Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields

A major challenge in the identification of material properties is handling different sources of uncertainty in the experiment and the modelling of the experiment for estimating the resulting uncertainty in the identified properties. Numerous improvements in identification methods have provided increasingly accurate estimates of various material properties. However, characterizing the uncertainty in the identified properties is still relatively crude. Different material properties obtained from a single test are not obtained with the same confidence. Typically the highest uncertainty is associated with respect to properties to which the experiment is the most insensitive. In addition, the uncertainty in different properties can be strongly correlated, so that obtaining only variance estimates may be misleading. A possible approach for handling the different sources of uncertainty and estimating the uncertainty in the identified properties is the Bayesian method. This method was introduced in the late 1970s in the context of identification [1] and has been applied since to different problems, notably identification of elastic constants from plate vibration experiments [2]-[4]. The applications of the method to these classical pointwise tests involved only a small number of measurements (typically ten natural frequencies in the previously cited vibration test) which facilitated the application of the Bayesian approach. For identifying elastic constants, full field strain or displacement measurements provide a high number of measured quantities (one measurement per image pixel) and hence a promise of smaller uncertainties in the properties. However, the high number of measurements represents also a major computational challenge in applying the Bayesian approach to full field measurements. To address this challenge we propose an approach based on the proper orthogonal decomposition (POD) of the full fields in order to drastically reduce their dimensionality. POD is based on projecting the full field images on a modal basis, constructed from sample simulations, and which can account for the variations of the full field as the elastic constants and other parameters of interest are varied. The fidelity of the decomposition depends on the number of basis vectors used. Typically even complex fields can be accurately represented with no more than a few dozen modes and for our problem we showed that only four or five modes are sufficient [5]. To further reduce the computational cost of the Bayesian approach we use response surface approximations of the POD coefficients of the fields. We show that 3rd degree polynomial response surface approximations provide a satisfying accuracy. The combination of POD decomposition and response surface methodology allows to bring down the computational time of the Bayesian identification to a few days. The proposed approach is applied to Moire interferometry full field displacement measurements from a traction experiment on a plate with a hole. The laminate with a layup of [45,- 45,0]s is made out of a Toray® T800/3631 graphite/epoxy prepreg. The measured displacement maps are provided in Figure 1. The mean values of the identified properties joint probability density function are in agreement with previous identifications carried out on the same material. Furthermore the probability density function also provides the coefficient of variation with which the properties are identified as well as the correlations between the various properties. We find that while the longitudinal Young's modulus is identified with good accuracy (low standard deviation), the Poisson's ration is identified with much higher uncertainty. Several of the properties are also found to be correlated. The identified uncertainty structure of the elastic constants (i.e. variance co-variance matrix) has potential benefits to reliability analyses, by allowing a more accurate description of the input uncertainty. An additional advantage of the Bayesian approach is that it provides a natural way (in the form of the prior probability density function) for accounting for prior information that may be available on the material properties thought. This is of great interest for reducing the uncertainty on properties that can only be determined with low confidence from the plate with a hole experiment, such as Poisson's ratio or transverse Young's modulus in our case.

Digital image correlation method is widely used in macro- and mesoscopic mechanical tests because of the advantages of non-contact, high precision, full field measurement, and simple experimental equipment. But it still has many shortcomings in theory and application. For example, the traditional DIC method has difficulty obtaining the desired result when the surface of the test object is rotated substantially or the deformation involves large rotation (i.e. measuring helicopter blade deformation dynamically). Some scholars argue that a rotation angle greater than 7° will not work with the DIC algorithm, and this phenomenon is called decorrelation [1-3]. The application of various nonlinear optimization algorithms greatly reduces the computation time of the DIC iteration process.

Relating age and micro-architecture with apparent-level elastic constants: a micro-finite element study of female cortical bone from the anterior femoral midshaft

Mode II- delamination modeling in multi-directional laminates using cohesive zone methodology under static and dynamic loading

Full-field force identification with high-speed digital holography

In-situ noncontact measurement system for nozzle throat deformation in high-temperature gas heating via laser speckle digital image correlation with wavelet smoothing of displacement field

Genetic algorithm reconstruction of orthotropic composite plate elastic constants from a single non-symmetric plane ultrasonic velocity data

The identification of cracks stress intensity factors (SIFs) in elastic solids from full-field in-plane displacement field measurements is addressed. Because it is known that significant three dimensional effects alter the values of plane stress computed SIFs, and that the overall geometry of the crack front plays also a role, the problem of SIF’s identification is tackled here in the full three-dimensional framework. First is derived a data completion method in elasticity enabling the determination of the elastic displacement and stress fields inside the solid, or in the part where the behavior remain elastic, from surface displacements including the case of only in-plane displacement fields measurements over a traction-free surface. Then usual numerical methods for the computation of SIF or energy release rates are used. Numerical applications in three-dimensional elasticityfor true 3D geometry and loading are presented.

Multidirectional (MD) composite laminates are extensively employed in structural applications owing to their superior mechanical characteristics. Nevertheless, the evaluation of the fracture toughness of composite laminates primarily relies on tests using unidirectional (UD) specimens. This study evaluates the reliability of characterizing mode II delamination behaviour in MD laminates by using UD specimens. The quantification of delamination area through Digital Image Correlation (DIC) analysis is integrated with a physical Energy Release Rate (ERR) method to ascertain the fracture resistance, which is compared with the ERR derived via a modified J-integral method and the standardized compliance methods. Fractographic analysis reveals similar fracture mechanisms in specimens with identical interfaces. The physical ERR increases notably due to large-scale fibre bridging induced by fibre nesting at 0∘//0∘ interfaces. Conversely, in 0∘//90∘ interfaces, large-area matrix cracking enhances the intrinsic fracture resistance, excluding the extrinsic toughening provided by fibre bridging.

Three-dimensional elastic constants for a fiber-reinforced lamina are often difficult to obtain from traditional mechanical tests. The relationships developed in thiswork enable the determination of any three of the five independent elastic constants, of a transversely isotropic lamina, from measurements of the remaining two elastic constants and the coefficients of thermal expansion (CTE’s) of [(+θ/−θ)n]s and unidirectional laminates. The approach is used to predict the elastic propertiesof a carbon fiber reinforced epoxy material and the predicted properties are shown to be in good agreement with quoted values. Further, the developed relationships can be used to determine elastic constants over a range of temperatures and, potentially, to study the effects of manufacturing on elastic properties. Therefore, this technique constitutes an additional method for evaluating the elastic constants that characterize a transversely isotropic, fiber-reinforced lamina.

In particular, CFRP (carbon fiber reinforced plastics) composite materials have found wide applicability because of their inherent design flexibility and improved material properties. CFRP composites were manufactured from uni-direction prepreg sheet in this paper. It is important to assess fiber orientation, material properties and part defect in order to ensure product quality and structural integrity of CFRP because strength and stiffness of composites depend on fiber orientation. It is desirable to perform nondestructive evaluation which is very beneficial. An new method for nondestructively determining the fiber orientation in a composite laminate is presented. A one-sided pitch-catch setup was used in the detection and evaluation of flaws and material anomalies in the unidirectional CFRP composite laminates. Two Rayleigh wave transducers were joined head-to-head and used in the pitch-catch mode on the surface of the composites. The pitch-catch signal was found to be more sensitive than normal incidence backwall echo of longitudinal wave to subtle flaw conditions in the composite. Especially, ultrasonic waves were extensively characterized in the CFRP composite laminates both normal to fiber and along to fiber with using a one-sided direction of Rayleigh wave transducers. Also, one-sided ultrasonic measurement was made with using a Rayleigh wave transducers and a conventional scanner was used in an immersion tank for extracting fiber orientation information from the ultrasonic reflection in the unidirectional laminate. Therefore, it is thought that the proposed method is useful to evaluate integrity of CFRP laminates.

Digital Image Correlation became one of the dominant optical full-field techniques used in experimental mechanics. It does not require sophisticated equipment to evaluate the full displacement vector field of the specimen under test with great accuracy. In this paper, we would like to put the reader's attention to the DIC technique as a solution that may identify the genuine character of the load applied to the object under test. Our experience with testing wind turbine blades using DIC proves that possibility. Full Text: PDF References E.M.C Jones, M.A. Iadicola, "A good practises guide for digital image correlation" International Digital Image Correlation Society, (2018), CrossRef B. Pan, "Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals", Meas. Sci. Technol. 29, 082001 (2018), CrossRef B. Pan, L.P. Yu, Q.B. Zhang, "Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement", Sci. China Technol. Sci. 61, 2 (2018), CrossRef S. Sharma, N. Iniyan Thiruselvam, S.J. Subramanian, G.S. Kumar, "Computation of strains from stereo digital image correlation using principal component analysis", Meas. Sci. Technol. 32, 105201 (2021), CrossRef IEC 61400-5:2020 Wind energy generation systems - Part 5: Wind turbine, DirectLink IEC 61400-23:2014 Wind turbines - Part 23: Full-scale structural testing of rotor blades, DirectLink

Full-field measurement and fracture and fatigue characterizations of asphalt concrete based on the SCB test and stereo-DIC

The paper presents an experimental application of a method leading to the identification of the elastic and damping material properties of isotropic vibrating plates. The theory assumes that the searched para meters can be extracted from curvature and deflection fields measured on the whole surface of the plate at two particular instants of the vibrating motion. The experimental application consists in an original excitation fixture, a particular adaptation of an optical full-field measurement technique, a data preprocessing giving the curvature and deflection fields and finally in the identification process using the Virtual Fields Method (VFM). The principle of the deflectom etry technique used for the measurements is presented. First results of identification on an acrylic plate are presented and compared to reference values. The used theoretical principle only assumes the global equilibrium of the observed part of the coupon. Therefore the identification remains insensible to the parasitic effects of the boundary conditions. This is confirmed by the results of the last presented experimentation. Keywords: vibration, identification, Virtual Fields Method, damping, deflectometry, slope fields, grid method, image processing.

A reduced-order modelling (ROM) approach for predicting steady, turbulent aerodynamic flows based on computational fluid dynamics (CFD) and proper orthogonal decomposition (POD) is presented. Model-order reduction is achieved by parameter space sampling, solution space representation via POD and restriction of a CFD solver to the POD subspace. Solving the governing equations of fluid dynamics is replaced by solving a non-linear least-squares optimisation problem. The method will be referred to as LSQ-ROM method. Two approaches of extracting POD basis information from CFD snapshot data are discussed: POD of the full state vector (global POD) and POD of each of the partial states separately (variable-by-variable POD). The method at hand is demonstrated for a 2D aerofoil (NACA 64A010) as well as for a complete industrial aircraft configuration (NASA Common Research Model) in the transonic flow regime by computing ROMs of the compressible Reynolds-averaged Navier-Stokes equations, pursuing both the global and the variable-by-variable POD approach. The LSQ-ROM approach is tried for extrapolatory flow conditions. Results are juxtaposed with those obtained by POD-based extrapolation using Kriging and the radial basis functions spline method. As a reference, the full-order CFD solutions are considered. For the industrial aircraft configuration, the cost of computing the reduced-order solution is shown to be two orders of magnitude lower than that of computing the reference CFD solution.