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.

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.

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.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

2021 ◽  
pp. 108128652110015
Author(s):  
YL Qu ◽  
GY Zhang ◽  
YM Fan ◽  
F Jin
Keyword(s):  
Classical Theory ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Constitutive Relations ◽  
Stress Theory ◽  
Isotropic Materials ◽  
Flexoelectric Effect ◽  
Beam Bending ◽  
Gradient Theories ◽  
Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

A size-dependent model for shear deformable laminated micro-nano plates based on couple stress theory

2021 ◽  
Vol 259 ◽  
pp. 113457
Author(s):  
Zanhang He ◽  
Jianghong Xue ◽  
Sishi Yao ◽  
Yongfu Wu ◽  
Fei Xia
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Dependent Model ◽  
Shear Deformable
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