Wood materials are characterized by complex, hierarchical material structures spanning across various length scales. The present work aims at establishing a relation between the hygro-elastic properties at the mesoscopic cellular level and the effective material response at the macroscopic level, both for softwood (spruce) and hardwood (balsa). The particular aim is to explore the influence on the effective hygro-elastic properties under variations in the meso-scale morphology. The multi-scale framework applied for this purpose uses the method of asymptotic homogenization, which allows to accurately and efficiently obtain the effective response of heterogeneous materials characterized by complex meso-structural geometries. The meso-structural model considered for softwood is based on a periodic, two-dimensional statistically representative volume element that is generated by a spatial repetition of tracheid cells. The tracheid cells are modeled as hexagonal elements characterized by a certain geometrical irregularity. The hardwood meso-structure consists of a region composed of hexagonal cellular fibers with large vessels embedded, which is connected to a ray region that is constructed of ray cells. The hardwood fibers are modeled as hexagonal cellular elements, similar to softwood tracheids. The rays are represented by quadrilateral cells oriented along the radial direction, whereby different arrangements are considered, i.e., the ray cells are either regularly stacked or organized as a staggered configuration. The interface between the fiber and ray regions may also be characterized by a regular or a staggered arrangement. The meso-structural models for softwood and hardwood are discretized by means of plane-strain, finite element models, which describe the hygro-elastic response of the wood material in the radial–tangential plane. For softwood, the sensitivity of the effective elastic and hygro-expansive properties is explored as a function of the geometrical irregularity of the tracheids. For hardwood, the effective properties are studied under a variation of the ray cell arrangement, the type of interface between ray and fiber regions, and the vessel volume fraction. The modeling results agree well with results obtained from other numerical homogenization studies and show to be in reasonable agreement with experimental data taken from the literature.

木质材料的特点是复杂的、层次化的材料结构跨越各种长度尺度。目前的工作旨在建立细观细胞水平的湿弹性特性与宏观水平的有效材料响应之间的关系，无论是软木（云杉）还是硬木（轻木）。特定目的是探索在中尺度形态变化下对有效湿弹性的影响。用于此目的的多尺度框架使用渐近均质化方法，可以准确有效地获得具有复杂细观结构几何特征的异质材料的有效响应。考虑用于软木的细观结构模型基于周期性的、由管胞细胞的空间重复生成的二维统计代表性体积元素。管胞细胞被建模为六边形元素，其特征在于一定的几何不规则性。硬木细观结构由嵌入大血管的六边形细胞纤维组成的区域组成，该区域连接到由射线细胞构成的射线区域。硬木纤维被建模为六边形细胞元素，类似于软木管胞。射线由沿径向定向的四边形单元表示，由此考虑不同的布置，即射线单元或者规则地堆叠或者组织为交错配置。光纤和射线区域之间的界面也可以以规则或交错排列为特征。软木和硬木的细观结构模型通过平面应变有限元模型进行离散化，该模型描述了木材在径向 - 切向平面中的湿弹性响应。对于软木，有效弹性和吸湿膨胀特性的敏感性被探索为管胞几何不规则性的函数。对于硬木，在射线单元排列、射线和纤维区域之间的界面类型以及容器体积分数的变化下研究了有效特性。建模结果与从其他数值均匀化研究中获得的结果非常吻合，并表明与文献中的实验数据具有合理的一致性。它描述了木质材料在径向-切向平面中的湿弹性响应。对于软木，有效弹性和吸湿膨胀特性的敏感性被探索为管胞几何不规则性的函数。对于硬木，在射线单元排列、射线和纤维区域之间的界面类型以及容器体积分数的变化下研究了有效特性。建模结果与从其他数值均匀化研究中获得的结果非常吻合，并表明与文献中的实验数据具有合理的一致性。它描述了木质材料在径向-切向平面中的湿弹性响应。对于软木，有效弹性和吸湿膨胀特性的敏感性被探索为管胞几何不规则性的函数。对于硬木，在射线单元排列、射线和纤维区域之间的界面类型以及容器体积分数的变化下研究了有效特性。建模结果与从其他数值均匀化研究中获得的结果非常吻合，并表明与文献中的实验数据具有合理的一致性。有效弹性和吸湿膨胀特性的敏感性被探索为管胞几何不规则性的函数。对于硬木，在射线单元排列、射线和纤维区域之间的界面类型以及容器体积分数的变化下研究了有效特性。建模结果与从其他数值均匀化研究中获得的结果非常吻合，并表明与文献中的实验数据具有合理的一致性。有效弹性和吸湿膨胀特性的敏感性被探索为管胞几何不规则性的函数。对于硬木，在射线单元排列、射线和纤维区域之间的界面类型以及容器体积分数的变化下研究了有效特性。建模结果与从其他数值均匀化研究中获得的结果非常吻合，并表明与文献中的实验数据具有合理的一致性。