characterization using a single T-shaped specimen

This paper deals with the direct identification of the in-plane elastic properties of orthotropic composite plates from heterogeneous strain fields. The shape of the tested specimen is that of a T subjected to a complex stress state. As a result, the entire set of unknown parameters is directly involved in the strain and displacement responses of the sample. No exact analytical solution is available for such a geometry, and a specific strategy is used to identify the different stiffness components from the whole-field displacements measured over the tested specimen with a suitable optical method. The paper focuses mainly on the experimental aspects of the procedure, and an example of mechanical characterization of a fabric-reinforced composite plate is given.

Estimation of the strain field from full-field displacement noisy data

In this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches.