scholarly journals A new analytical solution of pure bending beam in couple stress elasto-plasticity: Theory and applications

2010 ◽  
Vol 47 (6) ◽  
pp. 779-785 ◽  
Author(s):  
Ji Bin ◽  
Chen Wanji
Keyword(s):  
Analytical Solution ◽  
Couple Stress ◽  
Plasticity Theory ◽  
Pure Bending ◽  
Elasto Plasticity

Analytical Solution of a Borehole Problem Using Strain Gradient Plasticity

2002 ◽  
Vol 124 (3) ◽  
pp. 365-370 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Plastic Region ◽  
Yield Condition ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Spatial Gradient ◽  
Gradient Plasticity ◽  
Present Solution ◽  
Classical Plasticity

An analytical solution is presented for the borehole problem of an elasto-plastic plane strain body containing a traction-free circular hole and subjected to uniform far field stress. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. This gradient plasticity theory introduces a higher-order spatial gradient of the effective plastic strain into the yield condition to account for the nonlocal interactions among material points, while leaving other relations in classical plasticity unaltered. The solution gives explicit expressions for the stress, strain, and displacement components. The hole radius enters these expressions not only in nondimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size effect in a quantitative manner. The classical plasticity-based solution of the borehole problem is obtained as a special case of the present solution. Numerical results for the plastic region radius and the stress concentration factor are provided to illustrate the application and significance of the newly derived solution.

Elastic-Plastic Analogy for Examination of Softening Response for Strip Yield Models

2020 ◽  
Author(s):  
Don Metzger ◽  
Wolf Reinhardt
Keyword(s):  
Analytical Solution ◽  
Inelastic Deformation ◽  
Load Capacity ◽  
Pure Bending ◽  
Yield Model ◽  
Elastic Plastic ◽  
Bending Load ◽  
Strip Yield Model ◽  
Linear Softening ◽  
Plastic Case

Abstract The manner in which the spread of inelastic deformation of a softening cohesive zone affects the load capacity is examined. The analysis makes use of an elastic-plastic analogy to the strip yield model applied to pure bending. The example of pure bending is one case where inelastic deformation contributes to enhancing the load capacity. The analytical solution to the elastic-plastic case is developed for zero hardening (baseline for strip yield case for which analytical solution is known) as well as for a range of linear softening rates. Evaluation of the results shows that the maximu m bending load capacity is always reached before the stress at the surface becomes zero.

scholarly journals Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality

2017 ◽  
Vol 36 (3) ◽  
pp. 277-293 ◽  
Author(s):  
Yaghoub Tadi Beni ◽  
Fahimeh Mehralian ◽  
Mehran Karimi Zeverdejani
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Analytical Solution ◽  
Couple Stress ◽  
Solution Method ◽  
Couple Stress Theory ◽  
Careful Analysis ◽  
Single Walled Carbon Nanotube ◽  
Motion Equations ◽  
Stress Theory

In the present work, using the couple stress theory, a new model is provided for vibrating behavior of anisotropic carbon nanotubes. Carbon nanotubes have many applications, and careful analysis of their behavior is important. So far, using the isotropic models, several studies have been conducted on carbon nanotube vibration. According to the arrangement of carbon atoms on the nanotube walls, their properties will be different in various directions. Therefore, the behavior of carbon nanotubes must be considered as anisotropic materials. In this article, initially, using the Hamilton's principle, motion equations, and boundary conditions of carbon nanotubes are extracted based on couple stress theory. Afterwards, the equations are solved using the analytical solution method. In the results section, the effect of different parameters, particularly the anisotropic effect, on the carbon nanotube natural frequency is investigated.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

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