Accumulating DIC Experimental Experience - Understanding and Controlling the Sources of Differences Between Testing and Simulation

Keywords: simulation validation,DIC method for simulation validation, simulation model errors, sources of DIC experimental errors

Adjustment and validation of simulation

Simulation plays an enhanced role in the design, identification, and certification of industrial products by forming the basis for strategic decision-making. Therefore, the role of transitioning to experimental testing has also been modified. These tests are an important part of compliance proof, but now they have become a reference for numerical simulation validation.[1,2].

Therefore, adjusting and validating numerical simulations becomes crucial to make them as predictive as possible and closely reflect reality. This adjustment necessitates the use of data collected during one or more test periods.sMechanical properties of parts or structures to enrich the simulation.

Limitations of traditional methods

Traditionally, when conducting simple material tests, the applied forces are well controlled, and traditional instruments (such as strain gauges) are equipped with the test specimens. These standardized tests ensure uniform deformation in the samples to determine model parameters.[3]. In this case, determining complex models requires a large number of tests. Moreover, this strategy cannot be applied to structural tests with more complex geometries and constitutive models.

In the adjustment and/validation steps of numerical simulations, a loss of data continuity is observed. In fact, numerical simulations provide results for the entire part (including displacement fields). The information is extremely rich and helps identify key areas. However, during testing, whether using strain gauges, displacement sensors, or lasers as sensors, they are often located at given positions. These sensors do not cover the entire part, and their measurements are not represented in the reference frame of the simulation, making comparisons between testing and computation more difficult. Furthermore, if there is inconsistency between experimental data and simulation data, it is often challenging to determine the cause of such discrepancies, as measurements are local. Therefore, actual key areas may not have been detected. Does this gap arise from the mechanical behavior in the model, boundary conditions, and simplifications? To answer these questions, further simulations or even additional tests on the prototype are needed, which means cost and time overruns.

Three-dimensional models ensuring data continuity

To ensure numerical continuity, it is recommended to use3D models in CAD to validate simulations. This model is used to:•

Define test specifications,Design and execute virtual tests, connecting all sensors to the prototype in its testing environment,

Define test specifications,Measure during actual testing,

Define test specifications,Finally, adjust and validate the numerical simulation.

Define test specifications,To perform the last two steps, imaging devices are used to detect the tests, and the

model is used as a reference, measuring actual values during testing through digital image correlation3D[4].Thus, measurements are made directly within the reference frame of the numerical simulation, and results are represented on the finite element mesh. Therefore, comparisons between test data and simulation data are immediate. Additionally, if discrepancies exist, areas of significant difference can be identified. Furthermore, since displacement fields are collected, the measurement data is substantial. These measurements represented on the finite element mesh can also be automatically adjusted using the so-called Finite Element Model Updating (FEMU) method. This identification can be weighted by measurement uncertainty to obtain new model parameters and their uncertainties, and compared with the data used as a reference. The emergence of image-based measurement techniques enriches the measurement data, and due to the non-uniform fields of measurement, multiple model parameters can be identified simultaneously with just one test.

[5]The three-dimensional model becomes the basis for collecting data for the digital twin.Achieving accurate estimates of various sources of deviationFor finite element simulations, three common sources of errors are frequently encountered: discretization errors, model errors, and numerical errors. Checking discretization errors and numerical errors is a common process in numerical studies, and the validation process has matured enough to control them..

[6]

Therefore, only model errors are considered here. This is mainly due to:

Improper specification of boundary conditions, differing from actual test conditions,The constitutive parameters of the model cannot accurately reproduce the actual material behavior..

Integrating test data on the finite element mesh used for simulation can adjust the simulation using identification methods.

Define test specifications,And

Define test specifications,Recently published articles provide an optimal identification method based on selecting appropriate criteria and considering measurement uncertainties.

[7]S.RouxDigital Image Correlation (F.HildDIC).

Sources of measurement uncertainty include image noise and camera system calibration. It is also related to considering uncertainties under boundary conditions, due to gaps in components, misalignment of cylinders, or the distribution of applied boundary conditions.When adjusting simulations, it is necessary to check for constitutive model errors and separate them from errors caused by differences in boundary conditions selected in the simulation and applied during testing. To be completely unaffected by errors caused by external forces, digital image correlation based on finite element meshes is a suitable tool, as it allows for measuring boundary conditions and directly incorporating them into numerical simulations. Just like with the train chassis in collaboration with Alstom andCETIM.If we assume that the camera system calibration has been correctly completed, the related uncertainty can be ignored. Then, only the measurement uncertainty caused by sensor acquisition noise remains. This noise propagates through the digital image correlation method, affecting the measured displacement fields, and propagates through the identification method, affecting the identified parameters. By understanding the noise in image acquisition, quantifying this propagation can yield the uncertainty of the identified parameters.

调整模拟时，必须检查本构模型误差，并将其与模拟中选择的和试验期间应用的边界条件差异引起的误差分开。为了完全不受外力引起的误差影响，基于有限元网格的数字图像相关是合适的工具，因为这样可以测量边界条件并直接将其引入数值模拟。正如与阿尔斯通和CETIM合作的列车底盘一样。

如果我们假设摄像机系统校准已正确完成，则相关的不确定性可以忽略。然后，只有传感器采集噪声导致的测量不确定性仍然存在。该噪声通过数字图像相关方法传播，影响测量位移场，并通过识别方法传播，影响识别参数。由于对图像采集噪声的了解，量化这种传播能够获得识别参数的不确定性。

By enforcing measurement boundary conditions in the simulation and considering measurement uncertainty in the identification method, it can be assumed that the remaining differences between the measurement results and the simulation results are caused solely by the constitutive parameters of the model.

Conclusion

3DThe model is used as a digital twin model throughout the design cycle, and with the help of image processing technology, it can collect full-field experimental data. Therefore, it provides the following benefits:

Define test specifications,Ensuring the continuity of the design digital chain,

Define test specifications,Aggregating simulation data and test data,

Define test specifications,Validating numerical simulations, and adjusting the implemented mechanical model if the experimental and simulation data are inconsistent.

Considering the boundary conditions of digital image correlation measurements in numerical simulations can also separate the errors caused by the boundary conditions applied in the experiments from the errors of the constitutive model. Finally, the estimation of noise propagation in image acquisition allows for a quantitative estimation of the uncertainty in the identified parameters.

References:

[1]https://www.nafems.org/professional_development/nafems_training/training/verification-validation-des-modeles-et-analyses/

[2]https://www.asme.org/products/codes-standards/v-v-101-2012-illustration-concepts-verification

[3]https://en.wikipedia.org/wiki/Tensile_testing

[4] Dubreuil, L., Dufour, JE., Quinsat, Y. et al. Exp Mech (2016) 56: 1231.https://doi.org/10.1007/s11340-016-0158-x

[5] Jan Neggers, Olivier Allix, François Hild, Stéphane Roux. Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities.Archives of Computational Methods in Engineering, Springer Verlag, 2018, 25 (1), pp.143-164.https://dx.doi.org/10.1007/s11831-017-9234-3

[6] P. Ladevèze and D. Leguillon. Error estimate procedure in the finite element method and applications. SIAM J. Num. Analysis, 20(3) : 485 – 509, 1983.

[7] Stéphane Roux, François Hild. Optimal procedure for the identification of constitutive parameters from experimentally measured displacement fields.International Journal of Solids and Structures, Elsevier, In press,https://dx.doi.org/10.1016/j.ijsolstr.2018.11.008