Optimized Polynomial Virtual Fields Method for Constitutive Parameters Identification of Orthotropic Bimaterials

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.

Finite element-based virtual fields method with pseudo-real deformation fields for identifying constitutive parameters

Accurate measurement of material mechanics parameters is crucial for evaluating process quality and product reliability and is a major challenge in the development of 3D heterogeneous integration technology. Aiming to perform high-accuracy measurements of the elastoplastic nonlinear constitutive parameters of microelectronic materials using the nanoindentation testing technique, we take advantage of a neural network to construct a forward characterization model to characterize these response characteristic parameters for different materials, design an improved algorithm for obtaining a reverse iterative solution of the forward characterization model, and develop a material mechanics parameter measurement method to solve overdetermined equations using the least-squares method. This method was further improved by addressing the issues of algorithm stability and solution uniqueness, achieving high-precision and fast reverse solutions for elastoplastic constitutive parameters. The relative error of the material parameters is less than 3% (95% confidence interval), the maximum error is less than 8%, and the inversion convergence error of the key indentation response characteristic parameters is less than 0.1%. The difference between the measured material parameters and the theoretical model in the influence on the process stress of TCV (through ceramic via) products is verified through finite element simulation.

Identification of material parameters for aluminum foam at high strain rate

Direct observation of solid deformation at all points in a material test specimen is generally not possible. This becomes important when an internal point experiences the maximum effective deformation of the entire specimen. The simple reduction of load-displacement data to material constitutive parameters, as for inelastic tensile specimen necking, is precluded. Although the mechanics of necking has received considerable attention, the complementary issue of constitutive parameter determination from inelastic specimen experimental data has not. This investigation addresses both aspects of the problem for HY-100 steel. An experimental-computational procedure is demonstrated, which generates material constitutive parameters valid at strains beyond those at the onset of necking. Neck deformation, specimen size and specimen geometry effects are used to ensure the uniqueness of the parameters in the sense that a single uniaxial continuum true-stress–true-strain curve predicts the behaviour of laboratory specimens with different geometries. The solution parameters for HY-100 steel are developed, in the context of an incremental elastic–plastic constitutive formulation, by this procedure. These results support the view that tensile specimen necking is the result of the interaction between imperfection-free specimen geometry, material behaviour and applied load for relatively unsophisticated constitutive formulations if the constitutive parameters are accurately determined. In addition, broken symmetry of specimen deformation is computationally predicted and experimentally confirmed for long, slender specimen geometries.

An inverse analysis technique is proposed for identifying characteristics from experimental data using the virtual fields method with stress-sensitivity-based virtual fields. Two-dimensional digital image correlation is used to obtain the inplane displacement and strain distributions on the specimen surface. To determine the stress distributions under the plane-stress condition, the numerical Laplace transform is used to obtain the through-thickness strain from the inplane strains based on the correspondence principle. Using the virtual displacement fields based on the stress sensitivity, the bulk and shear relaxation moduli, which represent the viscoelastic characteristics, are simultaneously identified. The various stress states generated by the specimen shape and their time variation in a single test and the use of the stress-sensitivity-based virtual fields make it possible to simultaneously determine two independent viscoelastic material properties. Therefore, this method is expected to make a significant contribution to the mechanics of viscoelastic materials.

Extension of the virtual fields method to elasto-plastic material identification with cyclic loads and kinematic hardening

Regional mechanics of the heart is vital in the development of accurate computational models for the pursuit of relevant therapies. Challenges related to heart dysfunctioning are the most important sources of mortality in the world. For example, myocardial infarction (MI) is the foremost killer in sub-Saharan African countries. Mechanical characterisation plays an important role in achieving accurate material behaviour. Material behaviour and constitutive modelling are essential for accurate development of computational models. The biaxial test data was utilised to generated Fung constitutive model material parameters of specific region of the pig myocardium. Also, Choi-Vito constitutive model material parameters were also determined in various myocardia regions. In most cases previously, the mechanical properties of the heart myocardium were assumed to be homogeneous. Most of the computational models developed have assumed that the all three heart regions exhibit similar mechanical properties. Hence, the main objective of this paper is to determine the mechanical material properties of healthy porcine myocardium in three regions, namely left ventricle (LV), mid-wall/interventricular septum (MDW) and right ventricle (RV). The biomechanical properties of the pig heart RV, LV and MDW were characterised using biaxial testing. The biaxial tests show the pig heart myocardium behaves non-linearly, heterogeneously and anisotropically. In this study, it was shown that RV, LV and MDW may exhibit slightly different mechanical properties. Material parameters of two selected constitutive models here may be helpful in regional tissue mechanics, especially for the understanding of various heart diseases and development of new therapies.

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.

Regularized virtual fields method for mechanical properties identification of composite materials

The paper aims to investigate the influences of material constitutive and fracture parameters in addition to cutting speed on chip formation during high-speed cutting of Inconel 718. Finite element analyses for chip formation are conducted with Johnson–Cook constitutive and fracture models. Meanwhile, experiments of high-speed orthogonal cutting are performed to verify the simulation results with cutting speeds ranging from 50 m/min to 7000 m/min. The research indicates that the chip morphology transforms from serrated to fragmented at the cutting speed of 7000 m/min due to embrittlement of the workpiece material under ultra-high cutting speeds. The parameter of shear localization sensitivity is put forward to describe the influences of material mechanical properties on serrated chip formation. The results demonstrate that the effects of initial yield stress and thermal softening coefficient on chip shear localization are much more remarkable than the other constitutive parameters. For the material fracture parameters, the effects of initial fracture strain and exponential factor of stress state on chip shear localization are more much prominent. This paper provides guidance for controlling chip formation through the adjustment of material mechanical properties and the selection of appropriate cutting parameters.

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

In this work, the sensitivity-based virtual fields have been applied to identify two anisotropic plasticity models (Hill48, Yld2000-2D) using a deep-notched tensile test performed on flat samples of cold-rolled sheet of DC04 steel. The material was characterised using the standard protocol to obtain the reference sets of parameters. Deformation data was obtained during deep-notched tests using stereo digital image correlation and the virtual fields method was employed to identify material parameters. It was found that the sensitivity-based virtual fields outperform the standard user-defined virtual fields in terms of accuracy.

The image-based inertial impact test has previously shown that inertial effects generated with high-strain-rate loading can be used to measure the dynamic constitutive properties of composites at strain rates on the order of 1600,{rm s}^{-1}. This work represents an important next step in exploring the potential of this concept with two tests presented where loading heterogeneity is exploited to measure the interlaminar shear modulus and stress–strain behaviour at high strain rates. The first test configuration used a short-beam with asymmetric loading to activate the shear behaviour. The virtual fields method was used to directly identify the interlaminar shear modulus from heterogeneous full-field maps of strain and acceleration. Simulated experiments were used to optimise the test configuration, select optimal smoothing parameters, and quantify uncertainty from grid rotation on the shear modulus identifications. The test was validated experimentally with three different virtual fields identifying an average shear modulus ranging from 5.7 to 5.9 GPa measured at 1600,{rm s}^{-1}, representing a 16–19% increase compared to quasi-static measurements. The shear modulus could also be identified from shear introduced into specimens tested in the standard, end-on interlaminar IBII configuration from slight in-plane misalignments of the impactor. The identified value of 5.6 GPa validates measurements from the first configuration and also demonstrates the capability to identify multiple interlaminar stiffness parameters from a single test.

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.