Three-Dimensional Elastic Behavior of Oriental Plane ( Platanus orientalis L.) Wood and Investigation Via Finite Element Analysis

Wood is an anisotropic material with a complex structure. It is very difficult to examine the properties of complex structured materials. Finite element analysis is a technique that can be used to analyze the mechanical behavior of wood and wood-based materials. The objective of this study is to determine the mechanical properties of Oriental plane ( Platanus orientalis L.) wood both experimentally and using finite element analysis. For tensile strength and compressive strength, with the aim of determining the wood’s behavior depending on its anisotropic axes, samples were prepared in three axial directions: radial, tangential and longitudinal. Under the same conditions and with the same dimensions, longitudinal samples were modeled in a computer environment using finite element analysis. ANSYS Multiphysics/LS-DYNA was used for simulation. It was determined that the laboratory results and the simulation results were in good agreement, with a similarity ratio of over 90%


Introduction
Wood is a challenging material to describe [Ostapska and Malo 2020].As a naturally grown material, wood has a sophisticated hierarchical structure and random defects and heterogeneities [Ostapska and Malo 2021].Its unique physical properties are based on the structure of its cells and how they are arranged influences in a number of ways.For example, for safety reasons (when wood failure has to be assessed), or in biomimetic-biomechanics (the development of new technical materials that mimic natural structures), having sufficient knowledge about the wood material will provide an advantage.This knowledge is also of great theoretical value.Although mechanical research on wood has a long history, many basic relationships are still unknown [Keunecke 2008].Wood material has orthotropic properties and its axes are defined in three anatomical directions: longitudinal (parallel to the direction of the fiber or grain), radial (from the core to the bark), and tangential (parallel to the annual rings).The orthotropic character of wood affects almost all of its properties, including mechanical properties.This means that the elastic and strength properties of wood depend on its axial direction [Ożyhar 2013].The material can therefore be understood completely and accurately only via examination in all three axes.
Today, rapid virtual analyses have begun to be carried out relating to the prevention or reduction of material loss, along with long-term time-saving experiments carried out in a computer environment, i.e., using numerical methods.These studies also allow the materials to be tested at the same time in many forms different from the original, and provide the opportunity to carry out biomechanical studies.Numerical methods can provide not only details of the material deformation process, but also information on changes in mechanical parameters during loading [Zhong et al. 2021].Numerical methods are techniques in which problems are formulated mathematically so that they can be solved by arithmetic operations.In recent years, with the development of fast and efficient digital computers, numerical methods have played an important role in the solution of engineering problems.Numerical methods have the potential to solve a large number of equation systems, deviations from linearity, and complex geometries that are not at all uncommon in engineering applications and often cannot be solved by analytical methods [Arslantürk and Kara 2012].Modeling with the finite element method is one of the techniques found in such studies [Warguła et al. 2020].This is a numeric analysis method in which the problem is simulated while considering the physical conditions and features of the materials [Yörür 2012].Finite element analysis allows a substance or material to be examined by dividing it into a very small finite number of elements to be analyzed.Even at these small size levels, changes can be monitored.Thus, the finite element method can provide a full solution where complex problems are divided into simpler sub-problems, with each one being solved within itself [Gürer et al. 2008].
For this purpose, the method uses three-dimensional models which are prepared or transferred to the computer environment.The accuracy of the results is proportional to the accuracy of the information transferred to the computer.The graphs obtained can be read and analyzed easily [Alhijazi et al. 2020].Data obtained from experimental studies are necessary to create more accurate and effective numerical analyses.
Researchers deal with the experimental and numerical determination of material properties [Fajdiga et al. 2019] and have successfully applied this method in analyzing the properties of wood-based materials [Tabiei and Wu 2000;Moses 2004;Serrano 2004;Sheng et al. 2012].It has been shown in many studies that the results of experiments and analyses concerning the mechanics of solid wood exhibit good agreement.However, when studies close to the present day are considered, it can be said that there is not enough research with the finite element method on wood and wooden materials.Güntekin and Yılmaz [2013] carried out analyses of the bending stresses and deformation of wooden beams.Wang and Lee [2014] investigated the feasibility of design and analysis of an interference fit in a dowel-glued joint by the finite element method.A predictive finite element model for laminated timber and laminated beams was developed by El Houjeyri et al. [2021].This model was validated by comparison with experimental results.Toson et al. [2014] proposed a constitutive model for finite element modeling of balsa wood structures under severe loadings.Timbolmas et al. [2022] used the finite element method to analyze the behavior of poplar wood subjected to axial tensile stress.Hajdarević and Busuladžić [2015] presented a stiffness analysis of a statically indeterminate wooden chair side-frame.They reported good agreement between the results of numerical analysis and those of experimental testing of wood specimens.Dos Santos et al. [2015] proposed non-linear 3D finite element models to simulate T-joint behavior.In another study, the mechanical behavior of notched wood beams was studied using full-field measurements and modeled using finite element software [Toussaint et al., 2016].Pěnčík [2015] conducted research on the modeling of experimental tests of wooden specimens from Scots pine.Hu et al. [2019] studied the effect of size on the mechanical properties of European beech wood, using samples of different sizes.Meghlat et al. [2013] developed a new approach to model nailed and screwed timber joints using the finite element method.Fajdiga et al. [2019] studied computational and experimental results on the fracture behavior of spruce wood under quasi-static loading conditions during a three-point bending test.Kaygın et al. [2016] determined the strength properties of wood corner joints using finite element analysis, and obtained agreement at a level of about 90-97%.Zulkifli et al. [2021] performed numerical simulation of the behavior of wood materials under high strain rates using finite element software.They reported that the results differed from the experimental results by not more than 10%.
The main purpose of the present study was to examine the properties of wood samples in the tangential, radial and longitudinal axes using tensile and compressive strength tests, and to repeat the experiments in the same form in a computer environment.Thus, the aim was to determine the possibility of using finite element analysis instead of physical tests on solid wood.To accomplish this aim, the following operations were performed: 1.In a laboratory environment, mechanical experiments were conducted using Platanus orientalis L. trunk wood samples oriented in three different directions (radial, tangential and longitudinal).At this stage, the aim was to observe the behavior of the wood in different axial directions and to determine the rupture parameters.The collected data set was used to determine the material properties necessary to construct the model used in finite element analysis of the samples.2. Due to the natural growing process and growth direction, mechanical properties such as stiffness and strength are assumed to vary mainly in the longitudinal direction [Kandler et al. 2015].Numerical simulations were performed for longitudinally directed specimens.Parallel-to-fiber tensile strength and compressive strength tests were repeated using finite element analysis, and the results were computed for models under the same loading conditions.At this stage, the aim was to see how close the results obtained by simulating a natural structure in a computer environment could be to those obtained under natural conditions.

Test specimens
For the experimental determination of mechanical properties, Oriental plane (Platanus orientalis L.) wood was obtained from the Kozcağız district in the province of Bartın in northern Türkiye.All experiments were performed with samples from the same wood.Samples for compressive strength and two different types of tensile strength samples were prepared for the tests.Test samples were prepared after planks from Oriental plane were brought to 65% relative humidity and 12% equilibrium humidity at 20 °C.The DB-shaped samples and parallel-to-fiber tensile strength samples were prepared in a five-axis CNC machine.To obtain accurate results, the specimens were prepared in their final form for the tests by means of a one-month holding period in an acclimatization cabinet at 65% relative humidity and at 20 °C.Dog-bone shaped samples (DB) were used to test the tensile strength characteristics of the neck form in particular.After their final shape was formed, the two end faces of the DB specimens were supported by beech wood pieces.This meant that the samples were not damaged during the experiments.The material used for experimental samples did not include knots, reaction wood or heartwood.Figure 1 shows the sample dimensions.Modulus of elasticity was calculated using equation ( 1) in accordance with the relevant standards. ( In this equation, E is the modulus of elasticity in withdrawal, Δσᵢ is the difference between the two compressive values, Δɛᵢ is the difference between the two deformation values, and i is a variable representing tangential, radial and parallel-to-fiber axes. For compressive strength, eighty samples were prepared in tangential, radial and longitudinal directions.The test was carried out according to DIN 52185 (1976) andDIN 52192 (1979).Samples were prepared with dimensions of 15 × 15 × 45 mm.Experiments were carried out according to TSE in 90 ± 30 seconds.The Utest 10-ton powered universal test device was used for the experiments, with the machine speed set at 2 mm/min.Equation ( 1) was also used to calculate the compressive strength modulus of elasticity.
The values obtained from the test results were transferred to the computer environment and the ANSYS program was used for finite element analysis.The finite element model required for calculation was created in the same processor.The finite element model data files created in a three-dimensional environment were transferred to the LS-DYNA and analyzed.Solid 164 was chosen as the material for modelling.

Mechanical property findings
To determine the mechanical properties, tests were carried out after the radial, tangential and longitudinal compressive strength and tensile strength samples obtained from the trunk wood of the tree were brought to the appropriate humidity level.After completion of the experiments, the modulus of elasticity was calculated for each of the samples and the mean values were determined.The results were compared with the results of the finite element analysis.Due to its natural structure, Platanus orientalis L. contains a large amount of wide ray band.The sawdust formed from the tangential and radial axes samples contained large amounts of ray bands.
For the DB-shaped samples, the maximum force (Fmax) and tensile strength (TS) values obtained according to the results of the experiments are given in Tables 1  and 2 below.In nearly all of the samples, rupture occurred in the middle of the sample, as expected.From the tangential and radial measurements, it was observed that the radial samples exhibited higher resistance in tensile strength tests than the tangential samples.Table 3 shows the results of the LSD test for the tangential and radial axis samples.
For parallel-to-fiber tensile strength samples, the results obtained from the experiments are given in Table 4.
As was expected, the rupture occurred in the middle of all of the samples.The ruptured section was not very sharp, as in the case of the tangential and radial axis DB samples; however, in some samples it had been fragmented due to the effect of the fibers.
Figure 2 shows the relationship between tensile strength and density.According to these results, a high correlation was found between the tensile strength of the three axes and the density variation.The highest correlation was obtained for tensile strength in the radial axis (84%), and the lowest in the case of the tangential axis (73%).For compressive strength, the longitudinal specimens exhibited a bending behavior instead of sharp rupture.This behavior was seen at much lower rates in the tangential and radial samples.Due to its characteristic structure, plane tree wood exhibited bending behavior in some of the samples.This property of the wood is due to the large amount of wide rays that it contains, and also to its fiber structure.Therefore, when the experiment could not be conducted within the period defined by experimental standards, it was ended when 5% deformation of the sample size was reached.The tangential and radial axis samples were similar to each other in that they produced results in a shorter time than the longitudinal axis samples.Fmax and compressive strength (CS) measurements obtained from the experiments are given in Tables 5 and 6.
According to the tangential, radial and longitudinal axis measurements, the highest resistance was obtained in the longitudinal specimens.The tangential and radial samples exhibited lower resistance.In Table 7, LSD test results are given for the tangential, radial and longitudinal axes.
Figure 3 shows the relationship between compressive strength and density.According to these results, a high correlation was found between the compressive strength of the three axes and the density variation.The highest correlation was obtained for tensile strength in the tangential axis (78%), and the lowest correlation in the case of the radial axis (73%).
The results for the modulus of elasticity of the specimens in the DB radial and tangential axes and tensile strength in the parallel-to-fiber axis are shown in Table 8.According to the data for the tangential and radial axes, the modulus of elasticity values were similar, while parallel-to-fiber samples gave higher values.According to the DB measurements, the longitudinal axis samples exhibited the highest resistance.The tangential and radial samples demonstrated lower resistance.Table 9 shows the LSD test results.
The modulus of elasticity results for the compressive strength samples are given in Table 10.The maximum compressive strength is in the longitudinal direction and the minimum in the tangential direction.Table 11 shows the LSD test results.

Finite element analysis results
In the study, after using Platanus orientalis L. samples for laboratory tests of tensile strength and compressive strength in the tangential, radial and longitudinal axes, finite element analysis was performed for parallel-to-fiber tensile strength and longitudinal compressive strength test samples.The samples were simulated in three dimensions using the ANSYS finite element program.After determining the necessary and appropriate information for the samples, analyses were performed using LS-DYNA.The data obtained under laboratory conditions were used for the analysis in the simulation environment.The data transferred to the ANSYS/LS-DYNA program yielded deformation and stress values for the samples.All three axial directions were created in the simulation environment.
Analyses were conducted by selecting the longitudinal direction.Figures 4 and 5 show the simulation images obtained as a result of the parallel-to-fiber tensile strength and longitudinal compressive strength tests in the computer environment under the same conditions as those in the laboratory.
Figure 4 shows the stress distributions of tensile strength.The x-coordinate was chosen for the parallel-to-fiber tensile strength analysis in the simulation environment.The stress increased with the load, and it was found that the highest stress occurred in the middle sections where the ruptures had occurred.In the area where the stress is highest, the stress in the sample was observed with the help of Ls-prepost.Rupture occurred in the specimen after stress.In the analyses, it was determined that the stress decreased from these points to the edges of the sample.In the highest stress area, a measurement of 47.5 MPa was obtained.The value dropped after the rupture.In the analyses, it was seen that the results of the experiments under laboratory conditions and those of the computer environment were 90-98% compatible for the parallel-to-fiber tensile strength samples.Figure 5 shows the stress distributions in the compressive strength case.For the compressive strength analysis, the y-coordinate was chosen in the simulation environment.With the help of Ls-prepost, the stress in the sample was observed at the support and contact points where the force was applied.The stress increased with the load.The maximum stress value for the compression strength samples was 50.4 MPa.This value began to decline from the moment of rupture.In the analyses, it was seen that the results of the experiments under laboratory conditions and those of the computer analysis were 90-98% compatible for the compressive strength samples.Collins et al. [2023] constructed a numerical model to predict tensile strengths, and reported that it made the predictions successfully.In another study, simulated compressive curves for varying moisture contents and three grain directions were obtained by the finite element method, and were compared with curves obtained by experiment.It was reported that the trend seen in the results of the finite element analysis was consistent with the experiment in terms of the effects of moisture content and grain direction [Fu et al. 2021].
Table 12 shows the results obtained by testing and with the use of computer-aided analysis.
It is seen that the finite element models generated predict the values with relatively high accuracy.
The effectiveness of the simulations is evidenced by the comparison with the results of experimental tests.In the numerical analysis, the results are lower.This can be explained by the higher sensitivity of simulation analyses compared with experimental ones, and the anisotropy of wood materials.

Conclusions
In this study, Platanus orientalis L. trunk wood was investigated using various mechanical experiments and by the finite element method.The use of samples of "dog-bone" shape is important because of the varying properties of the wood according to the axial direction.Due to their size, it was possible to prepare these samples in the radial and tangential axial directions of the wood.In this way, more detailed information was obtained in smaller regions and for different directions of the anisotropic wood structure.Longitudinal tensile and compressive strength specimens were successfully simulated using the finite element method.The stress distribution was clearly visible in the simulation models.The results obtained from the experiments and from the numerical analysis were compared, and it was determined that there was a high degree of agreement.The research revealed that the finite element method used in the study provides a convenient method for determining the behavior of solid wood, and can be used in determination of the mechanical properties of Oriental plane wood.
The different behavior of wood in different axes, that is, its anisotropic structure, can create difficulties in analysis.However, this indicates a need to continue research on the development of the analyses performed and programs used.Finite element analysis is a powerful adjunct that has to be allied with experimental observation and material characterization [Vasic et al. 2005].With the results of computeraided analysis programs and modeling closely approximating those of experimental methods, it is predicted that finite element analysis methods will be used more effectively in the future.

Table 1 .
Fmax values for dog-bone samples

Table 2 .
TS values for dog-bone samples

Table 4 .
TS values for parallel-to-fiber tensile strength specimens

Table 5 .
Fmax values for compressive strength samples

Table 6 .
CS values for compressive strength samples

Table 7 .
LSD test results for tangential, radial and longitudinal samples

Table 8 .
Modulus of elasticity results for test specimens for tensile strength parallel to fibers and DB tangential and radial axis

Table 9 .
LSD results for modulus of elasticity of tensile strength samples for parallel-to-fiber longitudinal and DB tangential and radial axes

Table 10 .
Modulus of elasticity results for test specimens for compressive strength in the tangential, radial and longitudinal axes

Table 11 .
LSD results for modulus of elasticity for tangential, radial and longitudinal axis compressive strength samples

Table 12 .
Results of parallel-to-fiber tensile strength and longitudinal compressive strength tests obtained under laboratory conditions and via computer-aided analysis