摘要: 目的应压木细胞壁S ₂层中的大微纤丝螺旋角(MFA)是树木管胞对力学环境适应性生长的结果，故它有其特别的力学性能。但目前人们还不了解S ₂层中大MFA对其抗压性能的增韧机理。基于应压木细胞壁S ₂层的超微结构建立复合材料力学模型，采用数值模拟方法研究应压木细胞壁S ₂层中MFA对其抗压韧性的影响，可以探究其中的力学机理，并探索基于数值模型研究木细胞壁压缩韧性的建模与分析方法，进而为仿生材料设计奠定力学基础、�/sec> 方法首先将云杉木细胞壁S ₂层简化为连续微纤丝和基体组成的复合材料，并利用夹杂理论的自洽模型计算木细胞壁S ₂层基体的等效弹性常数。然后利用HyperWorks建立木细胞壁的纤维增强复合材料有限元分析模型，用Abaqus模拟不同MFA的应压木和正常木细胞壁S ₂层在压缩载荷下的力学行为，并用所得结果分析其MFA与抗压韧性的关系。在此基础上，对比是否考虑木细胞壁的S ₁、S ₃（或S ₂L，指的是S ₂层与S ₁层之间木质素和半纤维素含量高的区域）和MP层（P和ML层）对其受压力学行为的影响，并分析在应压木细胞壁数值模型中考虑各组分材料塑性行为的重要性、�/sec> 结果在压力作用下，当木细胞壁S ₂层的MFA增大时，其临界屈曲位移增大，临界屈曲压力先减小再增大�?5° MFA应压木细胞壁S ₂层的临界压力�?° MFA正常木细胞壁S ₂层相当，但前者的临界屈曲位移是后者的3.57倍，屈曲失稳前的应变能是后者的2.95倍。在相同压力下，45° MFA应压木细胞壁S ₂层微纤丝的von Mises应力低于0° MFA正常木。由于单个应压木细胞壁S ₂层中螺旋状微纤丝所具有的压−扭耦合变形受到周边管胞对扭转变形的约束，其抗压刚度和抗压韧性得到增强。应压木细胞壁中的S ₁、S ₂L和MP层对其受压屈曲有显著的约束作用，完整应压木细胞壁的临界压力比只考虑S ₂层的临界压力增大37.6%。压力作用下木细胞壁的破坏模式为塑性屈曲，所以考虑木细胞壁各组分材料的塑性行为对准确地计算其抗压韧性十分重要，忽略其塑性行为会使其临界压力的计算结果增�?.97倍、�/sec> 结论在受压状态下，应压木细胞壁S ₂层中微纤丝的螺旋形貌改变了微纤丝与基体间的应力传递，使得S ₂层的基体承受更多的压应力，木细胞壁的破坏模式变为局部塑性屈曲。所以在压力作用下，尽管应压木细胞壁的抗压刚度随S ₂层MFA的增大而减小，但应压木细胞壁的临界屈曲位移随MFA的增大而显著地增大，从而增强了它的抗压韧性。当MFA�?5°左右时，应压木细胞壁的抗压韧性最佳，此时不仅它的临界屈曲位移比正常木细胞壁S ₂层高两倍多，且它的临界屈曲压力也略高于后者、�/sec>

关键诌�
• 应压�?/a> /
• 木细胞壁/
• 微纤丝角（MFA（�/a> /
• 临界屈曲位移/
• 抗压韧�?/a> /
• 增韧机理/
• 数值模拞�/a>

Abstract: ObjectiveThe large microfibril helix angle (MFA) in the S ₂layer of the compression wood cell wall is the result of the adaptive growth of tree tracheids to the mechanical stimulation, so it has special mechanical functions. However, the toughening mechanism of large MFA in S ₂layer on the compressive properties of wood cell wall has not been understood yet by researchers. Based on a computational model of composite material for the ultrastructure of S ₂layer of the compression wood cell wall, the effects of MFA in S ₂layer on the compressive toughness of compression wood cell wall were simulated and the toughening mechanism was explored, and the method of modeling and analyzing the compressive toughness of the wood cell wall based on the numerical model was explored. The findings presented in this paper would provide useful guideline for the optimal design of biomimetic materials. MethodFirst, the S ₂layer of spruce wood cell wall was modeled as a composite cylinder composed of continuous microfibrils as well as matrix, and the equivalent elastic constants of the matrix of S ₂layer were calculated using the self-consistent model of inclusion theory. Then, the finite element analysis model of the fiber reinforced composite of wood cell wall was established by HyperWorks. The compressive mechanical behaviors of the S ₂layers of compression wood and normal wood with different MFA were simulated by Abaqus, and the relationship between MFA and the compressive toughness of S ₂layer was analyzed. On this basis, the compressive mechanical behaviors of wood cell wall with and without S ₁, S ₃(or S ₂L, it means the area between S ₂and S ₁layer with high lignin and hemicellulose content) and MP (P and ML) layers were investigated, and the importance of considering the plastic behavior of each constituent in the numerical model of compression wood cell wall was analyzed. ResultAs the increasing of MFA in S ₂layer, the critical buckling displacement of S ₂layer of wood cell wall was increasing, and the critical buckling pressure was first decreasing and then increasing. The critical pressure of S ₂layer of compression wood cell wall with MFA of 45° was equivalent to that of normal wood cell wall with MFA = 0°, but the critical buckling displacement of the former was 3.57 times of the latter, and the strain energy before buckling was 2.95 times of the latter. Under the same pressure, the von Mises stress of microfibrils in the compression wood S ₂layer with MFA = 45° was lower than that in the normal wood S ₂layer with MFA = 0°. The compressive stiffness and compressive toughness of S ₂layer with large MFA were enhanced because the compression-torsion coupling of spiral microfibrils in S ₂layer of a single compression wood cell wall was constrained by its surrounding tracheids. S ₁, S ₂L and MP layers had significant restraint effect on the buckling of the compression wood cell wall, and the critical pressure of the compression wood cell wall with the consideration of all the layers in the wood cell wall was 37.6% larger than that of the model only considering the S ₂layer. The failure mode of wood cell wall under pressure was of plastic buckling, so it is very important to include the plastic behavior of each component of wood cell wall to accurately calculate its compressive toughness. Ignoring the plastic behavior of wood cell wall will cause the computed result of its critical pressure increased by 2.97 times. ConclusionThe spiral morphology of microfibrils in the S ₂layer of compression wood cell wall changes the stress transfer between the microfibrils and the matrix, which results in the matrix of the S ₂layer bearing more compressive stress and the failure mode of the wood cell wall becoming local plastic buckling. Although the compressive stiffness of compression wood cell wall decreases with the increase of MFA in S ₂layer, the critical buckling displacement of cell wall increases significantly with the increase of MFA, thereby the compressive toughness of S ₂layer is enhanced. When MFA is about 45°, the compressive toughness of S ₂layer of compression wood cell wall reaches the highest, not only its critical buckling displacement is more than twice that of S ₂layer of normal wood cell wall, but also its critical buckling pressure is slightly higher than the latter.

Key words:
• compression wood/
• wood cell wall/
• microfibril angle (MFA)/
• critical buckling displacement/
• compressive toughness/
• toughening mechanism/
• numerical simulation

�?nbsp; 1木细胞壁微结枃�/p>

图片引自参考文献[20]和[21]。Pictures are cited from references [20] and [21].

Figure 1.Microstructure of wood cell wall

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�?nbsp; 2正常木和应压木细胞壁几何模型

Figure 2.Geometric models of cell walls of normal and compression wood

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�?nbsp; 3木细胞壁有限元网栻�/p>

Figure 3.Finite element mesh of wood cell wall

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�?nbsp; 4木细胞壁上端面载荷和外表面边界条仵�/p>

Figure 4.Load on the upper face and boundary conditions on the outer surface of wood cell wall

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�?nbsp; 5不同MFA木细胞壁S2层压力–位移曲纾�/p>

Figure 5.Force-displacement curves of S2 layers of wood cell wall with different MFA

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�?nbsp; 60° MFA的正常木�?5° MFA的应压木细胞壁S₂层压缩屈曲变形图

Figure 6.Compressive buckling deformation graphs of S₂layers of normal wood cell wall at 0° MFA and compression wood cell wall at 45° MFA

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�?nbsp; 70° MFA正常木和45° MFA应压木细胞壁S₂层轴向压缩过程中的应变能

Figure 7.Strain energy during axial compression of S₂layers of normal wood cell wall at 0° MFA and compression wood cell wall at 45° MFA

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�?nbsp; 80° MFA正常木和45° MFA应压木细胞壁S₂层微纤丝和基体von Mises应力分布云图

Figure 8.von Mises stress cloud diagrams of microfibrils and matrix of S₂layers of normal wood cell wall at 0° MFA and compression wood cell wall at 45° MFA

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�?nbsp; 9有无扭转约束�?5° MFA应压木细胞壁S₂层压力–位移曲纾�/p>

Figure 9.Force-displacement curves of S₂layers of compression wood cell walls with and without torsional restraint at 45° MFA

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�?nbsp; 10不同长径比的45° MFA应压木细胞壁S₂层应力–应变曲纾�/p>

Figure 10.Stress-strain curves of S₂layers of compression wood cell walls with different aspect ratios at 45° MFA

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�?nbsp; 11不同水体积分数的45° MFA应压木细胞壁S₂层压力–位移曲纾�/p>

Figure 11.Force-displacement curves of S₂layers of compression wood cell walls with different water volume ratio at 45° MFA

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�?nbsp; 12考虑所有层和只考虑S₂层的45°应压木细胞壁压力–位移曲纾�/p>

Figure 12.Force-displacement curves of compression wood cell walls considering all layers and considering only S₂layer at MFA 45°

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�?nbsp; 13线弹性和弹塑�?5°MFA应压木细胞壁压力–位移曲纾�/p>

Figure 13.Force-displacement curves of compression wood cell walls at 45° MFA using linear elastic and elastoplastic models

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�?nbsp; 1云杉木细胞壁各层尺寸

Table 1.Dimensions of layers in spruce wood cell wall

细胞壁层 Cell wall layer	厚度 Thickness/µm	占细胞壁厚度比例 Proportion to cell wall thickness/%
S1	0.318	9.0
S2	3.000	85.0
S3	0.112	3.2
P	0.100	2.8

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�?nbsp; 2S₂层基体成分材料的力学参数及体积分�?/p>

Table 2.Mechanical parameters of matrix component materials of S₂layer

成分 Component	体积模量 Bulk modulus/GPa	剪切模量 Shear modulus/GPa	在S2层中体积分数 Volume fraction in S2layer/%
半纤维素 Hemicellulose	8.89	2.96	17.0
木质� Lignin	5.00	2.30	28.0
水和提取� Water and extract	2.30	0	14.0

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�?nbsp; 3微纤丝弹性常�?/p>

Table 3.Elastic constants of microfibril

部分 Component	$ {E}_{\mathrm{A}} $/GPa	$ {E}_{\mathrm{T}} $/GPa	$ {\mu }_{\mathrm{A}} $	$ {\mu }_{\mathrm{T}} $	$ {G}_{\mathrm{A}} $/GPa
微纤东�br/>Microfibril	62.77	15.00	0.087	0.420	3.00
注：$ {E}_{\mathrm{A}} $�? {\mu }_{\mathrm{A}} $�? {E}_{\mathrm{T}}\mathrm{、}{\mu }_{\mathrm{T}} $分别表示微纤丝轴向和横向的弹性模量、泊松比�? {G}_{\mathrm{A}} $为剪切模量。Notes: $ {E}_{\mathrm{A}} $, $ {\mu }_{\mathrm{A}} $ and $ {E}_{\mathrm{T}}, \;{\mu }_{\mathrm{T}} $ represent the axial and lateral elastic modulus and Poisson’s ratio of the microfibril, $ {G}_{\mathrm{A}} $ is the shear modulus.

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�?nbsp; 4S₁、S₃、P和ML层的弹性常�?/p>

Table 4.Elastic constants of S₁, S₃, P and ML layers

细胞壁层 Cell wall layer	$ {E}_{\mathrm{c}} $/GPa	$ {E}_{\mathrm{r}} $/GPa	$ {\mu }_{\mathrm{c}} $	$ {\mu }_{\mathrm{r}} $	$ {G}_{\mathrm{c}} $/GPa
S1	25.64	8.74	0.226	0.035	2.88
S3	23.88	8.11	0.232	0.036	2.70
ML + P	11.51	11.51	0.200	0.200	4.80
注：下标c和r分别表示木细胞壁的周向和径向。Note: subscripts c and r indicate the circumferential and radial directions of the wood cell wall.

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�?nbsp; 5微纤丝和基体塑性材料参�?/p>

Table 5.Plastic material parameters of microfibril and matrix

部分 Component	屈服应力 Yield stress/GPa	极限压应劚�br/>Ultimate compressive stress/GPa	极限塑性应受�br/>Ultimate plastic strain
基体 Matrix	0.054	0.243	0.770
微纤东�br/>Microfibril	0.318	0.636	0.107

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