scholarly journals Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress

2021 ◽  
pp. 108128652110615
Author(s):  
KP Soldatos
Keyword(s):  
Couple Stress ◽  
Fibrous Composite ◽  
Couple Stress Theory ◽  
Bending Stiffness ◽  
Theoretical Development ◽  
Theoretical Formulation ◽  
Elastic Deformations ◽  
Spherical Part ◽  
Fibre Bending Stiffness

The indeterminacy of the spherical part of couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already but, so far, has been left unexplained and unexploited; namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term that does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory previously presented without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending.

scholarly journals Determination of the spherical part of the couple-stress in a polar fibre-reinforced elastic plate subjected to pure bending

2021 ◽  
Author(s):  
K. P. Soldatos
Keyword(s):  
Stress Tensor ◽  
Couple Stress ◽  
Fibrous Composite ◽  
Strain Energy Function ◽  
Problem Solution ◽  
Single Family ◽  
Pure Bending ◽  
Spherical Part ◽  
Rotation Field

AbstractThis communication provides initial information and understanding of the manner in which a newly developed theoretical mechanism (Soldatos in Int J Solids Struct 202:217–225, 2020) is applied in specific boundary value problems met in polar linear elasticity of fibrous composites and thus enables the determination of the spherical part of the couple-stress tensor. In this context, it tests the applicability of the implied mechanism/method in the case that a rectangular plate reinforced by a single family of unidirectional fibres is subjected to pure bending. The problem solution is obtained for either non-polar or polar material behaviour, where fibres are considered perfectly flexible or resistant in bending, respectively, and provides clear evidence of the correctness of the principal argument that underpins the proposed method. Namely, that the general rotation field of the plate deformation differs from the fibre rotation field. That newly discovered method enables an extra energy term that emerges in the strain energy function of the fibrous composite plate to relate with the spherical part of the couple-stress tensor outside conventional equilibrium conventions. It thus leads to the determination of the spherical part of the couple-stress and its distribution throughout the plate body in a complete and comprehensive manner.

Elastostatic Fields of an Embedded Circular Rigid Nano/Micro-Fiber with Interfacial Damage in Anti-Plane Couple Stress Elasticity

2015 ◽  
Vol 784 ◽  
pp. 80-85
Author(s):  
Behdad Hashemian ◽  
H.M. Shodja ◽  
Azadeh Goodarzi
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Analytical Determination ◽  
Interfacial Damage ◽  
Stress Theory ◽  
Elastic Fields ◽  
Couple Stress Elasticity ◽  
Continuum Theories

It is well-known that classical continuum theory has certain deficiencies in predicting the nanoscopic behavior of materials in the vicinity of defects. Couple stress theory is one of the higher order continuum theories which can overcome such difficulties by introducing new characteristic length. An accurate analytical determination of the elastic fields of an embedded circular nano/micro-rigid fiber with damaged interface under remote anti-plane loading in the context of couple stress elasticity is of particular interest.

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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