scholarly journals An evaluation of higher-order plasticity theories for predicting size effects and localisation

2006 ◽  
Vol 43 (7-8) ◽  
pp. 1857-1877 ◽  
Author(s):  
R.A.B. Engelen ◽  
N.A. Fleck ◽  
R.H.J. Peerlings ◽  
M.G.D. Geers
Keyword(s):  
Size Effects ◽  
Higher Order

scholarly journals Symmetric Plasmonic Slot Waveguides with a Nonlinear Dielectric Core: Bifurcations, Size Effects, and Higher Order Modes

Plasmonics ◽  
2014 ◽  
Vol 10 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Wiktor Walasik ◽  
Alejandro Rodriguez ◽  
Gilles Renversez
Keyword(s):  
Size Effects ◽  
Higher Order ◽  
Nonlinear Dielectric ◽  
Higher Order Modes ◽  
Slot Waveguides

Higher-order ion-size effects in pseudopotential theory

1982 ◽  
Vol 15 (12) ◽  
pp. L361-L366 ◽  
Author(s):  
L Emery ◽  
C H Leung ◽  
K S Song
Keyword(s):  
Size Effects ◽  
Higher Order ◽  
Pseudopotential Theory ◽  
Ion Size

scholarly journals A Method to Determine Material Length Scale Parameters in Elastic Strain Gradient Theory

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Jingru Song ◽  
Yueguang Wei
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Elastic Strain ◽  
Higher Order ◽  
Experimental Results ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Face Centered Cubic ◽  
Scale Parameters

Abstract With specimen size decrease for advanced structural materials, the measured mechanics behaviors display the strong size effects. In order to characterize the size effects, several higher-order theories have been presented in the past several decades, such as the strain gradient theories and the micro-polar theories, etc. However, in each higher-order theory, there are several length scale parameters included, which are usually taken as the material parameters and are determined by using the corresponding theoretical predictions to fit experimental results. Since such kind of experimental approaches needs high techniques, it is very difficult to be performed; therefore, the obtained experimental results are very few until now; in addition, the physical meanings of the parameters still need to be investigated. In the present research, an equivalent linkage method is used to simply determine the elastic length parameters appeared in the elastic strain gradient theory for a series of typical metal materials. We use both the elastic strain gradient theory and the higher-order Cauchy-Born rule to model the materials mechanics behaviors by means of a spherical expanding model and then make a linkage for both kinds of results according to the equivalence of strain energy densities. The values of the materials length parameters are obtained for a series of typical metal systems, such as the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals.

Size Effects of Hair-Sized Structures – Torsion

2004 ◽  
Vol 261-263 ◽  
pp. 11-22 ◽  
Author(s):  
Pin Tong ◽  
Fan Yang ◽  
David C.C. Lam ◽  
Jun Wang
Keyword(s):  
Size Effects ◽  
Torsional Rigidity ◽  
Higher Order ◽  
Torsional Stiffness ◽  
Length Scale ◽  
Warping Function ◽  
Thin Wall ◽  
Order Partial Differential Equation ◽  
Strain Gradients ◽  
Scale Parameters

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include the strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scaled structure [1]. This paper focus on the structural size effects on torsion of cylinders. The torsional stiffness of cylinders can be higher than conventional expectation when the cylinder size is in the nanometer - or micron-scale. Following the Saint-Venant theory of torsion, we established the equation of torsion in terms of the warping function on the basis of the nano-mechanical theory of elasticity. The torsional equations contain two higher order material length scale parameters and two conventional Lame constants. The equilibrium equation is a fourth order partial differential equation which can be reduced to two second order equations. Two formulations in terms of pseudo warping function and stress function are presented. Closed-form solutions for circular and thin wall section and series solutions for rectangular microbars have been obtained. The total torque depends only on the stresses conjugated to the strain and is only implicitly dependent on the higher order stress metrics. The solution reveals that the torsional rigidity is dependent on the higher order length scale parameters and strain gradients and increases asymptotically upward when the cylinder size is reduced to the size of the higher order length scale material parameters. The increase is most marked for thin walled cylinders, stiffening to more then 10 times the conventional value when the cylinder size is near that of the higher order length scaled parameters.

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