Anisotropy of fibrous tissues in relation to the distribution of tensed and buckled fibers
Anisotropy of fibrous tissues in relation to the distribution of tensed and buckled fibers
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DOI：
10.1115/1.2486179
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发表时间：
2007-04-01
影响因子：
1.7
通讯作者：
Ateshian, Gerard A.
中科院分区：
文献类型：
--
作者：
Ateshian, Gerard A.
纤维组织的特点是拉伸时比压缩时刚度高得多。本研究采用微结构模型分析拉伸和压缩纤维组织的材料对称性，以更好地了解材料对称性与拉伸和屈曲纤维分布的关系。该分析还用于确定从微观结构模型预测的行为是否可以由现象学连续统模型完全描述。分析证实，当所有纤维在当前构形中处于张力状态时，相应参考构形中纤维组织的材料对称性由其在该构形中纤维角分布的对称性决定。然而，如果应变场表现为拉伸和压缩主正常应变的混合，则纤维组织表示为仅由处于拉伸状态的纤维组成的材料体；该体的材料对称性可由应变对称面与纤维角分布对称面叠加而得。因此，材料的对称性是由那些处于张力状态的纤维的角分布的对称性决定的。给出了各种纤维角分布对称的实例。特别地，发现具有各向同性纤维角分布的纤维组织在受到拉伸和压缩主法向应变的混合作用时表现出正交各向异性对称性，对称面垂直于应变的主方向。这种各向异性即使在无限小的应变下也会发生，与纤维有限旋转引起的各向异性不同。还需要注意的是，纤维材料在所有应变状态下都不是稳定的，因为纤维不能沿其轴承受压缩；这种不稳定性可以通过结合接地矩阵来克服。结果表明，用纤维微观结构模型预测的材料响应不能用现象学连续统模型准确描述。这些结果同样适用于非生物纤维复合材料。
Fibrous tissues are characterized by a much higher stiffness in tension than compression. This study uses microstructural modeling to analyze the material symmetry of fibrous tissues undergoing tension and compression, to better understand how material symmetry relates to the distribution of tensed and buckled fibers. The analysis is also used to determine whether the behavior predicted from a microstructural model can be identically described by phenomenological continuum models. The analysis confirms that in the case when all the fibers are in tension in the current configuration, the material symmetry of a fibrous tissue in the corresponding reference configuration is dictated by the symmetry of its fiber angular distribution in that configuration. However, if the strain field exhibits a mix of tensile and compressive principal normal strains, the fibrous tissue is represented by a material body which consists only of those fibers which are in tension; the material symmetry of this body may be deduced from the superposition of the planes of symmetry of the strain and the planes of symmetry of the angular fiber distribution. Thus the material symmetry is dictated by the symmetry of the angular distribution of only those fibers which are in tension. Examples are provided for various fiber angular distribution symmetries. In particular, it is found that a fibrous tissue with isotropic fiber angular distribution exhibits orthotropic symmetry when subjected to a mix of tensile and compressive principal normal strains, with the planes of symmetry normal to the principal directions of the strain. This anisotropy occurs even under infinitesimal strains and is distinct from the anisotropy induced from the finite rotation of fibers. It is also noted that fibrous materials are not stable under all strain states due to the inability of fibers to sustain compression along their axis; this instability can be overcome by the incorporation of a ground matrix. It is concluded that the material response predicted using a microstructural model of the fibers cannot be described exactly by phenomenological continuum models. These results are also applicable to nonbiological fiber-composite materials.