Foundations of consistent couple stress theory
arXiv:1509.06299
Abstract
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.
28 pages, 7 figures
References in corpus (3)
- On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
- Evolution of generalized couple-stress continuum theories: a critical analysis
- Correct traction boundary conditions in the indeterminate couple stress model
Cited by in corpus (5)
- On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
- Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective
- Comparison of theoretical elastic couple stress predictions with physical experiments for pure torsion
- Pure plate bending in couple stress theories
- Size-dependent couple stress Timoshenko beam theory