Objective  The large microfibril helix angle (MFA) in the S₂ layer 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 S₂ layer 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 S₂ layer of the compression wood cell wall, the effects of MFA in S₂ layer 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.

  Method  First, the S₂ layer 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 S₂ layer 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 S₂ layers of compression wood and normal wood with different MFA were simulated by Abaqus, and the relationship between MFA and the compressive toughness of S₂ layer was analyzed. On this basis, the compressive mechanical behaviors of wood cell wall with and without S₁, S₃ (or S₂L, it means the area between S₂ and S₁ layer 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.

  Result  As the increasing of MFA in S₂ layer, the critical buckling displacement of S₂ layer of wood cell wall was increasing, and the critical buckling pressure was first decreasing and then increasing. The critical pressure of S₂ layer 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 S₂ layer with MFA = 45° was lower than that in the normal wood S₂ layer with MFA = 0°. The compressive stiffness and compressive toughness of S₂ layer with large MFA were enhanced because the compression-torsion coupling of spiral microfibrils in S₂ layer of a single compression wood cell wall was constrained by its surrounding tracheids. S₁, S₂L 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 S₂ layer. 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.

  Conclusion  The spiral morphology of microfibrils in the S₂ layer of compression wood cell wall changes the stress transfer between the microfibrils and the matrix, which results in the matrix of the S₂ layer 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 S₂ layer, the critical buckling displacement of cell wall increases significantly with the increase of MFA, thereby the compressive toughness of S₂ layer is enhanced. When MFA is about 45°, the compressive toughness of S₂ layer of compression wood cell wall reaches the highest, not only its critical buckling displacement is more than twice that of S₂ layer of normal wood cell wall, but also its critical buckling pressure is slightly higher than the latter.