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A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data

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Abstract

Background

Digital Image and Volume Correlation (DIC and DVC) are non-contact measurement techniques that are used during mechanical testing for quantitative mapping of full-field displacements. The relatively high noise floor of DIC and DVC, which is exasperated when differentiated to obtain strain fields, often requires some form of filtering. Techniques such as median filters or least-squares fitting perform poorly over high displacement gradients, such as the strain localisation near a crack tip, discontinuities across crack flanks or large pores. As such, filtering does not always effectively remove outliers in the displacement field.

Objective

This work proposes a robust finite element-based filter that detects and replaces outliers in the displacement data using a finite element method-based approximation.

Methods

A method is formulated for surface (2D and Stereo DIC) and volumetric (DVC) measurements. Its validity is demonstrated using analytical and experimental displacement data around cracks, obtained from surface and full volume measurements.

Results

It is shown that the displacement data can be filtered in such a way that outliers are identified and replaced. Moreover, data can be smoothed whilst maintaining the nature of the underlying displacement field such as steep displacement gradients or discontinuities.

Conclusions

The method can be used as a post-processing tool for DIC and DVC data and will support the use of the finite element method as an experimental–numerical technique.

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Notes

  1. Common filters include the mean and median filters that are used in most commercial DIC systems.

  2. A small amount (5 · 10−6 mm) of Gaussian noise floor was added to the FE data for numerical stability in the identification of outliers.

  3. Near-zero values are equal or less than \({E}_{min}\).

Abbreviations

BC:

Boundary condition

DIC:

Digital image correlation

DVC:

Digital volume correlation

FE:

Finite Element

MAD:

Median absolute deviation

ROI:

Region of interest

θ:

Median of |f_n |

Ω:

FE domain

α:

Yield offset

σ_o:

Yield strength

ρ:

Density

ρ_l:

Elemental density, ∈ [0,1]

C1, C2, C3:

Convergence criteria 1, 2 and 3.

E:

Young’s modulus

E_l:

Elemental Young’s modulus

E_min:

Nominal Young’s modulus of the masked region

E_0:

Nominal Young’s modulus of the material

e:

Essential boundary condition

f:

Force vectors

f_n:

Displacement resultant force vectors

f_e:

Replacement force vectors, ∈ [0]

K:

Stiffness matrix

K_l:

Element stiffness matrix

K_l^0:

Element stiffness matrix with nominal Young’s modulus of the material

m:

Hardening coefficient

n:

Neutral boundary condition

u:

Displacement vectors

u_n:

Measured displacement vectors

u_e:

Replacement displacement vectors

v:

Poisson’s ratio

x:

Cartesian coordinate system

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Acknowledgments

The authors acknowledge the Stereo-DIC and DVC data and contributions from Matthew Molteno, and the X-CT reconstructions undertaken by the Central Analytical Facility at the Stellenbosch University.

Funding

This work is based on the research supported in part by the National Research Foundation of South Africa for the grant, Unique Grant Nos. 87955 and 106932.

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Authors and Affiliations

  1. Department of Mechanical and Mechatronic Engineering, Mechanical Engineering Building, Stellenbosch University, Joubert Street, Stellenbosch, 7600, South Africa

    T. H. Becker

  2. Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, UK

    T. J. Marrow

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Correspondence to T. H. Becker.

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Becker, T.H., Marrow, T.J. A Robust Finite Element-based Filter for Digital Image and Volume Correlation Displacement Data. Exp Mech 61, 901–916 (2021). https://doi.org/10.1007/s11340-021-00718-5

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