Performance Analysis of the Mesh‐Free Random Grid Method for Full‐Field Synthetic Strain Measurements

Abstract: In responding to the needs of the material characterization community, the recently developed mesh‐free random grid method (MFRGM) has been exhibiting very promising characteristics of accuracy, adaptability, implementation flexibility and efficiency. To address the design specification of the method according to an intended application, we are presenting a sensitivity analysis that aids into determining the effects of the experimental and computational parameters characterizing the MFRGM in terms of its performance. The performance characteristics of the MFRGM are mainly its accuracy, sensitivity, smoothing properties and efficiency. In this paper, we are presenting a classification of a set of parameters associated with the characteristics of the experimental set‐up and the random grid applied on the specimen under measurement. The applied sensitivity analysis is based on synthetic images produced from analytic solutions of specific isotropic and orthotropic elasticity boundary value problems. This analysis establishes the trends in the performance characteristics of the MFRGM that will enable the selection of the user controlled variables for a desired performance specification.     

Optimised Experimental Characterisation of Polymeric Foam Material Using DIC and the Virtual Fields Method

This article presents a methodology to optimise the design of a realistic mechanical test to characterise the material elastic stiffness parameters of an orthotropic PVC foam material in one single test. Two main experimental techniques were used in this study: Digital Image Correlation (DIC) and the Virtual Fields Method (VFM). The actual image recording process was mimicked by numerically generating a series of deformed synthetic images. Subsequent to this, the entire measurement and data processing procedure was simulated by processing the synthetic images using DIC and VFM algorithms. This procedure was used to estimate the uncertainty of the measurements (systematic and random errors) by including the most significant parameters of actual experiments, e.g. the geometric test configuration, the parameters of the DIC process and the noise. By using these parameters as design variables and by defining different error functions as object functions, an optimisation study was performed to minimise the uncertainty of the material parameter identification and to select the optimal test parameters. The confidence intervals of the identified parameters were predicted based on systematic and random errors obtained from the simulations. The simulated experimental results have shown that averaging multiple images can lead to a significant reduction of the random error. An experimental determination of the elastic coefficient of a PVC foam material was conducted using the optimised test parameters obtained from the numerical study. The identified stiffness values matched well with data from previous tests, but even more interesting was the fact that the experimental uncertainty intervals matched reasonably well with the predictions of the simulations, which is a highly original result and probably the main outcome of the present paper.     

Modelling Strategies for Property Identification Based on Full‐Field Surface Displacement Data

Abstract: The use of full‐field displacement measurements in mechanical testing provides detailed response information that can be used, in conjunction with modelling and optimisation, for precise material property identification. One limitation of this technique is that the collection of response data and the sectioning of a specimen to reveal the material microstructure are both destructive tests and mutually exclusive, as the displacement measurement occurs only on the exposed surface. Therefore, modelling of an experiment to interpret a full‐field experiment requires assumptions about the structure of the material below the visible surface. This study evaluates the effects of several possible modelling assumptions on the errors in model‐predicted response and on the resulting material property estimates. A 3‐D microstructural model, for which the subsurface grain geometry and orientations are known, provides the basis for comparison of several common modelling assumptions based on the grain geometry and orientations on the visible surface of a specimen.     

Addendum to ‘Characterising the Strain and Temperature Fields in a Surrogate Bone Material Subject to Power Ultrasonic Excitation’

Recently, a very interesting article was published in Strain where a rigid polyurethane foam specimen was submitted to longitudinal vibrational excitation in the ultrasonic range. The authors showed that it was possible to measure time‐resolved strain response maps by combining digital image correlation and ultra‐high‐speed imaging. The objective of this discussion is to propose further analysis of the data published in that article, showing that it is possible to extract meaningful values for Young's modulus by using the acceleration field in the specimen as a load cell. The aim here is not to provide a complete solution to this problem but to alert the readers on the possibilities offered by this kind of test. This method is an interesting alternative where the energy is input repeatedly instead of in one go as in impact‐based tests. Full‐field vibration measurements have already been used in the past to identify stiffnesses but only in bending and at much lower strain rates. This article shows that the method can be extended to cover a much wider strain rate range. Finally, only global stiffness values were identified then, whereas here, maps of stiffnesses can be derived.     

Performance Assessment of a Numerical Simulation Tool for Wooden Boards with Knots by Means of Full‐Field Deformation Measurements

In wooden boards, knots and the resulting fibre deviations in their vicinities are mainly responsible for qualitative downgrading of timber elements. Thus, the development of reliable numerical simulation tools for the determination of effective strength and stiffness properties of timber elements and, in a next step, for the development and evaluation of grading criteria is highly desirable. Due to the complexity of such tools, a comprehensive validation is required. Within this work, the suitability of full‐field deformation measurements for four‐point bending tests on wooden boards with knots is evaluated first. Next, the test series is used to validate a previously developed three‐dimensional numerical simulation tool, which combines a geometrical model for the grain course and a micromechanical model for a density and moisture dependent characterisation of the clear‐wood material. The digital image correlation technique proved to be capable to reproduce the strain fields in the vicinity of knots under bending load. Moreover, a very good correlation between numerical and experimental results was obtained.     

Influence of Wooden Board Strength Class on the Performance of Cross‐laminated Timber Plates Investigated by Means of Full‐field Deformation Measurements

Although cross‐laminated timber (CLT) plates are increasingly used in high‐performance building structures, a tailored composition of them or, at least, a performance‐based classification scheme is not available. Especially, the influence of the quality of the ‘raw’ material (wooden boards) on the load carrying capacity of CLT elements is hardly investigated yet. For this reason, within this work, bending tests on 24 CLT plates consisting of wooden boards from three different strength classes have been carried out. The global mechanical response as well as the formation of failure mechanisms were investigated, including a full‐field deformation measurement system, which allowed for a qualitatively as well as quantitatively identification of board failure modes. Interestingly, no influence of the board strength class on the elastic limit load of the CLT plates was observed, but the situation was different for the load displacement history beyond the elastic regime, where basically, two different global failure mechanisms could be distinguished. The obtained knowledge about the ‘post‐elastic’ behaviour of CLT plates may serve as a basis for the optimisation of CLT products and the development or improvement of design concepts, respectively. Moreover, the obtained large ‘post‐elastic’ capacity reserve of CLT consisting of high quality boards could lead to a better utilisation of the raw material.     

The incremental Virtual Fields Method and prestretching method applied to rubbers under uniaxial medium‐strain‐rate loading

Conventional dynamic experiments on rubbers have several limitations including low signal‐to‐noise ratio and a long time period during which the specimen is not in static equilibrium, which causes difficulties separating constitutive material behaviour from specimen response. In order to overcome these limitations, we build on previous research in which the Virtual Fields Method (VFM) is applied to dynamic tensile experiments. A previous study has demonstrated that the VFM can be used to identify the material parameters of a hyperelastic model for a given rubber based on optical measurements of wave propagation in the rubber, eliminating the need for force measurements by instead using acceleration fields as a “virtual load cell.” In order for us to successfully characterise the strain hardening in the material, large deformations are required, and these were achieved by applying static preloads to the specimen before the dynamic loading. In order for us to then apply the VFM, measurements of the static force, or strain, or both, are required. This paper explores different methods for applying the VFM, in particular, comparing the use of a static force measurement, as in the previous research, to methods that only require strain fields in order to apply the incremental equation of motion. Finite element method simulations were conducted to compare the identification sensitivity to experimental error sources between the 2 VFM implementations; the experimental data used in the previous studies were then applied to the incremental VFM. A further experimental comparison is provided between constitutive parameters obtained in tensile experiments using the VFM and compressive measurements from a modified split Hopkinson bar technique equipped with a piezoelectric force transducer. Finally, there is a discussion of the effects of preloading and relaxation in the material.     

In‐Field Measurement of Forces and Deformations at the Rear End of a Motorcycle and Structural Optimisation: Experimental–Numerical Approach Aimed at Structural Optimisation

Abstract: The present study concerns the analysis of the asymmetric displacement behaviour of the rear part of a motorcycle. Stylistic reasons led to the design of a vehicle with only one suspension located on the left‐hand side. Experimental tests performed on a circuit with seven obstacles along a straight line confirmed that the bending displacement is higher on the right‐hand side than on the left. This study aimed to perform a structural optimisation of the components involved at the rear end of the motorcycle, to find a solution to the problem. A hybrid approach is applied: the force acting on the suspension and bending displacements at the rear end were simultaneously measured in working conditions; a finite‐element method model was then set up, validated and applied for design optimisation purposes. Both methodological aspects and applicative results are presented and discussed. Finally, a solution in accordance with design specifics is proposed.     

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

The grid method is a technique suitable for the measurement of in‐plane displacement and strain components on specimens undergoing a small deformation. It relies on a regular marking of the surfaces under investigation. Various techniques are proposed in the literature to retrieve these sought quantities from images of regular markings, but recent advances show that techniques developed initially to process fringe patterns lead to the best results. The grid method features a good compromise between measurement resolution and spatial resolution, thus making it an efficient tool to characterise strain gradients. Another advantage of this technique is the ability to establish closed‐form expressions between its main metrological characteristics, thus enabling to predict them within certain limits. In this context, the objective of this paper is to give the state of the art in the grid method, the information being currently spread out in the literature. We propose first to recall various techniques that were used in the past to process grid images, to focus progressively on the one that is the most used in recent examples: the windowed Fourier transform. From a practical point of view, surfaces under investigation must be marked with grids, so the techniques available to mark specimens with grids are presented. Then we gather the information available in the recent literature to synthesise the connection between three important characteristics of full‐field measurement techniques: the spatial resolution, the measurement resolution and the measurement bias. Some practical information is then offered to help the readers who discover this technique to start using it. In particular, programmes used here to process the grid images are offered to the readers on a dedicated website. We finally present some recent examples available in the literature to highlight the effectiveness of the grid method for in‐plane displacement and strain measurement in real situations.     

A Review of the Challenges and Limitations of Full‐Field Measurements Applied to Large Heterogeneous Deformations of Rubbers

Abstract: This paper presents an overview of the use of full‐field measurement techniques, more precisely digital image correlation (DIC) and coupled DIC and infrared thermography, for the material and structure characterisation of rubber reported in the literature. Even though such techniques have increasingly been applied for approximately 30 years for moderate deformations in metal and composite materials, they are still under‐employed in the measurement of full kinematic and thermal fields in the case of large deformations undergone by rubber materials. To date, the applications addressed are crack propagation at both macroscopic and microscopic scales, model validation and constitutive parameter identification.     

High‐Speed 3D Printing of Millimeter‐Size Customized Aspheric Imaging Lenses with Sub 7 nm Surface Roughness

Advancements in three‐dimensional (3D) printing technology have the potential to transform the manufacture of customized optical elements, which today relies heavily on time‐consuming and costly polishing and grinding processes. However the inherent speed‐accuracy trade‐off seriously constrains the practical applications of 3D‐printing technology in the optical realm. In addressing this issue, here, a new method featuring a significantly faster fabrication speed, at 24.54 mm³ h^?1, without compromising the fabrication accuracy required to 3D‐print customized optical components is reported. A high‐speed 3D‐printing process with subvoxel‐scale precision (sub 5 µm) and deep subwavelength (sub 7 nm) surface roughness by employing the projection micro‐stereolithography process and the synergistic effects from grayscale photopolymerization and the meniscus equilibrium post‐curing methods is demonstrated. Fabricating a customized aspheric lens 5 mm in height and 3 mm in diameter is accomplished in four hours. The 3D‐printed singlet aspheric lens demonstrates a maximal imaging resolution of 373.2 lp mm^?1 with low field distortion less than 0.13% across a 2 mm field of view. This lens is attached onto a cell phone camera and the colorful fine details of a sunset moth's wing and the spot on a weevil's elytra are captured. This work demonstrates the potential of this method to rapidly prototype optical components or systems based on 3D printing.     

Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full‐field measurements

Full‐field optical measurements like digital image correlation or the grid method have brought a paradigm shift in the experimental mechanics community. While inverse identification techniques like finite element model updating or the virtual fields method have been the object of significant developments, current test methods, inherited from the age of strain gauges or linear variable displacement transducers, are generally not well adapted to the rich information provided by these new measurement tools. This paper provides a review of the research dealing with the design and optimization of heterogeneous mechanical tests for the identification of material parameters from full‐field measurements, christened here Material Testing 2.0 (MT2.0).     

Identification of Johnson–Cook's Viscoplastic Model Parameters Using the Virtual Fields Method: Application to Titanium Alloy Ti6Al4V

Abstract: The identification of viscoplastic material parameters is addressed using a new powerful method: the virtual fields method (VFM). Contrary to classical procedures that are statically determined, the VFM is applied to heterogeneous mechanical fields. Without any hypotheses of homogeneity required, the exploitation of tests with the VFM is not limited to small levels of strains anymore and it can be taken advantage of the large amount of information available thanks to full‐field measurements. In the case of viscoplastic models, the characterisation of strain‐rate sensitivity with the VFM is attempted in this paper using only one test under high‐speed loading conditions, whereas several tests performed at different constant strain‐rates are required for the classical procedures. This article focuses on the development of the VFM for the characterisation of Johnson–Cook's (JC) viscoplastic model. To his aim a return‐mapping algorithm was developed according to the JC's model with an implicit Euler scheme implemented to integrate the constitutive relations. The whole viscoplastic behaviour of a Titanium alloy (Ti6Al4V) is successfully characterised by the VFM using only two tensile tests on notched flat specimens, with full‐field strain measurements by digital image correlation.     

A general linear method to evaluate the hardening behaviour of metals at large strain with full‐field measurements

The hardening behaviour of metals is generally described in terms of a stress‐strain curve derived from experiments. In this paper, a linear method to identify the stress‐strain curve starting from full‐field measurement data is presented. This method can be applied to any stress state using a generic yield function, the only requirement is that the full‐field measurement is extended up to the border of the specimen. The method is presented and validated using a finite element model of a notched specimen. Moreover, experiments were performed on specimens cut from a BH340 steel sheet to illustrate the viability to actual cases. Two geometries were considered, a standard uniaxial test, where the method was used to evaluate the post‐necking behaviour, and a notched specimen with a heterogeneous strain field. The proposed method, named linear stress‐strain curve identification (LSSCI), can be a useful tool in combination with inverse methods to identify the constitutive behaviour of metals in large strain plasticity.     

Digital Image Correlation and Noise‐filtering Approach for the Cracking Assessment of Massive Reinforced Concrete Structures

This paper describes the use of Digital Image Correlation (DIC) techniques for the cracking assessment of reinforced concrete (RC) massive beams and walls. DIC is known to provide accurate and detailed information on displacement and strain fields. Non‐contact measurements can be used to evaluate concrete cracking of destructive tests carried out on a wide range of specimen scales. When applied to large RC structures tested outdoors or in difficultly controllable conditions, DIC‐based methods may lead to erroneous results. In this study a post‐processing procedure is presented to cope with noisy full‐field measurements. The proposed cracking assessment approach is validated on a large experimental campaign. Four points bending tests are carried out on RC beams: firstly on full‐scale rectangular beams and then on mock‐ups scaled down by 1/3. In addition, fours RC walls are tested under in‐plane cyclic shear up to failure. Digital images taken throughout the tests are processed by DIC techniques to provide in‐plane displacement and strain fields. Full‐field measurements are post‐processed by the noise‐filtering technique and the cracks patterns are identified. Crack widths are measured and compared with measurements obtained from conventional point‐based sensors (linear variable differential transformer LVDT and fibre‐optic FO transducers). The proposed DIC‐based post‐processing provides accurate estimation of cracks width for most of the tests. The analyses carried out on the two groups of RC beams show a scale‐effect on the cracks width.     

Investigation of the 2D assumption in the image‐based inertial impact test

The image‐based inertial impact (IBII) test has shown promise for measuring properties of composites at strain rates where existing test methods become unreliable due to inertial effects (> 10² s^?1 ). Typically, the IBII tests are performed with a single camera, and therefore, to use surface measurements for material property identification, it is necessary to assume that the test is two‐dimensional. In this work, synchronised ultra‐high‐speed cameras are used to quantify the relevance of this assumption when nonuniform, through‐the‐thickness loading is applied to interlaminar samples. Initial experiments revealed that an angular misalignment of approximately 1° between the impact faces of the waveguide and projectile created a bending wave that propagated along the sample behind the axial pulse. Even under these conditions, consistent measurements of stiffness were made by assuming a linear distribution of the behaviour through‐the‐thickness. When the misalignment was reduced to 0.2°, the effects on single‐sided measurements were significantly reduced. The two alignment cases were compared to show that three‐dimensional loading had a small effect on stiffness identification (approximately 5% bias) relative to failure stress (approximately 30% bias). This study highlights the importance of impact alignment for reliable characterisation of the interlaminar failure stress and was used to establish guidelines for diagnosing loading issues from single‐sided measurements.     

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

An analytical formulation based on Irwin's integral and combined with the extended finite element method is proposed to extract mixed‐mode components of strain energy release rates in linear elastic fracture mechanics. The proposed formulation extends our previous work to cracks in arbitrary orientations and is therefore suited for crack propagation problems. In essence, the approach employs high‐order enrichment functions and evaluates Irwin's integral in closed form, once the linear system is solved and the algebraic degrees of freedom are determined. Several benchmark examples are investigated including off‐center cracks, inclined cracks, and two crack growth problems. On all these problems, the method is shown to work well, giving accurate results. Moreover, because of its analytical nature, no special post‐processing is required. Thus, we conclude that this method may provide a good and simple alternative to the popular J‐integral method. In addition, it may circumvent some of the limitations of the J‐integral in 3D modeling and in problems involving branching and coalescence of cracks. Copyright © 2013 John Wiley & Sons, Ltd.     

Time‐resolved identification of mechanical loadings on plates using the virtual fields method and deflectometry measurements

This paper describes an approach for identifying the magnitude and location of both stationary and transient mechanical loadings applied to a thin rectangular simply supported plate. Full‐field deflectometry measurements and the virtual fields method are used with the local equilibrium equation of the plate in the time domain to solve the force reconstruction problem, whereas previous work by the authors used this last equation in the frequency domain. As a result, it is possible to reconstruct load time history in addition to magnitude and location. Experimental results of this complete identification are presented for two different instrumented mechanical exciters: electrodynamic shaker and impact hammer for stationary and transient excitations, respectively. The approach is then applied to determine the location and time of multiple unknown transient excitations produced by a set of impacting metal marbles.