Finite element formulation for a digital image correlation method

Yaofeng Sun; John H. L. Pang; Chee Khuen Wong; Fei Su

doi:10.1364/AO.44.007357

Applied Optics
Vol. 44,
Issue 34,
pp. 7357-7363
(2005)
•https://doi.org/10.1364/AO.44.007357

Finite element formulation for a digital image correlation method

Yaofeng Sun, John H. L. Pang, Chee Khuen Wong, and Fei Su

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Yaofeng Sun, John H. L. Pang, Chee Khuen Wong, and Fei Su, "Finite element formulation for a digital image correlation method," Appl. Opt. 44, 7357-7363 (2005)

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- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: January 27, 2005
- Revised Manuscript: April 12, 2005
- Manuscript Accepted: April 14, 2005
- Published: December 1, 2005

Abstract

A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust.

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Cases	Method	ū − u₀ (pixels)	$\bar{v} - v_{0} (pixels)$	σ_u (pixels)	σ_v (pixels)	σ_{ε_xx}	σ_{ε_yy}	σ_{ε_xy}
1^a	Element	8.39 × 10⁻⁴	9.68 × 10⁻³	10.73 × 10⁻³	12.02 × 10⁻³	2.23 × 10⁻⁴	2.22 × 10⁻⁴	2.97 × 10⁻⁴
	Subset	1.13 × 10⁻⁴	8.37 × 10⁻³	7.75 × 10⁻³	7.99 × 10⁻³	7.35 × 10⁻⁴	7.36 × 10⁻⁴	9.57 × 10⁻⁴
2^b	Element	8.94 × 10⁻⁴	9.10 × 10⁻⁴	8.88 × 10⁻³	10.37 × 10⁻³	1.90 × 10⁻⁴	1.89 × 10⁻⁴	3.22 × 10⁻⁴
	Subset	5.93 × 10⁻⁴	−1.10 × 10⁻⁴	7.09 × 10⁻³	6.83 × 10⁻³	7.80 × 10⁻⁴	7.02 × 10⁻⁴	9.82 × 10⁻⁴

Cases	Method	${\bar{ɛ}}_{x x} - {ɛ_{x x}}^{0}$	${\bar{ɛ}}_{y y} - {ɛ_{y y}}^{0}$	${\bar{ɛ}}_{x y} - {ɛ_{x y}}^{0}$	σ_{ε_xx}	σ_{ε_yy}	σ_{ε_xy}
1^a	Element	−2.80 × 10⁻⁵	−1.04 × 10⁻⁶	−2.71 × 10⁻⁶	3.57 × 10⁻⁴	1.39 × 10⁻⁴	2.72 × 10⁻⁴
	Subset	−1.3 × 10⁻⁴	−8.37 × 10⁻⁵	5.49 × 10⁻⁶	1.96 × 10⁻³	7.21 × 10⁻⁴	8.22 × 10⁻⁴
2^b	Element	−2.43 × 10⁻⁵	−2.05 × 10⁻⁵	−8.67 × 10⁻⁶	3.70 × 10⁻⁴	3.88 × 10⁻⁴	3.43 × 10⁻⁴
	Subset	−1.10 × 10⁻⁴	−5.84 × 10⁻⁵	−5.15 × 10⁻⁵	1.93 × 10⁻³	2.23 × 10⁻³	1.08 × 10⁻³
3^c	Element	5.00 × 10⁻⁷	3.98 × 10⁻⁶	2.60 × 10⁻⁷	2.38 × 10⁻⁴	1.99 × 10⁻⁴	2.89 × 10⁻⁴
	Subset	1.96 × 10⁻⁴	3.37 × 10⁻⁴	−2.1 × 10⁻⁴	7.29 × 10⁻⁴	7.55 × 10⁻⁴	1.09 × 10⁻³

Method	$\bar{θ} - θ_{0}$ ^a (rad)	σ_θ (rad)	σ_{ε_xx}	σ_{ε_yy}	σ_{ε_xy}
Element	2.14 × 10⁻⁴	2.50 × 10⁻⁴	3.42 × 10⁻⁴	3.19 × 10⁻⁴	4.56 × 10⁻⁴
Subset	4.57 × 10⁻⁴	6.80 × 10⁻⁴	8.96 × 10⁻⁴	9.13 × 10⁻⁴	1.33 × 10⁻³

Method	$\bar{θ} - θ_{0}$ ^a (rad)	σ₀ (rad)	σ_εx	σ_εy	σ_εxy
Element	1.95 × 10⁻⁴	2.27 × 10⁻⁴	3.04 × 10⁻⁴	3.20 × 10⁻⁴	4.54 × 10⁻⁴
Subset	4.72 × 10⁻⁴	7.07 × 10⁻⁴	1.04 × 10⁻³	1.05 × 10⁻³	1.62 × 10⁻³

Cases	Method	ū − u₀ (pixels)	$\bar{v} - v_{0} (pixels)$	σ_u (pixels)	σ_v (pixels)	σ_{ε_xx}	σ_{ε_yy}	σ_{ε_xy}
1^a	Element	8.39 × 10⁻⁴	9.68 × 10⁻³	10.73 × 10⁻³	12.02 × 10⁻³	2.23 × 10⁻⁴	2.22 × 10⁻⁴	2.97 × 10⁻⁴
	Subset	1.13 × 10⁻⁴	8.37 × 10⁻³	7.75 × 10⁻³	7.99 × 10⁻³	7.35 × 10⁻⁴	7.36 × 10⁻⁴	9.57 × 10⁻⁴
2^b	Element	8.94 × 10⁻⁴	9.10 × 10⁻⁴	8.88 × 10⁻³	10.37 × 10⁻³	1.90 × 10⁻⁴	1.89 × 10⁻⁴	3.22 × 10⁻⁴
	Subset	5.93 × 10⁻⁴	−1.10 × 10⁻⁴	7.09 × 10⁻³	6.83 × 10⁻³	7.80 × 10⁻⁴	7.02 × 10⁻⁴	9.82 × 10⁻⁴

Abstract

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Equations (22)

Applied Optics