Many tree species are planted in China with variable properties and usage. Toward exploring the structure-properties relationships of wood and classifying the species more reasonably, the physiomechanical properties of the domestic wood species in China were analyzed statistically. According to the correlation analysis, the mechanical properties were closely related to the wood density. Except impact toughness and cleavage strength, the correlation coefficients between mechanical properties and densities were more than 0.8. However, shrinkage properties showed fewer correlations with densities, and the coefficient was no more than 0.7. Primary component analysis was proved to be feasible to explore the information of the physiomechanical properties. Two principal components (PC1 and PC2) could account for most of the information. PC1 and PC2 were designated as density-dominated and shrinkage-associated factors, respectively. The domestic wood species in China could be classified into 4 clusters based on their physiomechanical properties. According to the cluster results, reasonable grading was proposed for air-dried density, volume shrinkage, modulus of rupture, compression strength parallel to grain and hardness in cross section. The statistical results brought insights into analyzing the physiomechanical properties of domestic Chinese wood species, which was helpful for developing strategies of tree breeding and technologies of wood processing.

Wood is a biologically renewable resource in the process of human life and production. There are more than 60,000 tree species recorded worldwide, and more than 4,000 species are found in China [

It is widely recognized that wood can be classified based on its structural features, including the anatomical characteristics [

Wood is composed of a certain proportion of cellulose, hemicellulose and lignin. The chemical composition of wood varies at different levels (species, cell and cell wall). The chemical spectroscopy is capable of extracting and analyzing the difference of chemical components, and wood species can be classified consequently [

The variations of structure and chemical characteristics behave as different physiomechanical properties of wood. Among the numerous properties, density determines the physiomechanical properties of wood to a large extent, which is reflected in the availability of a wide range of wood materials properties [

Although statistical analysis has been used for processing complex data in wood science, the classification of wood species with respect to their physiomechanical properties is rare. The reason is twofold: 1) There are many physiomechanical properties, and these properties have certain variations among and within wood species [

Original data of the physiomechanical properties were adopted from the book “Wood Physical and Mechanical Properties of Main Tree Species in China” [_{en}), air-dried density (AD_{en}), radial shrinkage coefficient (Sh_{R}), tangential shrinkage coefficient (Sh_{T}), volume shrinkage coefficient (Sh_{V}), modulus of elasticity (MOE), modulus of rupture (MOR), shear strength in radial section (SS_{R}), shear strength in tangential section (SS_{T}), compression strength in longitudinal (CS_{L}), radial (CS_{R}) and tangential direction (CS_{T}), local compression strength in radial (LCS_{R}) and tangential direction (LCS_{T}), tension strength in longitudinal direction (TS_{L}), impact toughness (IT), hardness in cross (H_{C}), radial (H_{R}) and tangential section (H_{T}), cleavage strength in radial (ClS_{R}) and tangential section (ClS_{T}). The above-mentioned properties of all the wood species are compiled in Supplementary Material

For ease of the description for the statistical analysis, in this study, the wood species were taken as samples, and the properties were taken as variables.

Correlation analysis refers to the analysis of two or more correlated variables factors, so as to measure the closeness of the two variables [_{XY} was calculated as:

where _{XY} is the covariance of _{X} and Var_{Y} are the variances of _{XY} ranges between –1 and 1. When the value was higher than 0, there was a positive correlation between

PCA refers to replacing the original variables with fewer new variables, and making these fewer variables retain as much of the information reflected by the original variables as possible [

PCA was carried out by the statistical software, SPSS version 17.0 (SPSS Inc., Chicago, IL, USA). Firstly, the average value _{ik} or _{jk}) to make sure the value of the variance of each variable was 1. Then, the correlated matrix R of the variable and the standardized correlation coefficient _{ij} were calculated

where _{p}) and eigenvectors were calculated with a total number of p (λ_{1} > λ_{2} > … > λ_{p} ≥ 0) [_{s}), new variables (_{1}, _{2}, _{p}) were created to present all the physiomechanical properties.

Dimensionality reduction was carried out by calculating the ratio of variances (

where _{ik} and _{jk} are the variances. Once the value of _{1}, _{2}, …, _{p}) was basically remained.

Cluster analysis is a method for merging data structures into categories when there is no prior classification. When using the cluster analysis, the tree species were classified based on their physical and mechanical properties [

(1) A standardized transformation was performed by the

(2) The Euclidean distance (_{ij}) between any two samples was calculated as:

(3) The distance between category and category was calculated.

where _{i} is the number of samples of category I. Two categories (Gp, Gq) in the samples were assumed. If Gp and Gq were combined into G_{k}, the sum of the squares of the deviations increased after the combination

where S_{k}, S_{p}, S_{q} are the sum of squares of deviations of classes G_{k}, G_{p}, G_{q}, respectively. The two categories with the smallest increase in the sum of squared deviations were selected and merged into a new category. Step 3 was repeated until all samples were combined into one category.

(4) A clustering pedigree diagram was drawn.

(5) The optimal number of categories was determined according to the aggregation coefficient.

The correlation coefficient of any two properties among the 21 ones is shown in _{en} or AD_{en}). The wood density represented the amount of polymeric substances in the wood cell wall per unit volume. Wood with higher density could bear greater forces, behaving as stronger mechanical capacity [

However, the correlation coefficient between TS_{L} and BD_{en} (or AD_{en}) was only around 0.8, which was obviously lower than that between CS_{L} and density (>0.87). When subjected to longitudinal tension, the mechanical capacity was mainly dependent on the covalent bond of the molecular chain in cellulose, and the microfibril angle had a significant influence on the value of TS_{L} [

The correlation coefficient between shrinkage and density was less than 0.7, because shrinkage was largely dependent on micro-structure of wood, such as the microfibril angle, the arrangement of fiber and ray cells, the ratio of early- and latewood, and the radial position of wood [_{en} and Sh_{T} were the key characteristics for domestic gymnosperms species in China, while AD_{en} and Sh_{R} were the key characters of angiosperms. Such a variation was attributed to different forms of wood rays.

Based on the results shown in

The plotted scores of PC1 _{T}, Sh_{R} and Sh_{V} concentrated together as another group. The scatter between the two groups confirmed the lower correlations between shrinkage and other properties. Based on the results shown in

The PC1 and PC2 scores of all the wood species were calculated and are displayed in _{en} (_{v} (_{L} (_{en} or Sh_{v}. However, the boundary in _{en} and Sh_{v}, and PCA results were effective when classifying wood species.

The optimal number of clusters was determined by the elbow method when evaluating the aggregation coefficient [

To evaluate the performances of the cluster analysis, the average values of the properties in each cluster were calculated, and those of the selected properties are displayed in

Based on the results in the 4 clusters, the grading levels for the properties were calculated. In _{en} as an example (^{3}, respectively. However, the spans were 0.5, 0.13 and 0.1 g/cm^{3}, for the grading levels # 1, # 2 and # 3, respectively. The compact spans for # 2 and # 3 were also found for the properties of S_{v} (_{L} (

Previous studies showed that the classification and identification of certain wood species, and the classification was merely used to analyze the physiomechanical properties of wood. Reasonable classification was the inevitable development approach and effective way to improve the technology for wood utilization. In this study, the grading results brought insights into analyzing the properties of domestic Chinese wood species, especially for the plantation species, and the findings extended the understanding of the “structure-properties-applications” relationships.

The physiomechanical properties of the domestic wood species in China were statistically analyzed for classification of these species. Based on the correlation analysis, PCA and cluster analysis, the conclusions were as follows:

1) The mechanical properties were closely related to the air-dried (or basic) density. Except impact toughness and cleavage strength, the correlation coefficients between mechanical properties and densities were higher than 0.8. Shrinkage properties showed less correlations with densities, and the coefficients was around and even lower than 0.7.

2) PCA was feasible to explore the information of the physiomechanical properties of wood. Two principal components (PC1 and PC2) could account for most of the information. The densities and mechanical properties had larger loading with PC1, and shrinkages were much associated with PC2. Hence, PC1 and PC2 were designated as density-dominated and shrinkage-associated factors, respectively.

3) The domestic species in China could be classified into 4 clusters based on their physiomechanical properties. According to the cluster results, reasonable gradings for the air-dried density, volume shrinkage, modulus of rupture, compression strength parallel to grain and hardness in cross section were proposed.

This work was financially supported by the National Natural Science Foundation of China (No. 32171705) and the Advanced analysis and testing center of Nanjing Forestry University.