一致偶应力理论的基础
Foundations of consistent couple stress theory
摘要：
本文考察了新近发展起来的斜对称偶应力理论，论证了它的内在一致性、自然简单性以及与经典力学的根本联系。这有望帮助科学界克服对这一理论的任何歧义和怀疑，特别是偶应力张量的反对称特征的有效性。我们证明，在一个一致的连续介质力学，在每一点的物质的无穷小元素的响应自然分解成一个刚体部分，加上这些元素在连续介质的相邻点的相对平移和旋转。这种相对平移和旋转分别捕获拉伸和曲率方面的变形。其结果是，连续位移场及其相应的旋转场是主要变量，这与刚体力学完全一致，从而提供了统一的基础。为了进一步澄清，我们还研究了偏对称偶应力理论，反过来，提供了更多的洞察力一致连续介质力学的基本方面。
英文摘要：
In this paper, we examine the recently developed skew-symmetric couple stress theory and demonstrate its inner consistency, natural simplicity and fundamental connection to classical mechanics. This hopefully will help the scientific community to overcome any ambiguity and skepticism about this theory, especially the validity of the skew-symmetric character of the couple-stress tensor. We demonstrate that in a consistent continuum mechanics, the response of infinitesimal elements of matter at each point decomposes naturally into a rigid body portion, plus the relative translation and rotation of these elements at adjacent points of the continuum. This relative translation and rotation captures the deformation in terms of stretches and curvatures, respectively. As a result, the continuous displacement field and its corresponding rotation field are the primary variables, which remarkably is in complete alignment with rigid body mechanics, thus providing a unifying basis. For further clarification, we also examine the deviatoric symmetric couple stress theory that, in turn, provides more insight on the fundamental aspects of consistent continuum mechanics.
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