Introduction

The digital image correlation (DIC) system is a noncontact device used to measure displacement and strain on specimens subjected to loading. In contrast to traditional contact extensometers and strain gauges, which measure uniaxial strain at specific points, the DIC system can assess multiaxial strain distribution across an area. Moreover, it can measure strain in extreme environments, such as high temperatures or around a crack where traditional strain measurement techniques are ineffective. Owing to these capabilities, the DIC system is critical in the fields of engineering and materials science.

Typically, a DIC system employs an industrial camera equipped with either a standard or a telecentric lens. A standard lens offers a wide field of view (FOV) but has a limited depth of field (DOF), leading to potential measurement errors due to out-of-plane deformation of the specimen. Conversely, a telecentric lens, while providing a narrower FOV, offers a greater DOF, thereby enhancing accuracy in situations of out-of-plane deformations (Pan et al. 2013). This study utilises a DIC system with a bilateral telecentric lens.

The application of DIC systems in wood research spans from material-level investigations (Iraola et al. 2021; Jeong et al. 2016; Kumpenza et al. 2018; Matsuda et al. 2019; Matsuda et al. 2017; Totsuka et al. 2022; Xavier et al. 2012) to structural testing at the component level (Bakalarz et al. 2023; Navaratnam et al. 2020; Sirumbal-Zapata et al. 2019; Timbolmas et al. 2022). Within these studies, DIC is employed for a variety of purposes, including exploring damage mechanisms (Matsuda et al. 2018, 2017; Navaratnam et al. 2020), determining mechanical properties such as Young’s modulus and Poisson’s ratio (Jeong et al. 2016; Kumpenza et al. 2018), and verifying the accuracy of finite-element analysis (FEA) (Sirumbal-Zapata et al. 2019; Timbolmas et al. 2022). Establishing methods to quantitatively evaluate the errors associated with DIC is essential for its effective adaptation to specific investigative needs.

The accuracy of DIC systems has been extensively documented by numerous researchers (Demizu et al. 2012; Li et al. 2018; Pan et al. 2013, 2014). The focus has predominantly been on metallic materials, owing to their macroscopic homogeneity and isotropy. The strain measurement accuracy of DIC systems in metals is investigated by comparing its results with those obtained from strain gauges or FEA results. Furthermore, a method for verifying the accuracy of the DIC system in metals under multi-axial stress fields, in addition to uniaxial stress fields, has also been proposed. Despite the robust validation processes in metals, there is few research on DIC accuracy in wood (Xavier et al. 2012). Xavier et al. (2012) conducted full-field compression tests on wood, comparing the Young’s modulus derived from DIC systems with those obtained from strain gauges. However, this examination is limited to the uniaxial stress field in the fibre direction and does not address the accuracy of a DIC system in the direction orthogonal to the fibres, where local deformation occurs due to the differences in the mechanical properties of earlywood and latewood. In addition, to the best of the authors’ knowledge, few studies have explored the accuracy verification of DIC systems in wood under multiaxial stress conditions.

This study aims to investigate the accuracy of a DIC system equipped with a bilateral telecentric lens, specifically on wood. The DIC accuracy verification in uniaxial stress fields was performed using full compression tests in the fibre direction and the direction orthogonal to the fibre. The DIC accuracy verification in multiaxial stress fields was examined through partial compression testing. Additionally, to evaluate the influence of wood’s anisotropic and macroscopically heterogeneous nature on DIC accuracy, comparative tests were conducted using A6063 (an aluminium alloy), which is isotropic and homogeneous.

Experiment

Materials and specimens

Douglas fir (Pseudotsuga menziesii), imported from Canada, was selected for the test specimens. Because of the imported nature of the wood, it was challenging to ascertain the exact age and region of origin of the tree. Wooden boards were cut from a Douglas fir log, and the bending moduli of these boards were assessed using a grading machine in accordance with the Japan Agricultural Standard 1083 (JAS 2019). The Douglas fir was classified as grade E150, indicating a nominal Young’s modulus of 15,000 MPa.

To evaluate the accuracy of a DIC system between the fibre direction and the direction orthogonal to the fibre under a uniaxial stress field, test specimens for uniform compression in longitudinal (L) and radial (R) directions were prepared, as depicted in Fig. 1a and b, respectively. The specimens for full compression tests in the L and R directions of Douglas fir were designated as DF-L-FC and DF-R-FC, respectively. Additionally, two types of partial compression test specimens were prepared, as shown in Fig. 1 (c) and (d); these were named DF-PC-A and DF-PC-B, respectively, with the location of strain gauges on these specimens determined based on strain distribution data from FEA, as detailed in Sect. "FEA of partial compression test". The experimental procedures for both full and partial compression tests adhered to the Japan Industrial Standard (JIS) Z 2101 (JIS 2020). The compressive load was applied by the universal testing machine. The displacement control mode of the universal testing machine was used with constant speed that reached the yield stress within 1–2 min from the start of loading. However, in the compression tests, the imposed displacement was stopped for a few seconds during imaging for DIC, so it was not strictly at a constant displacement speed. Table 1 lists the numbers, densities, and moisture contents of the specimens.

Fig. 1
figure 1

Dimension, loading schematic, DIC imaging region, and gauge placement and DIC averaging area of interest for specimens a DF-L-FC, b DF-R-FC, c DF-PC-A, and d DF-PC-B (colour figure online)

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Table 1 Properties of test specimens
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To facilitate the application of the DIC method on the surfaces of test specimens, a speckle pattern was created using the following procedure:

  1. (1)

    Uniaxial and triaxial strain gauges (KFGS-series, Kyowa, Japan) were attached to the surfaces of the full and partial compression test specimens, respectively.

  2. (2)

    The surface of each specimen was coated two or three times with a white lacquer spray (Aspen, Japan) to achieve opacity.

  3. (3)

    Maintaining a distance of 30 cm from the nozzle, a black lacquer spray (Aspen, Japan) was applied to the surface to form a speckle pattern.

After the tests, the speckle patterns were sanded off, and the moisture content of the specimens was measured using the oven-dry method in accordance with the JIS Z 2101 standard (JIS 2020).

In addition to the tests on wood, full and partial compression test specimens made of an aluminium alloy (A6063) were also prepared with strain gauges and a speckle pattern to compare the accuracy of the DIC method between anisotropic and isotropic materials. The dimensions of the A6063-T5 specimens matched those of the Douglas fir (Fig. 1). These specimens were labelled with the initial ‘AL-’ in place of ‘DF-’, as detailed in Table 1.

The quality of speckle pattern was assessed using the mean subset fluctuation \(S_{f}\) (Hua et al. 2011).

$$S_{f} = \frac{{\sum\nolimits_{P \in F} {S_{P} } }}{H \times V}$$
(1)

where \(S_{P}\) is the subset fluctuation at point P. F is the class of points. \(H \times V\) is the size of a speckle pattern. The mean and standard deviation of \(S_{f}\) in all specimens are 173 and 40.6, respectively. Hua et al. (2011) exihibited that a speckle pattern with large \(S_{f}\) produces a small mean bias error. In addition, their results exihibited that the reduction rate of mean bias error associated with the increase in \(S_{f}\) decreases as \(S_{f}\) increases. Since the maximum value of \(S_{f}\) shown in their study is 114, the \(S_{f}\) in this study is sufficiently large. Based on the above, it is assumed that the quality of the speckle pattern in this study is roughly uniform.

DIC system

Figure 2 illustrates the DIC system, comprising a digital camera (EG600-B, Shodensya, Japan; active pixels: 3072 × 2048, frame rate: 17fps, sensor: 1/1.8''), a bilateral telecentric lens (RT1, Shodensya, Japan; magnification: 0.1 × , working distance: 230 mm, telecentric depth: 34.8 mm), and a ring light (LED-120MM, Shodensya, Japan). The size of field of view (FOV) is 63.1 mm × 47.3 mm.

Fig. 2
figure 2

DIC system

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During the experiments, the surface images of the test specimens were captured using the DIC system. To compute the displacement and strain distributions from the captured images, an open-source two-dimensional DIC MATLAB program, Ncorr, was utilised (Blaber et al. 2015). The subset radius and subset spacing were configured to 20 pixels and 0, respectively.

If the goal is simply to compare strains measured by strain gauges and DIC systems, 63.1 mm × 47.3 mm FOV is unnecessary. It would be better to use a smaller FOV, similar in size to the strain gauges, to enhance the accuracy of the DIC system. However, wood is composed of heterogeneous materials, including earlywood and latewood, which can lead to localized strain concentrations near their interfaces. To observe the trend of complex strain distributions over most of the specimen’s surface, 63.1 mm × 47.3 mm field of view (FOV) was employed. Additionally, considering that many studies (Iraola et al. 2021; Totsuka et al. 2022; Xavier et al. 2012) have reported DIC imaging of large portions of the specimen surface in compression tests similar to those in this research, it is important from a practical perspective to examine the accuracy of such DIC systems. In the case of the partial compression test specimens illustrated in Fig. 1(c) and (d), it is possible to capture two strain gauges within a single image frame. However, these tests were conducted separately for each strain-gauge attachment position to minimise potential errors in strain measurement due to lens distortion in the central imaging area of the DIC system.

Figure 3 shows images of each specimen without a speckle pattern. The ij component of strains measured by strain gauges and the DIC system are designated as \(\varepsilon_{ij}^{G}\) and \(\varepsilon_{ij}^{D}\), respectively. The \(\varepsilon_{ij}^{D}\) values exhibit variability at each point, complicating the direct comparison of \(\varepsilon_{ij}^{G}\) values from each strain gauge. Therefore, considering the size of the strain gauge in the image, as shown in Fig. 3, the average value of \(\varepsilon_{ij}^{D}\) (denoted as \(\varepsilon_{ij}^{D,ave}\)) were computed across a 100-pixel square region centred on the strain gauge part which reads the change in resistance of a material.

Fig. 3
figure 3

Images of a DF-L-FC, b DF-R-FC, c DF-PC-A, and d DF-PC-B without speckle pattern

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FEA of partial compression test

The FEA of the partial compression tests on Douglas fir and A6063 was conducted to determine the strain distribution, which informed the attachment positions of the tri-axial strain gauges. Three-dimensional finite-element models, utilising twenty-node brick elements (C3D20), were developed, replicating the dimensions of the partial compression test specimens depicted in Fig. 1(c) and (d). The interface between Douglas fir (or A6063) and steel was modelled using a contact condition with a Lagrange multiplier. A forced displacement of 0.2 mm in the y-direction was applied to the steel plate to simulate a partial compression test on Douglas fir or A6063. In the models, Douglas fir was characterised using Hill’s anisotropic yield condition, while A6063 and S45C (steel plate and steel base) were modelled according to the von Mises yield criterion. The mechanical properties of Douglas fir and S45C were sourced from the literature (Teranishi et al. 2024). The Young’s modulus, Poisson’s ratio, and yield stress for A6063 were determined through uniaxial material testing, with values recorded as 59,462 MPa, 0.34, and 213 MPa, respectively. Figure 4 shows the strain distribution (εxx, εyy, and εxy) for A6063 and Douglas fir. Based on these findings, strain gauge A was positioned beneath the edge of the steel plate, where shear strain is pronounced, whereas strain gauge B was located at the centre of the specimen, where shear strain is minimal and significant compressive strain in the y-direction occurs. Table 2 summarises the signs of each strain component and major strain components for the FEA at strain gauge attachment points A and B.

Fig. 4
figure 4

Strain distributions of A6063 and Douglas fir calculated from FEA

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Table 2 Signs of each strain component and major strain components for FEA at strain gauge attachment points
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Results and discussion

Uniaxial material tests

Figure 5 presents representative \(\sigma_{yy}^{{}}\) versus \(\varepsilon_{yy}^{G}\) relationships and \(\varepsilon_{yy}^{D}\) distributions at the initial stage of elastic deformation (2nd step), just before yielding (5th step) and after yielding (6th or 8th step) for AL-FC, DF-L-FC, and DF-R-FC. \(\sigma_{yy}^{{}}\) is calculated by dividing the compressive force by the entire cross-sectional area of the specimen. In the initial stage (2nd step) of elastic deformation of AL-FC and DF-L-FC, variations in the strain distribution occur owing to partial contact on the top and bottom surfaces caused by geometrical initial imperfections of the test specimen caused by processing. Just before yielding (5th step) of AL-FC and DF-L-FC, the partial contact is relieved, leading to a nearly uniform compressive strain state as compared to initial stage of elastic deformation. However, after yielding of AL-FC and DF-L-FC, bending deformation due to local plastic deformation occurred, reintroducing variability in the strain distribution. Despite AL-FC being a homogeneous material and DF-L-FC being heterogeneous, their tendencies regarding \(\varepsilon_{yy}^{{}}\) distribution are similar. The specimens of DF-R-FC exhibited noticeable differences in strain distribution between the earlywood and latewood sections, in contrast to AL-FC and DF-L-FC. Owing to the discontinuous change in mechanical properties between earlywood and latewood (Kang et al. 2014), significant compressive strain occurred in the earlywood near the boundary with the latewood. The trend of localised deformation of radial compressive specimens was similar to that reported by Murata et al. (2003).

Fig. 5
figure 5

\(\sigma_{yy}^{{}}\) versus \(\varepsilon_{yy}^{G}\) relationships and \(\varepsilon_{yy}^{D}\) distributions of AL-FC-3, DF-L-FC-2, and DF-R-FC-3

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Figure 6 shows the \(\varepsilon_{yy}^{D,ave}\) versus \(\left| {\varepsilon_{yy}^{G} } \right|\) relationships. The maximum values of \(\left| {\varepsilon_{yy}^{G} } \right|\) for AL-FC, DF-L-FC, and DF-R-FC were 0.02, 0.008, and 0.012, respectively, with some variability. The cause of this variability is that the specimens of DF-L-FC and DF-R-FC experienced localised deformation in their upper and lower contact regions after yielding, causing fractures such as brooming and crushing, respectively (ASTM 2000).

Fig. 6
figure 6

\(\varepsilon_{yy}^{D,ave}\) versus \(\varepsilon_{yy}^{G}\) relationships of a AL-FC, b DF-L-FC, and c DF-R-FC

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To evaluate the differences between \(\varepsilon_{yy}^{D,ave}\) and \(\varepsilon_{yy}^{G}\), the following variables are defined as:

$$\Delta_{ij}^{{}} = \varepsilon_{ij}^{G} - \varepsilon_{ij}^{D,ave}$$
(2)
$$\Delta_{ij}^{rel} = \left( {1 - \frac{{\varepsilon_{ij}^{D,ave} }}{{\varepsilon_{ij}^{G} }}} \right) \times 100$$
(3)

Figure 7 shows the \(\Delta_{yy}^{{}}\) versus \(\left| {\varepsilon_{yy}^{G} } \right|\) and \(\Delta_{yy}^{rel}\) versus \(\left| {\varepsilon_{yy}^{G} } \right|\) relationships. Across all test specimens, there is a tendency for \(\Delta_{yy}^{{}}\) to increase as the strain magnitude increases. Notably, the specimens of DF-R-FC exhibit a higher rate of increase in \(\Delta_{yy}^{{}}\) compared to those of AL-FC and DF-L-FC. In all specimens, \(\Delta_{yy}^{rel}\) is substantial (> 10.0%) when \(\left| {\varepsilon_{yy}^{G} } \right|\) is small (< 0.002), owing to predominant errors of the DIC system such as lens distortion, variations in ambient lighting, self-heating, and temperature variations. When \(\left| {\varepsilon_{yy}^{G} } \right|\) in the specimens of AL-FC and DF-L-FC exceeds 0.002, \(\Delta_{yy}^{rel}\) stabilises at approximately \(\pm\) 6.0% or lower, whereas for DF-R-FC, \(\Delta_{yy}^{rel}\) continues to increase with \(\left| {\varepsilon_{yy}^{G} } \right|\).

Fig. 7
figure 7

a \(\Delta_{yy}^{{}}\) versus \(\left| {\varepsilon_{yy}^{G} } \right|\) and b \(\Delta_{yy}^{rel}\) versus \(\left| {\varepsilon_{yy}^{G} } \right|\) relationships

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Figure 8 illustrates \(\varepsilon_{yy}^{D,ave}\) along the \(\eta\)-axis at the initial stage of elastic deformation, just before yielding and after yielding for (a) AL-FC, (b) DF-L-FC, and (c) DF-R-FC. The \(\eta\)-axis is detailed in the strain distribution diagrams of Fig. 5. There is variability in \(\varepsilon_{yy}^{D,ave}\) along the axial distribution in all specimens, which intensifies as axial deformation increases. Specifically, in DF-R-FC-3, this variability is linked to localised strain concentrations at the interface between earlywood and latewood, resulting in higher values of \(\Delta_{yy}^{{}}\) and \(\Delta_{yy}^{rel}\) for DF-R-FC compared to AL-FC and DF-L-FC.

Fig. 8
figure 8

\(\varepsilon_{yy}^{D}\) on \(\eta\)-axis for a AL-FC-3, b DF-L-FC-2, and c DF-R-FC-3

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It is standard practice to determine the stress–strain relationship of a material in uniaxial material tests using a DIC system to measure the Young’s modulus of the material (Chen et al. 2020; Jeong et al. 2016; Pan et al. 2013). Hence, differences in Young’s modulus measured by the DIC system and a strain gauge for each specimen are investigated, as listed in Table 3. The average differences in Young’s modulus for the specimens AL-FC and DF-L-FC are − 1.23% and 2.26%, respectively, showing nearly similar magnitudes. However, for the specimens of DF-R-FC, the difference is 12.5%, indicating a significantly larger discrepancy compared to the specimens of AL-FC and DF-L-FC. This suggests the importance of recognising the differences in measuring Young’s modulus using a DIC system in the radial direction of wood compared to using a uniaxial strain gauge.

Table 3 Young’s modulus of each full compression specimen
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Table 3 also indicates a significant discrepancy in the errors of the Young’s moduli for DF-R-FC-1 or 2 and DF-R-FC-3. Figure 9 shows the \(\varepsilon_{yy}^{D}\) distributions of DF-R-FC-2 and DF-R-FC-3, where the averaging region for \(\varepsilon_{yy}^{D,ave}\) is indicated. It can be seen that the \(\varepsilon_{yy}^{D}\) gradient in the averaging region is larger for DF-R-FC-3 compared to DF-R-FC-2. In the DIC system employing the Ncorr program (Blaber et al. 2015), strain components are calculated using numerical differentiation of deformation gradients, which are notably sensitive to noise arising from deformation variations. The Ncorr program utilises the strain window algorithm (Pan et al. 2009), designed to practically calculate strain distributions. However, in this algorithm, displacement gradients are approximated on a plane to mitigate noise, which may lead to decreased accuracy in the numerical differentiation of strain at points with significant nonlinear displacement gradients. On the other hand, it is known that in regions with high strain gradients, errors from strain gauges can also arise due to averaging effects (Younis et al. 2011). In addition, deriving theoretical formulas from elasticity mechanics for the partial compression problem of wood, which is both orthotropic and heterogeneous, presents significant challenges. Based on the above, in high strain gradient regions, it is necessary to develop methods to accurately evaluate both DIC system and strain gauge. Figures 5 (a), (b), and 9 also show that the lower strain area is the junction of the strain gauge leads because the junction has higher stiffness than the averaged area.

Fig. 9
figure 9

\(\varepsilon_{yy}^{D}\) distributions of DF-R-FC-2 and DF-R-FC-3 at 2nd recording point, where the load value is approximately 1.0 kN

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Partial compressive material tests

The partial compressive material tests on A6063 and Douglas fir were conducted. Triaxial strain gauges were affixed to the surfaces of the partial compressive test specimens at two locations, as shown in Fig. 1(c) and (d), and designated as gauges A and B. As illustrated in the top-right corner of Fig. 10, the normal strains measured by these triaxial strain gauges are denoted as \(\varepsilon_{0}^{{}}\), \(\varepsilon_{45}^{{}}\), and \(\varepsilon_{90}^{{}}\), corresponding to angles of 0°, 45°, and 90° with respect to the x-axis. As shown in Fig. 10, Mohr’s strain circle can be illustrated using \(\varepsilon_{0}^{{}}\), \(\varepsilon_{45}^{{}}\), and \(\varepsilon_{90}^{{}}\), from which the shear strain \(\varepsilon_{xy}^{{}}\) can be calculated as follows:

$$\varepsilon_{xy}^{{}} = \varepsilon_{m} - \varepsilon_{45} = \frac{{\varepsilon_{0} + \varepsilon_{90} }}{2} - \varepsilon_{45}$$
(4)
Fig. 10
figure 10

Mohr’s strain circle

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Figures 11 and 12 present the \(\varepsilon_{ij}^{D,ave}\) versus \(\varepsilon_{ij}^{G}\) relationships for the specimens of AL-PC-A, DF-PC-A, AL-PC-B, and DF-PC-B. These results, alongside Table 2, indicate that the signs of each strain component and the major strain components measured from the triaxial strain gauge and DIC correspond with those derived from the FEA results. As \(\varepsilon_{ij}^{G}\) increases, the difference between \(\varepsilon_{ij}^{D,ave}\) and \(\varepsilon_{ij}^{G}\) in the specimens of AL-PC-A and AL-PC-B increases gradually. Conversely, in the specimens of DF-PC-A and DF-PC-B, the difference increases rapidly beyond a certain value of \(\varepsilon_{ij}^{G}\).

Fig. 11
figure 11

\(\varepsilon_{ij}^{D,ave}\) versus \(\varepsilon_{ij}^{G}\) relationships of AL-PC-A and DF-PC-A

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Fig. 12
figure 12

\(\varepsilon_{ij}^{D,ave}\) versus \(\varepsilon_{ij}^{G}\) relationships of AL-PC-B and DF-PC-B

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Figures 13 and 14 illustrate the \(\Delta_{ij}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) and \(\Delta_{ij}^{rel}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) relationships of PC-A and PC-B, respectively. The observed trends are as follows:

  1. (1)

    In the specimens of DF-PC-A and DF-PC-B, \(\Delta_{ij}\) tends to increase with the increase in \(\left| {\varepsilon_{ij}^{G} } \right|\), but it suddenly increases beyond a certain magnitude of \(\left| {\varepsilon_{ij}^{G} } \right|\). In the specimens of AL-PC-A and AL-PC-B, \(\Delta_{ij}\) tends to increase with the increase in \(\left| {\varepsilon_{ij}^{G} } \right|\), and the values do not exhibit a rapid increase, unlike DF-PC-A and DF-PC-B.

  2. (2)

    Within the range of \(\left| {\varepsilon_{ij}^{G} } \right| < 0.002\), \(\Delta_{ij}^{rel}\) of all the specimens was large (> 20%) owing to unavoidable errors of the DIC system. Within the range of \(\left| {\varepsilon_{ij}^{G} } \right| > 0.002\), \(\Delta_{ij}^{rel}\) of AL-PC-A and AL-PC-B generally remains within \(\pm\) 20%, while that of DF-PC-A and DF-PC-B increases with the increase in \(\left| {\varepsilon_{ij}^{G} } \right|\).

  3. (3)

    In the partial compression tests, \(\Delta_{ij}\) and \(\Delta_{ij}^{rel}\) of DF-PC-A and DF-PC-B are larger than those of AL-PC-A and AL-PC-B. \(\Delta_{ij}\) and \(\Delta_{ij}^{rel}\) in the partial compression tests are larger than \(\Delta_{yy}\) and \(\Delta_{yy}^{rel}\) in the full compression tests.

Fig. 13
figure 13

\(\Delta_{ij}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) and \(\Delta_{ij}^{rel}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) relationships of AL-PC-A and DF-PC-A

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Fig. 14
figure 14

\(\Delta_{ij}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) and \(\Delta_{ij}^{rel}\) versus \(\left| {\varepsilon_{ij}^{G} } \right|\) relationships of AL-PC-B and DF-PC-B

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To investigate the cause of the rapid increase in \(\Delta_{ij}\), as noted in (2), the details of DF-PC-B-3 were examined. Figure 15 shows the P versus u and \(\Delta_{ij}\) versus u relationships of DF-PC-B-3. The results indicate that \(\Delta_{ij}\) increases when the P–u relationship exhibits nonlinear behaviour from the 4th to the 7th recording points. At the 7th recording point, \(\Delta_{ij}\) increases sharply owing to delamination of the speckle pattern near the strain gauge. Figure 16 shows the surface images and distributions of \(\varepsilon_{xx}^{D}\), \(\varepsilon_{yy}^{D}\), and \(\varepsilon_{xy}^{D}\) of DF-PC-B-3 at the 4th, 5th, and 6th recording points. The images show that as the plastic deformation of wood underneath the steel plate progresses, wrinkles form on the surface because of the local deformation of earlywood. The distributions of \(\varepsilon_{yy}^{D}\) and \(\varepsilon_{xy}^{D}\) are discontinuous owing to differences in mechanical properties between the earlywood and latewood (Kang et al. 2014). The discontinuity in the \(\varepsilon_{yy}^{D}\) distribution extends over a wide range from the top to the bottom of the specimen. In contrast, discontinuities in the distribution of \(\varepsilon_{xy}^{D}\) are observed from beneath the corner of the steel plate and in the vicinity of the wrinkled portion of the speckle pattern. The discontinuity in \(\varepsilon_{xy}^{D}\) and \(\varepsilon_{yy}^{D}\) is mainly observed at the location of strain gauge A, while that in \(\varepsilon_{yy}^{D}\) is dominant at the location of strain gauge B.

Fig. 15
figure 15

P versus u and \(\left| {\Delta_{ij} } \right|\) versus u relationships of DF-PC-B-3

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Fig. 16
figure 16

Images and distributions of \(\varepsilon_{xx}^{D}\), \(\varepsilon_{yy}^{D}\), and \(\varepsilon_{xy}^{D}\) of DF-PC-B-3

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Conclusion

This study investigated the accuracy of a DIC system equipped with a bilateral telecentric lens when applied to wood. Full compression tests and partial compression tests were conducted on Douglas fir and A6063 (aluminium alloy) to examine the differences in the accuracy of the DIC system between homogeneous and heterogeneous materials. The accuracy of the DIC system was assessed by comparing the results with those obtained from strain gauges. In the full compression tests, the accuracy of axial strain measured by the DIC system was similar for the specimens of A6063 and Douglas fir (L: Longitudinal), but the specimens of Douglas fir (R: Radial) exhibited lower accuracy compared to both A6063 and Douglas fir (L). This is because the specimens of Douglas fir (R) exhibited the discontinuous distribution of normal strain in compressive direction owing to differences in mechanical properties between the earlywood and latewood produces high strain gradients.

The differences in Young’s modulus obtained from the DIC system and strain gauge for the specimens of A6063, Douglas fir (L), and Douglas fir (R) were − 1.23%, 2.26%, and − 12.5%, respectively. In the partial compression tests, the accuracy of strain components measured by the DIC system in the specimens of Douglas fir was lower than that in A6063, because of high strain gradients. In partial compression tests, unlike full compression tests, the distribution of multiple strain components exhibits discontinuities and high strain gradients, leading to reduced accuracy of DIC. On the other hand, it is known that in regions with high strain gradients, errors from strain gauges can also arise due to averaging effects. The estimation of errors on orthotropic and heterogeneous materials is challenging. Therefore, in high strain gradient regions, it is necessary to develop methods to accurately evaluate the errors of both DIC system and strain gauge.