Regularized virtual fields method for mechanical properties identification of composite materials

Material Testing 2.0 (MT2.0) is a paradigm that advocates for the use of rich, full-field data, such as from digital image correlation and infrared thermography, for material identification. By employing heterogeneous, multi-axial data in conjunction with sophisticated inverse calibration techniques such as finite element model updating and the virtual fields method, MT2.0 aims to reduce the number of specimens needed for material identification and to increase confidence in the calibration results. To support continued development, improvement, and validation of such inverse methods—specifically for rate-dependent, temperature-dependent, and anisotropic metal plasticity models—we provide here a thorough experimental data set for 304L stainless steel sheet metal. The data set includes full-field displacement, strain, and temperature data for seven unique specimen geometries tested at different strain rates and in different material orientations. Commensurate extensometer strain data from tensile dog bones is provided as well for comparison. We believe this complete data set will be a valuable contribution to the experimental and computational mechanics communities, supporting continued advances in material identification methods.

Inferring material parameters of soft materials, especially soft tissues from experiments, has always been a challenge because of the inaccuracy of specimen geometry, difficulty in proper gripping and difficulty in obtaining reliable displacement data. If one is able to obtain full field data with Digital Image Correlation or other similar techniques, we show that in spite of poor quality experimental data, it is still possible to get the material parameters using Virtual Fields Method with carefully chosen virtual fields. We demonstrate the approach by two cases. The first is Ecoflex (silicone rubber) under biaxial deformations at controlled loading rates, and the second is rat skin samples with imperfect shape under biaxial deformations at controlled loading rates. In both cases, rather than trying to obtain homogeneous deformation conditions, we use a technique based on the Virtual Fields Method to extract the material properties from the deformation of the specimen collected by Digital Image Correlation (DIC) and the force load measured by the load sensor. In order to apply loads in two principal directions simultaneously, a custom biaxial set-up was built and mounted into a uniaxial Instron tensile set-up. We show here that in spite of significant inhomogeneity in the deformation, errors, and missing data in the measured displacement field, we are still able to recover the material properties of the soft solid by suitable choices of virtual fields.

The paper is focused on the process of identifying stress fields from strain fields in the specimen with a hole. The experiment was realized on the specimen with a hole made from anisotropic material. The main attention is paid to the analysis of deformation in the areas of stress (near the hole). That geometry generates a heterogeneous strain field which has been measured during the test using a digital image correlation system. The advantage of using heterogeneous strain fields in the identification procedure is that a complex state of stress-strain can be analyzed at the same time. On the other hand the stress field cannot be directly computed from the test and a suitable identification procedure has to be developed. Here, the virtual fields method (VFM) adapted for plastic strain has been used to identify the hardening behaviour and the anisotropy of the material. The values obtained by the VFM have been compared with the results coming from a standard identification made with uniaxial tensile tests.

Study of Tailor Heat Treated Blanks Using the Fourier-series-based VFM

Characterization of the post-necking strain hardening behavior using the virtual fields method

Some comments on “The determination of best fit linear failure envelopes to Mohr circles” by J. V. Stafford, E. Audsley and J. R. Sharp

The aim of this work is to identify parameters driving constitutive equations of materials with displacement field measurements carried out by image stereo-correlation during an unidirectional tensile test. We evaluate two identification techniques. The first one is the virtual fields method which consists in writing the principle of virtual work with particular virtual fields. It is generally used in the case of linear elasticity and it requires a perfect knowledge of the model in terms of boundary condition since the virtual fields used must be kinematically admissible. This method allows to determine parameters by a direct and fast calculation, without iterations. The second method is the finite element model updating method. It consists in finding constitutive parameters that achieve the best match between finite element analysis quantities and their experimental counterparts. This method is more adaptable than the virtual field method but it needs to spend more calculation time.

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 (FEMU) or the Virtual Fields Method (VFM) have been the object of significant developments, current test methods, inherited from the age of strain gauges or LVDTs, are not generally well adapted to the rich information provided by these new measurement tools. This paper provides a short review of the research dealing with the design and optimization of heterogeneous mechanical tests for identification of material parameters from full-field measurements.

Heterogeneous materials are widely applied in many fields. Owing to the spatial variation of its constitutive parameters, the mechanical characterization of heterogeneous materials is very important. The virtual fields method has been used to identify the constitutive parameters of materials. However, there is a limitation: constitutive parameters of one material have to be a priori; then, constitutive parameters of the other one can be identified. Aiming at this limitation, this article presents a method to identify the constitutive parameters of heterogeneous orthotropic bimaterials under the condition that constitutive parameters of both materials are all unknown from a single test. A constitutive parameter identification method of orthotropic bimaterials based on optimized virtual field and digital image correlation is proposed. The feasibility of this method is verified by simulating the deformation fields of a two‐layer material under three‐point bending load. The results of numerical experiments with FEM simulations show that the weighted relative error of the constitutive parameter is less than 1%. The results suggest that the variation coefficient‐to‐noise ratio can perform a priori evaluation of a confidence interval on the identified stiffness components. The results of numerical experiments with DIC simulations show that the weighted relative error is 1.44%, which is due to the noise in the strain data calculated by DIC method.

Applying the virtual fields method to determine the through-thickness moduli of thick composites with a nonlinear shear response

Evaluation of crack tip stress and strain fields under nonproportional loading in a viscoelastic material

This paper deals with the direct identification of parameters governing anisotropic elastic constitutive equations. These parameters are identified from heterogeneous strain fields with the virtual fields method. This method is based on a relevant use of the principle of virtual work. Different numerical aspects of the implementation of the method are discussed in the paper, mainly in terms of stability of the identified parameters when noisy data are processed. It is shown that the sensitivity of the method to noisy data is compatible with a practical use during experiments. Copyright © 2004 John Wiley & Sons, Ltd.

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.

This study deals with an experimental methodology developed in order to identify the elastic properties of super- conducting ring-shaped windings, constituents of the main coil winding of a magnetic resonance imaging magnet (MRI). Mechanical tensile tests were conducted on real scale specimens associated to an optical full-field displacement measurement technique (stereo image correlation). Strain fields were then obtained from the measured displacement fields by numerical dif- ferentiation. Finally, the four in-plane orthotropic stiffnesses of the windings were determined using the Virtual Fields Method (VFM). Experimental set-up also allows detecting a possible occurrence of a delamination thanks to in-plane displacement fields.

Direct identification of the damage behaviour of composite materials using the virtual fields method