Identification of material model parameters using full-field metrology, inverse techniques and uncertainty quantification

Fayad, Samuel Saiid

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https://hdl.handle.net/2142/125751 Copy

Description

Title

Identification of material model parameters using full-field metrology, inverse techniques and uncertainty quantification

Author(s)

Fayad, Samuel Saiid

Issue Date

2024-07-02

Director of Research (if dissertation) or Advisor (if thesis)

• Lambros, John
• Jones, Elizabeth

Doctoral Committee Chair(s)

Sofronis, Petros

Committee Member(s)

• Chew, Huck Beng
• Beaudoin, Armand

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• finite element model updating
• digital image correlation
• validation

Abstract

The accurate capture of the mechanical response of a physical system using finite element analysis (FEA) intimately depends on the underlying model which dictates the material behavior. For a chosen model form, the material model parameters that define the material behavior are identified through meticulous experimentation which can be costly and time consuming, particularly with increasing complexity of material response (e.g. anisotropy, inhomogeneity, etc.). Recent advancements in full-field motion metrology, such as digital image correlation (DIC), have allowed for the identification of material model parameters using fewer experiments than those needed when solely relying on far-field quantities (i.e., boundary load/displacement). The material model parameter identification is performed through an inverse technique, such as for example finite element model updating (FEMU), which aims to match the model output to the experimental measurements. Unlike uniaxial tensile data, which capture the material model parameters for a single material orientation, DIC measurements in conjunction with finite element model updating can be used to capture the material hardening and the anisotropic parameters that define it simultaneously. Although DIC errors have become well characterized in the past two decades, how these errors propagate to identification errors of the material model parameters is not well understood. DIC errors can be separated into two major categories: biases, which do not vary with time; and random errors, which do vary with time. This work serves to study the influence of DIC error sources on the identification accuracy of material model parameters, and mitigate these errors through meticulous experimental design. To study the influence of DIC biases without the existence of model form error, synthetically generated data were produced simulating the DIC measurements of an hourglass sample governed by an elastoplastic material model meant to replicate a 304 stainless steel. The material model parameters were identified through finite element model updating, resulting in an agreement between the synthetic data and the numerical model. It was shown that filtering biases inherent to the DIC algorithm contribute to a bias in the identified material model parameters. A technique was then introduced here, dubbed direct-levelling, to process the kinematic output of the FEA through the exact same numerical filtering procedures used in DIC. It was shown that such direct-levelling rectifies the spatial resolution disparity between FEA and DIC, producing a more accurate identification of material model parameters. Unlike the systematic DIC biases, Random DIC measurement error from image noise cannot be fully modeled and rectified. Therefore, an optimal experimental design (OED) approach was used to reduce the influence of this noise in the inverse identification. The optimization of the prescribed loading conditions for a cruciform geometry was used to study the identification uncertainty of the material model parameters due to the noise. The identification uncertainty was calculated using a sensitivity based framework which hinged on assumptions of the material behavior and the characteristics of the noise. From these uncertainty measurements, scalar criteria were evaluated for their ability to holistically capture the uncertainty for all parameters, providing an objective scalar metric for assessing the prescribed loading. From this framework, it was found that the identification uncertainty of the material model parameters depended on the prescribed boundary conditions, as well as the ground-truth set of material model parameters. These predictions were then validated using two sets of synthetically generated data with varying levels of conformity to real experimental data. The first data set, which came directly from the FEA, validated the framework despite nonlinearities in the model output. The second data set, derived from DIC measurements of synthetically generated deformed images, showed a spatial correlation of the noise between neighboring DIC measurements, affecting the estimate of the identification uncertainty. It was found that this spatial correlation could be accounted for in the estimate of the identification uncertainty through careful selection of settings of the DIC algorithm, or a correction factor meant to account for redundant measurements. The OED framework was then scrutinized using simulated data for its ability to determine an optimal load path in-situ (i.e. as loading is conducted, deciding upon a load path and load step that minimizes uncertainty in the inverse fitting of material model parameters). When the model was correctly specified (i.e., without model form error), it was found that the framework would predict a consistent load path that optimized predictions. However, significant bias was introduced into the experiment through the identification of misspecified material models, which were unable to accurately conform to the material behavior of the synthetic data. It was found that while the optimized load path was consistent for each instantiation of noise, the material model form error had a larger biasing effect on the identified material model parameters than the effect of random noise. This bias was objectively measured by the change in the material model parameters with increasing load steps, which was much larger in magnitude than the variability of the material model parameters due to noise alone. It was concluded that material model form error would have to be reduced to the order of the identification uncertainty for this OED framework to provide significant improvement for material model parameter identification. Elements of the OED framework were then lastly applied to the identification of material model parameters in a mildly anisotropic 304L stainless steel material. In the experiment, an hourglass-shaped sample was loaded in uniaxial tension while images were captured for DIC. FEMU was performed to identify the material model parameters that best describe the kinematic and load response of the material. As the material model form was unknown several common models were used. It was found that for a standard Ludwik hardening model and Hill48 yield surface a misspecification of the material model form occurred, as the kinematic response of the calibrated model did not fully conform to the motion measured in the experiment. Similar to the earlier analyses using synthetic data, the mean identified parameters varied as a function of the applied loading more than the variation due to random noise. The material models extracted from the hourglass geometry data were then validated using a separate, more complicated, sample with elliptical perforations which creating a highly heterogeneous deformation. The validation process illustrated that the models calibrated through FEMU were better able to capture the force in the experiment than an isotropic material model whose hardening was determined through a conventional tensile test. Additionally, the validation showed that the more expressive hardening model was able to more accurately capture the kinematics in the experiment than all other models, specifically along the loading orientation. However, some bias remained in the kinematics in the off-loading orientations, showing remaining material model form error, suggesting areas for future research.

Graduation Semester

2024-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/125751

Copyright and License Information

Copyright 2024 Samuel Fayad

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