Evolution of generalized couple-stress continuum theories: a critical analysis

Abstract

In this paper, we examine different generalized couple-stress continuum mechanics theories, including couple stress, strain gradient and micropolar theories. First, we investigate the fundamental requirements in any consistent size-dependent couple stress continuum mechanics, for which satisfying basic rules of mathematics and mechanics are crucial to establish a consistent theory. As a result, we show that continuum couple stress theory must be based on the displacement field and its corresponding macrorotation field as degrees of freedom, while an extraneous artificial microrotation cannot be a true continuum mechanical concept. Furthermore, the idea of generalized force and independent generalized degrees of freedom show that the normal component of the surface moment traction vector must vanish. Then, with these requirements in mind, various existing couple stress theories are examined critically, and we find that certain deviatoric curvature tensors create indeterminacy in the spherical part of the couple stress tensor. We also examine micropolar and micromorphic theories from this same perspective.

arXiv comment47 pages, 4 figures, 2 tables, 35 references

References in corpus (1)

• On Dislocations in a Special Class of Generalized Elasticity

Cited by in corpus (9)

• On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
• A new view on boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model
• Foundations of consistent couple stress theory
• Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective
• A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions
• 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
• An assessment of higher gradient theories from a continuum mechanics perspective