Transient Study of Couple Stress Effects in Compact Bone: Torsion

1981 ◽  
Vol 103 (4) ◽  
pp. 275-279 ◽  
Author(s):  
J. F. C. Yang ◽  
R. S. Lakes
Keyword(s):  
Couple Stress ◽  
Characteristic Length ◽  
Unit Area ◽  
Couple Stress Theory ◽  
Compact Bone ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Stress Effects ◽  
Apparent Stiffness ◽  
Transient Study

Couple stress theory, which admits an internal moment per unit area as well as the usual force per unit area, is a generalization of classical elasticity. Experimentally we have demonstrated the existence of couple stress by measuring the effect of size on apparent stiffness of compact bone in quasi-static torsion. From these measurements, we obtain the characteristic length for bone in couple stress theory.

Dynamical Study of Couple Stress Effects in Human Compact Bone

1982 ◽  
Vol 104 (1) ◽  
pp. 6-11 ◽  
Author(s):  
R. S. Lakes
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Compact Bone ◽  
Dynamical Study ◽  
Additional Material ◽  
Low Frequencies ◽  
Stress Theory ◽  
Stress Effects ◽  
Human Compact Bone ◽  
Material Coefficient

Torsional resonance experiments performed on wet human compact bone disclose effects due to couple stress. The characteristic length, which is an additional material coefficient which appears in couple-stress theory, is of the order of the size of osteons and appears to be smaller at high frequencies than at low frequencies. The presence of couple-stress effects implies a reduction in the stress concentration factor around holes, particularly small holes.

Rayleigh wave equations with couple stress: modeling and dispersion characteristic

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Yanqi Wu ◽  
Jianwei Ma
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Scale Effect ◽  
Linear Elasticity ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Homogeneous Half Space

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodynamics, wave propagation equations are usually based on linear elasticity. Thus, nonlinear elasticity must be introduced to study the scale effect on wave propagation. In this work, we introduce one of the generalized continuum theories—couple stress theory—into solid earth geophysics to build a more practical model of underground medium. The first-order velocity-stress wave equation is derived to simulate the propagation of Rayleigh waves. Body and Rayleigh waves are compared using elastic theory and couple stress theory in homogeneous half- space and layered space. The results show that couple stress causes the dispersion of surface waves and shear waves even in homogeneous half-space. The effect is enhanced by increasing the source frequency and characteristic length, despite its insufficiently clear physical meaning. Rayleigh waves are more sensitive to couple stress effect than body waves. Based on the phase-shifting method, it was determined that Rayleigh waves exhibit different dispersion characteristics in couple stress theory than in conventional elastic theory. For the fundamental mode, the dispersion curves tend to move to a lower frequency with an increase in characteristic length l. For the higher modes, the dispersion curves energy is stronger with a greater characteristic length l.

Effects of microstructure and liquid loading on velocity dispersion of leaky Rayleigh waves at liquid–solid interface

2018 ◽  
Vol 96 (1) ◽  
pp. 11-17 ◽  
Author(s):  
Vikas Sharma ◽  
Satish Kumar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Liquid Layer ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Liquid Loading ◽  
Stress Theory ◽  
Leaky Rayleigh Waves

Inner atomic interactions at the micro scale produce new effects that cannot be accounted for by the classical theory of elasticity. To study the impact of the microstructures of the material, generalized continuum theories involving additional microstructural material parameters are preferred. One such microcontinuum theory involving an additional material parameter called internal characteristic length (l) is a consistent couple stress theory. The study of leaky Rayleigh waves generated at the interface of solid half-space with liquid layer is of great importance for quick scanning and imaging of large civil engineering structures. The problem of leaky Rayleigh waves propagating in elastic half-space under liquid loading has been studied in the context of this consistent couple stress theory. Dispersion equations are obtained by developing the mathematical model of the problem. Phase velocity of leaky Rayleigh waves is studied for three different values of characteristic length parameter (l), which is of the order of internal cell size of the material. Effects of thickness of liquid layer are also studied on the phase velocity profiles.

Step-by-Step Simplification of the Micropolar Elasticity Theory to the Couple-Stress and Classical Elasticity Theories

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Elasticity Theory ◽  
Linear Theory ◽  
Elastic Constants ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Material Model ◽  
Micropolar Elasticity ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Special Case

The micropolar elasticity theory provides a useful material model for dealing with fibrous, coarse granular, and large molecule materials. Though being a well-known and well-developed elasticity model, the linear theory of micropolar elasticity is not without controversy. Specially simplification of the microppolar elasticity theory to the couple-stress and classical elasticity theories and the required conditions on the material elastic constants for this simplification have not been discussed consistently. In this paper the linear theory of micropolar elasticity is reviewed first. Then the correct approach for a consistent and step-by-step simplification of the micropolar elasticity model with six elastic constants to the couple-stress elasticity model with four elastic constants and the classical elasticity model with two elastic constants is presented. It is shown that the classical elasticity is a special case of the couple-stress theory which itself is a special case of the micropolar elasticity theory.

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half-space

1974 ◽  
Vol 64 (2) ◽  
pp. 387-392
Author(s):  
M. Farshad ◽  
G. Ahmadi
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Material Parameters ◽  
Surface Wave Propagation

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.

Investigating the Size-Dependent Static and Dynamic Behavior of Circular Micro-Plates Subjected to Capillary Force

2015 ◽  
Author(s):  
M. H. Kahrobaiyan ◽  
I. Vardi ◽  
M. T. Ahmadian ◽  
S. Henein
Keyword(s):  
Elasticity Theory ◽  
Capillary Force ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Size Dependency ◽  
Size Dependent ◽  
Modified Couple Stress

The size-dependent static deflection, pull-in instability and resonant frequency of a circular microplate under capillary force have been studied using modified couple stress elasticity theory. Size-dependency is a phenomenon in which the normalized quantities that classical elasticity theory predicts to be independent of the structure size, such as normalized deflection or normalized frequency, vary significantly as the structure size changes. This phenomenon has been observed in micro-scale structures such as micro-electro-mechanical-systems (MEMS). Since classical elasticity theory is unable to predict the size-dependency, non-classical elasticity theories such as modified couple stress theory have been developed recently. In this paper, modified couple stress theory is used for the first time to develop the governing equation and boundary conditions of circular microplates when subjected to capillary force. Consideration of capillary force is important since it is has a significant role in the mechanical behavior and stability of micro-scale structures in the presence of a liquid bridge. We investigated the static deflection and pull-in instability of microplates using the Galerkin method to assess the effect of size-dependency for static deflection. We observed that, as the ratio of the microplate thickness to length scale parameter (an additional material property suggested in modified couple stress theory to capture the size-dependency) decreases, the normalized deflection of the microplate also decreases. We further observed that the difference between the normalized deflection predicted by classical elasticity theory and the one evaluated using modified couple stress theory is significant when thickness of the microplate is small, but diminishes as thickness increases. Furthermore, we defined a dimensionless number called the dimensionless capillary tension (DCT) as a function of the mechanical, geometrical and size-dependent properties of the microplate as well as the characteristics of the liquid bridge such as the contact angle and the interfacial tension. We showed that for DCT values greater than a threshold evaluated in this paper, pull-in instability happens and the microplate collapses to the substrate. Moreover, we evaluated the size-dependent resonant frequency of the microplate under capillary force as a function of the DCT and obtained the result that the frequency decreases as DCT increases. In addition, our investigation of size-dependency revealed that as the ratio of the microplate thickness to length scale parameter increases, the frequency decreases in a way that for large values of the ratio, it asymptotically approaches the value predicted by classical elasticity theory.

scholarly journals Interaction problems between cracks and crystal defects in constrained Cosserat elasticity

2018 ◽  
Vol 03 (03n04) ◽  
pp. 1840011
Author(s):  
K. P. Baxevanakis ◽  
H. G. Georgiadis
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Singular Integral Equations ◽  
Crystal Defects ◽  
Configurational Forces ◽  
Strengthening Effect ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Crack Problems ◽  
Opening Mode

In this work, interaction problems between a finite-length crack with plane and antiplane crystal defects in the context of couple-stress elasticity are presented. Two alternative yet equivalent approaches for the formulation of crack problems are discussed based on the distributed dislocation technique. To this aim, the stress fields of climb and screw dislocation dipoles are derived within couple-stress theory and new ‘constrained’ rotational defects are introduced to satisfy the boundary conditions of the opening mode problem. Eventually, all interaction problems are described by single or systems of singular integral equations that are solved numerically using appropriate collocation techniques. The obtained results aim to highlight the deviation from classical elasticity solutions and underline the differences in interactions of cracks with single dislocations and dislocation dipoles. In general, it is concluded that the cracked body behaves in a more rigid way when couple-stresses are considered. Also, the stress level is significantly higher than the classical elasticity prediction. Moreover, the configurational forces acting on the defects are evaluated and their dependence on the characteristic material length of couple-stress theory and the distance between the defect and the crack-tip is discussed. This investigation reveals either a strengthening or a weakening effect in the opening mode problem while in the antiplane mode a strengthening effect is always obtained.

Physical and Mathematical Representations of Couple Stress Effects on Micro/Nanosolids

2015 ◽  
Vol 07 (01) ◽  
pp. 1550012 ◽  
Author(s):  
M. Shaat
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Elastic Materials ◽  
Additional Material ◽  
Stress Theory ◽  
Couple Stresses ◽  
Linear Elastic ◽  
Stress Effects ◽  
Points Of View ◽  
Alternative Theories

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects. In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects. It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.

FREE VIBRATION AND BUCKLING ANALYSIS OF BEAMS WITH A MODIFIED COUPLE-STRESS THEORY

2012 ◽  
Vol 04 (03) ◽  
pp. 1250026 ◽  
Author(s):  
J. V. ARAÚJO DOS SANTOS ◽  
J. N. REDDY
Keyword(s):  
Free Vibration ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Ritz Method ◽  
Modified Couple Stress Theory ◽  
Classical Elasticity ◽  
Buckling Loads ◽  
Stress Theory ◽  
Modified Couple Stress

A model based on a modified couple stress theory for the free vibration and buckling analyses of beams is presented. The model also incorporates the Poisson's effect and allows the analysis of Timoshenko beams with any arbitrary end boundary condition. The natural frequencies and buckling loads are computed using the Ritz method. Parametric studies show that, while the natural frequencies and the buckling loads increase monotonically with the increase of the material length scale, they present a minimum in certain values of the Poisson's ratio. A study relating the classical elasticity and the couple stress strain energies is also presented. By establishing this relation, explicit formulas to obtain the natural frequencies and buckling loads, in which the couple stress and Poisson's effects are accounted for, in terms of the buckling loads of the classical elasticity are found. These formulas, which are valid when the shear strain and stress are zero, allow an expedite computation of natural frequencies and buckling loads of beams with couple stress and Poisson's effect.

An Embedded Elliptic Nano-Fiber in Anti-Plane Strain Couple Stress Elasticity

2008 ◽  
Author(s):  
Hossein M. Shodja ◽  
Hamed Haftbaradaran
Keyword(s):  
Size Effect ◽  
Isotropic Material ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Infinite Medium ◽  
Stress Theory ◽  
Couple Stress Elasticity ◽  
Nano Fiber ◽  
Continuum Theories

The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem.

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