We present a stochastic approach combining Bayesian Inference (BI) with homogenization theories in order to identify, on the one hand, the parameters inherent to the model assumptions and, on the ...other hand, the composite material constituents behaviors, including their variability. In particular, we characterize the model parameters of a Mean-Field Homogenization (MFH) model and the elastic matrix behavior, including the inherent dispersion in its Young’s modulus, of non-aligned Short Fibers Reinforced Polymer (SFRP) composites. The inference is achieved by considering as observations experimental tests conducted at the SFRP composite coupons level. The inferred model and material law parameters can in turn be used in Mean-Field Homogenization (MFH)-based multi-scale simulations and can predict the confidence range of the composite material responses.
•Definition of an inverse identification protocol based on the Virtual Fields Method with enhanced robustness and efficiency for the calibration of anisotropic plasticity models.•The method provides ...a diagnostic strategy for the evaluation of a suitable smoothing of strain data in order to reduce the effects of experimental noise.•The formulation of the adopted virtual fields and the VFM settings can considerably increase the accuracy of the identification results.•The method was capable of identifying the YLD2000-2D yield function in the case of a bake-hardened steel by using deep-notched specimen at three material orientations.
The Virtual Fields Method (VFM) is a well established inverse technique used to identify the constitutive parameters of material models using heterogeneous full-field strain data. When VFM is employed to retrieve the coefficients of advanced plasticity models, including non linear hardening and anisotropy, however, the procedure may become computationally intensive. Furthermore, the impact of experimental uncertainties is still not entirely scrutinized. In this paper, an identification strategy based on uncoupling the hardening behaviour and the anisotropic yield function is proposed. The approach, based on VFM, allows to carry on the identification with low computational time, and provides also indications on the optimal smoothing level to use in the full-field measurement.
The identification framework is applied on the linear transformation-based yield condition Yld2000-2D, employing numerical data for the validation and, afterwards, using actual experimental data on a bake-hardenable steel, i.e. BH340. Moreover, several aspects of the identification procedure are investigated in dept, namely, the effect of smoothing, the influence of VFM settings (type of virtual fields used, discretization method) and the computational time. The identification results are compared with the standard calibration process, demonstrating that the proposed strategy is capable of identifying properly the material anisotropic behaviour using only three tests on notched specimens.
•A novel approach for the hardening parameters identification of cell-wall of closed-cell aluminum foam.•The objective function considers both the indentation curve and the pile-up information.•The ...optimization process combines 2D with 3D numerical simulations to improve the efficiency.•The material properties of cell-wall of aluminum foam are experimentally verified.
This study aims to develop an inverse approach to identifying the cell-wall material properties of closed-cell aluminum (Al) foams, which is based upon indentation tests, numerical simulation and optimization technique. Vickers nano-indentation tests are conducted on the cell-wall of foams, and the residual surface deformation is measured by a high definition confocal microscopy. To enhance identification efficiency, a combined 2D with 3D micromechanics modeling strategy is proposed here, in which the load-depth curve and residual imprint (pile-up) of the indentation tests are considered. In this study, the cell-wall material properties such as the yield strength and strain-hardening exponent are identified using this proposed inverse approach, while the Young's modulus is obtained directly for the unloading part of the indentation load-depth curves. The identification results indicate that the proposed inverse procedure can provide a well-posed solution to the cell-wall material properties by introducing the pile-up information. Microscopic computed tomography (μCT) technique is also utilized to reconstruct accurate 3D image-based representative volume element (RVE) model of foam structure, through which the numerical simulation is conducted for uniaxial compression. The identified cell-wall material parameters are validated by comparing the numerical simulation with the experimental data in terms of the deformation/failure modes and quantitative results. It is noted that the cell-wall of aluminum foams that are commonly made of melt foaming processes exhibits a quite different stress-strain relation when compared with the raw material of cell-wall. This study is expected to provide an effective approach for identifying the material properties that may be not easily determined through conventional testing methods.
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The identification of the plastic behaviour of sheet metals at severe deformation is extremely important for many industrial application such as metal forming, crashworthiness, automotive, aerospace, ...piping, etc. In this paper, the virtual fields method (VFM) was employed to identify the constitutive parameters of anisotropic plasticity models. The method was applied using the finite deformation theory in order to account for large strains. First the theoretical principles to implement the method are described in details, especially how to derive the stress field from the strain field. Afterwards a numerical validation was performed using the Hill48 model. Several aspects were studied with the numerical model: the effect of the used virtual fields, the minimum number of specimens required to identify the parameters, the stress distribution obtained from the specimen and its influence in the identification performance. A brief analysis on the influence of noise is also conducted. Finally a series of experiments was conducted on notched specimens of stainless steel, cut along different anisotropic directions. The displacement and strain fields were obtained by digital image correlation. Afterwards, the VFM was used to identify the parameters of the Hill48 model and the Yld2000-2D model. In this case, the Hill48 model was not able to correctly describe the material behaviour, while a rather good agreement was found with the Yld2000-2D model. The potential and the limitation of the proposed method are finally discussed.
Today, simulation of cutting processes still relies, in most cases, on the phenomenological representation of flow stress properties of workpiece materials. This investigation presents a ...physics-based (dislocation-based) constitutive model to simulate the flow stress properties of Ti6Al4V titanium alloy at elevated temperatures and a large range of strain rates. The Split Hopkinson Pressure Bar (SHPB) data and inverse modelling of orthogonal cutting tests are combined using a novel approach to obtain flow stress properties and to calibrate the damage and friction models. The applicability of the presented model for cutting simulation is critically discussed.
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•A novel weight-based FEMU framework is proposed to inversely identify an anisotropic yield function.•The inverse identification quality significantly improves by two non-conventional ...experiments.•Weight-based FEMU has a large potential to reduce advanced anisotropic yield function calibration effort.
In theory, a single non-conventional mechanical experiment generating inhomogeneous strain fields enables to inversely identify an anisotropic yield function. However, several studies have shown that it is challenging to design such a sufficiently data-rich experiment, particularly when it must be conducted on a standard uniaxial tensile machine. Instead of relying on a single non-conventional uniaxial tensile experiment, combining multiple non-conventional experiments is proposed to inversely identify an advanced anisotropic yield function. The feasibility of the proposed method is verified through the inverse identification of the Yld2000-2d yield function using synthetically generated Digital Image Correlation (DIC) data. This approach accounts for the metrological aspects of DIC while avoiding potential experimental errors and uncertainties related to the selected material model. It has been demonstrated that when a single unconventional tensile test is combined with a non-conventional biaxial tensile test, the inversely identified anisotropy parameters are in good agreement with those found through the conventional method. This finding is contingent on maintaining an equal contribution of the strain states from each experiment to the cost function. Excluding overlapping data points and assigning proper weights to the trustworthy data based on the strain state and the level of plastic deformation is found to be key. The numerical results are experimentally validated, thereby revealing the crucial role of the adopted anisotropic yield function. Furthermore, the uncertainty associated with the inversely identified parameters based on three repetitions of the same experiment is discussed.
An inverse strategy is developed for identifying the parameters of a recent phenomenological constitutive model (Vaiana et al., 2021) that simulates asymmetric hysteresis loops. The model, based on a ...limited set of parameters, permits the definition of either stress–strain or load–displacement asymmetric relationships by closed-form expressions that do not require any iterative algorithm for the computation of the non-linear response. The identification strategy consists in a combination of optimization procedures aiming to minimize least-square residuals defined in terms of response amplitude, stiffness and limit curves of the hysteretic cycle. The robustness and effectiveness of the proposed identification strategy has been proved by identifying the mechanical parameters of three experimental responses.
In this paper, a parameterized multi-partitioning method is presented for modeling arbitrary multi-ring hard coating treatment for the thin-walled cylindrical shell under different ring numbers and ...coating ratios, while the Rayleigh–Ritz method and the Chebyshev orthogonal polynomials of the second kind are employed to derive the governing equations of motion and the admissible displacement, respectively. Moreover, a unified formulation of external load based on the trigonometric and Chebyshev series is developed for forced vibration analysis of the shell with arbitrary axial half-wave number and circumferential wave number. Based on the experimental resonant frequencies, an improved inverse identification procedure is proposed in which the genetic algorithm and pattern search algorithm are sequentially employed to identify the stiffness coefficients of elastic constraint. Good agreement between the experimental and numerical resonant frequencies and responses exhibits the reliability and effectiveness of both the stiffness identification method and semi-analytical model. The identified results happen to find that the constraint stiffness may have the inherent property of frequency dependence due to the existence of micro sliding which would further result in soft nonlinearity in frequency response curve as shown in experimental results. Additionally, the influences of ring number and coating ratio on vibration and damping characteristics of the thin-walled cylindrical shell are investigated by introducing the average strain energy density and average modal loss factor.
•A parameterized multi-partitioning method for arbitrary multi-ring hard coating.•A load formula with arbitrary axial half-wave number and circumferential wave number.•An improved stiffness identification procedure with frequency dependence.•Effects of ring number and coating ratio on vibration and damping characteristics.
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