Smoothing Measured Displacements and Computing Strains Utilising Finite Element Method

Abstract

A method for smoothing measured displacements and computing strains utilising finite element and least-squares methods is proposed. Nodal displacement values of a finite element model are determined by fitting the interpolation functions of elements to measured displacement values using the method of least-squares. The displacements in the region where the measurement values are not obtained or unreliable are determined by solving finite element equations. Then, strains are obtained using a displacement-strain relationship. The validity is demonstrated by applying the proposed method to the displacement distributions of a plate with a hole obtained using finite element method and those around a crack tip obtained using digital image correlation. Results show that the displacements and the strains can be determined accurately by the proposed method. Furthermore, the strains near free boundaries and strain concentration region can be computed. As strains can be evaluated easily and accurately, the proposed method can be used as one of the data processing methods for optical methods.KEY WORDS: digital image correlation, displacement, finite element method, hybrid method, least-squares method, optical methods, strain 258 Ó

J-Integral Calculation by Finite Element Processing of Measured Full-Field Surface Displacements

“…In the context of the J-integral evaluation, data are also missing near to the traction-free surfaces of the crack. One solution to this problem has been proposed by Molteno [50] who used linear interpolation in the crack tip and crack flank region, whilst Yoneyama [51] proposed a finite element method to smooth the measured DIC displacement field using the measured boundary conditions; smoothing algorithms that are not based on FE approaches have also been used [52]. Full-field measurements of the boundary conditions as inputs to FE have previously been used to calculate strain and stress fields; for instance, one of the first applications was in 1990 when Morton et al [53,54] uses FE to extract stresses from moiré interferometry measurements of the crack displacement field, and more recently, Caimmi [55] made use of FE to compute the stresses from DIC-measured strains, using a hyperplastic material model.…”

A new methodology to identify minimum strain anatomical lines based on 3-D digital image correlation

“…Generally, the NR method is used in DIC to obtain displacement gradients, but this method cannot adequately estimate the strain field due to the unavoidable influences of different types of noises (Quan et al, 2008). In this sense, it has been found that Savitzy-Golay (SG) filter is able to improve the strain fields compared to NR process (Tang et al, 2010;Quan et al, 2008;Yoneyama, 2011;Begonia et al, 2017). For this reason, an approach proposed by Tang et al (2010) based a 2-D SG filter differentiator is used in this work in order to obtain the strain field.…”

Path-independent digital image correlation with high accuracy, speed and robustness

“…5(b)), which indicates a discernible scattering of calculated y u among the POIs. To obtain precise strain field from DIC results, further processing is required [36][37][38][39].…”