Abstract Part II (Soldatos, 2018b) identified some theoretical disagreement between the generally anisotropic polar linear elasticity of Mindlin and Tiersten (1962) and its counterpart developed in (Spencer and Soldatos, 2007; Soldatos, 2014) for fibrous composites with embedded fibres resistant in bending. The present communication shows that this disagreement is essentially due to inherent features of fibre-splay types of deformation and, consequently, generalises the Cosserat and Cosserat (1909) couple-stress theory in a manner that creates room for newly emerged fibre-splay type of kinematic variables to enter and be accounted for. Relevant fundamental theorems, associated in Part II with the Mindlin and Tiersten model, are generalised accordingly to meet the needs and requirements of the proposed new formulation. Interestingly and importantly, the outlined generalisation enables formation of a convincing answer to a long-standing question regarding the indeterminacy of the spherical part of the couple-stress tensor, at least as far as polar elasticity of fibre-reinforced materials is concerned. The manner thus is demonstrated in which the spherical part of the couple-stress can be determined in polar linear elasticity of fibrous composites that exhibit transverse isotropy due to an embedded family of fibres resistant in bending.

中文翻译：

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当纤维抗弯时极性纤维复合材料的表征——第三部分：耦合应力的球形部分

摘要 第二部分 (Soldatos, 2018b) 确定了 Mindlin 和 Tiersten (1962) 的一般各向异性极性线性弹性与其在 (Spencer and Soldatos, 2007; Soldatos, 2014) 中开发的对应物之间的一些理论分歧，用于嵌入纤维的纤维复合材料弯曲。目前的交流表明，这种分歧主要是由于纤维张开类型变形的固有特征，因此，以一种为新出现的纤维张开类型的变形创造空间的方式概括了 Cosserat 和 Cosserat (1909) 耦合应力理论。要输入和考虑的运动学变量。在第二部分中与 Mindlin 和 Tiersten 模型相关的相关基本定理被相应地概括以满足提议的新公式的需要和要求。有趣且重要的是，概述的概括能够对一个长期存在的关于耦合应力张量的球形部分的不确定性的问题形成令人信服的答案，至少就纤维增强材料的极性弹性而言。这样就证明了其中耦合应力的球形部分可以在纤维复合材料的极性线性弹性中确定的方式，这些纤维复合材料由于嵌入的抗弯曲纤维族而表现出横向各向同性。