Related papers: Foundations of consistent couple stress theory
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…
In this paper, the concept of moment and couple in mechanics is examined from a fundamental perspective. It turns out that although representing a couple by its moment vector is very useful in rigid body mechanics and strength of materials,…
Fundamental solutions for two- and three-dimensional linear isotropic size-dependent couple stress elasticity are derived, based upon the decomposition of displacement fields into dilatational and solenoidal components. While several…
We show that the reasoning in favor of a symmetric couple stress tensor in Yang et al.'s introduction of the modified couple stress theory contains a gap, but we present a reasonable physical hypothesis, implying that the couple stress…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
In this paper, we examine theoretical and practical aspects of several versions of couple stress theory. This includes indeterminate Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), indeterminate symmetric modified couple stress…
The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps…
We investigate the consistency of the fundamental governing equations of motion in continuum mechanics. In the first step, we examine the governing equations for a system of particles, which can be considered as the discrete analog of the…
The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of…
By investigating the benefits and shortcomings of the existing form of continuous defect theory (CDT) and using recent advancements in size-dependent continuum mechanics, we develop a fully coherent theoretical framework, denoted as…
In this paper, we examine the pure bending of plates within the framework of modified couple stress theory (M-CST) and consistent couple stress theory (C-CST). In this development, it is demonstrated that M-CST does not describe pure…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming…
We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity…
A geometrically nonlinear continuum mechanical theory is formulated for deformation and failure behaviors of amorphous polymers. The model seeks to capture material response over a range of loading rates, temperatures, and stress states…
We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction…
In this paper we venture a new look at the linear isotropic indeterminate couple stress model in the general framework of second gradient elasticity and we propose a new alternative formulation which obeys Cauchy-Boltzmann's axiom of the…
We formulate a thermodynamically consistent continuum theory for compressible, viscous, heat-conducting fluids in which the velocity entering the balance of mass is distinguished from the specific linear momentum entering the balances of…