Gradient elasticity and size effect for the borehole problem

2018 ◽  
Vol 229 (8) ◽  
pp. 3305-3318 ◽  
Author(s):  
Haoxiang Chen ◽  
Chengzhi Qi ◽  
G. Efremidis ◽  
M. Dorogov ◽  
E. C. Aifantis
Keyword(s):  
Size Effect ◽  
Gradient Elasticity

scholarly journals 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY

2016 ◽  
Vol 7 ◽  
pp. 33-37 ◽  
Author(s):  
Christian Liebold ◽  
Wolfgang H. Müller
Keyword(s):  
Finite Element ◽  
Size Effect ◽  
Numerical Solution ◽  
Stiffness Matrix ◽  
Gradient Elasticity ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Additional Material ◽  
Hermite Finite Elements

We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution.

The use of nanoindentation for determining internal lengths and the constitutive response of monument materials: models and experiments

2016 ◽  
Vol 25 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Avraam A. Konstantinidis ◽  
George Frantziskonis ◽  
Harm Askes ◽  
Elias C. Aifantis
Keyword(s):  
Experimental Data ◽  
Size Effect ◽  
Indentation Size Effect ◽  
Gradient Elasticity ◽  
Alternative Interpretation ◽  
Indentation Size ◽  
Elasticity Equation ◽  
Constitutive Response

AbstractAn alternative interpretation of nanoindentation experimental data and the associated phenomenon of indentation size effect (ISE) is proposed on the basis of a simple gradient elasticity equation, used to account for the development of elastic gradients generated by the geometry characterizing the indenter-specimen system. An application is considered for marble, i.e. a construction/restoration material.

scholarly journals Micro-cantilever bending tests for understanding size effect in gradient elasticity

2022 ◽  
pp. 110398
Author(s):  
Jae-Hoon Choi ◽  
Hojang Kim ◽  
Ji-Young Kim ◽  
Kwang-Hyeok Lim ◽  
Byung-Chai Lee ◽  
...  
Keyword(s):  
Size Effect ◽  
Gradient Elasticity ◽  
Bending Tests ◽  
Micro Cantilever ◽  
Cantilever Bending

Theoretical investigation on wave propagation in embedded DWBNNT conveying ferrofluid via stress and strain–inertia gradient elasticity

2016 ◽  
Vol 232 (9) ◽  
pp. 719-732
Author(s):  
A Ghorbanpour Arani ◽  
A Jalilvand ◽  
E Haghparast
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Boron Nitride ◽  
Size Effect ◽  
Gradient Elasticity ◽  
Boron Nitride Nanotubes ◽  
Stress And Strain ◽  
Flowing Fluid ◽  
Phase Velocities ◽  
Conveying Fluid

In the present study, wave propagation characteristics of double-walled boron nitride nanotubes (DWBNNTs) conveying ferrofluid is investigated. Magnetite (Fe3O4) nanofluid is selected as a conveying fluid which reacted in presence of magnetic field. Shear effects of surrounded medium are taken into account using Pasternak model. Stress and strain–inertia gradient elasticity theories are used due to their capability to interpret size effect. Based on Hamilton’s principle and employing Euler–Bernoulli, Timoshenko and Reddy beam models, wave equations of motion in double-walled boron nitride nanotubes are derived and solved by harmonic solution. Regarding the various types of flow regimes in fluid–structure interaction, the upstream and downstream phase velocities of double-walled boron nitride nanotubes conveying ferrofluid are calculated. A detailed parametric study is conducted to clarify the influences of the beam models, size effect theories, magnetic field, surrounding elastic medium and fluid velocity on the wave propagation of double-walled boron nitride nanotubes conveying ferrofluid. The results indicated that in lower wave numbers, the effect of flowing fluid and the difference between the upstream and downstream phase velocities were considerable. The results of this work can be used in design and manufacturing of nanopipes and nanovalves conveying fluid flow to avoid water hammer phenomenon.

A gradient elasticity approach to the indentation size effect at very small depths

2011 ◽  
Vol 20 (1-3) ◽  
pp. 35-40 ◽  
Author(s):  
George P. Mokios ◽  
Elias C. Aifantis
Keyword(s):  
Plastic Deformation ◽  
Size Effect ◽  
Indentation Size Effect ◽  
Gradient Elasticity ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
The Past ◽  
Small Depth ◽  
Alternative Approach ◽  
Macroscopic Plasticity

AbstractOver the past two decades, the indentation size effect (ISE) has been studied extensively by several authors. A common point among all these studies has been the premise that during the indentation process sufficient plastic deformation is developed so that a gradient plasticity framework can be employed in order to capture this effect. However, recent studies have shown that a more detailed analysis of the deformation mechanism during nanoindentation reveals often situations that vary significantly from commonly held beliefs, i.e., configurations where plastic deformation is almost absent, yet an ISE is still observed. This paper deals with such situations and proposes an alternative approach based on a gradient elasticity framework that is capable of capturing the ISE in nanoindentations of small depth, where traditional macroscopic plasticity approaches may not be adopted.

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