On the Effective Properties of Elastic Materials and Structures at the Micro- and Nano-Scale Considering Various Models of Surface Elasticity

2016 ◽  
pp. 29-41 ◽  
Author(s):  
Victor A. Eremeyev
Keyword(s):  
Effective Properties ◽  
Surface Elasticity ◽  
Elastic Materials ◽  
Nano Scale

On the Effective Properties of 3D Metamaterials

2016 ◽  
Author(s):  
Mohamed Abdelhamid ◽  
Aleksander Czekanski
Keyword(s):  
Elastic Modulus ◽  
Effective Properties ◽  
Lattice Structure ◽  
Surface Elasticity ◽  
Geometric Parameters ◽  
Stiffness Tensor ◽  
Loading Direction ◽  
Octet Truss ◽  
The Impact ◽  
Effective Mechanical Properties

A continuum-based model is developed for the octet-truss unit cell in order to describe the effective mechanical properties (elastic modulus) of the lattice structure. This model is to include different geometric parameters that impact the structural effects; these parameters are: lattice angle, loading direction, thickness to diameter ratio, diameter to length ratio, and ellipticity. All these geometric parameters are included in the stiffness matrix, and the impact of each parameter on the stiffness tensor is investigated. Specifically, the effect of the lattice angle on the elastic moduli is discussed, and the loading direction of the highest elastic modulus is investigated for different lattice angles. Furthermore, the Gurtin-Murdoch model of surface elasticity is used to include the size effect in the stiffness tensor, as well as anisotropy of this model is investigated.

Modeling of Piezoelectric Bimorph Nano-Actuators With Surface Effects

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Chunli Zhang ◽  
Chuanzeng Zhang ◽  
Weiqiu Chen
Keyword(s):  
Effective Properties ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Driving Voltage ◽  
Two Dimensional ◽  
Piezoelectric Bimorph ◽  
Simply Supported ◽  
Size Dependent ◽  
Spring Force ◽  
Plate Type

Two-dimensional (2D) equations of piezoelectric bimorph nano-actuators are presented which take account of the surface effect. The surface effect of the bimorph structure is treated as a surface layer with zero thickness. The influence on the plate's overall properties resulted from the surface elasticity and piezoelectricity is modeled by a spring force exerting on the boundary of the bulk core. Using the derived 2D equations, the anti-parallel piezoelectric bimorph nano-actuators of both cantilever and simply supported plate type are investigated theoretically. Numerical results show that the effective properties and the deflections of the antiparallel bimorph nano-actuators are size-dependent. The deflection at the resonant frequency achieves nearly 50 times as that under the static driving voltage.

scholarly journals Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Lin Fang ◽  
Quan Yuan ◽  
Bin Wu ◽  
Honglin Li ◽  
Mengyang Huang
Keyword(s):  
Young’S Modulus ◽  
Effective Properties ◽  
Young's Modulus ◽  
Axial Strain ◽  
Surface Elasticity ◽  
Volume Ratio ◽  
Field Equations ◽  
Surface Residual Stresses ◽  
Residual Strains ◽  
Displacement Approach

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.

Acoustics of permeo-elastic materials

2017 ◽  
Vol 828 ◽  
pp. 135-174 ◽  
Author(s):  
Rodolfo Venegas ◽  
Claude Boutin
Keyword(s):  
Mechanical Properties ◽  
Fluid Flow ◽  
Sound Propagation ◽  
Effective Properties ◽  
Fluid Film ◽  
Macroscopic Description ◽  
Elastic Materials ◽  
Acoustic Behaviour ◽  
Poroelastic Materials

In the dynamics of Biot poroelastic materials, the fluid flow is not affected by the deformation of the solid elastic frame. In contrast, in permeable materials whose solid stiff frames have flexible thin flat films attached, i.e. permeo-elastic materials, the fluid flow can be significantly modified by the presence of the films. As a consequence of the local fluid–film interaction, and in particular of the local resonances, the classical local physics is changed and departs from that leading to the Biot description. In this paper, the two-scale asymptotic homogenisation method is used to derive the macroscopic description of sound propagation in air-saturated permeo-elastic materials. This description is asymptotically analysed to determine the conditions for which the geometrical and mechanical properties of the films strongly affect the effective properties of the material. The developed theory is illustrated numerically and validated experimentally for a prototype material, evidencing the atypical acoustic behaviour.

scholarly journals Wave Scattering by Cracks at Macro- and Nano-Scale in Anisotropic Plane by Boundary Integral Equation Method

2016 ◽  
Vol 46 (4) ◽  
pp. 19-35 ◽  
Author(s):  
Petia Dineva ◽  
Tsviatko Rangelov
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Wave Scattering ◽  
Surface Elasticity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Boundary Integral Equation Method ◽  
Equation Method ◽  
Nano Scale ◽  
Subsequent Step

AbstractElastic wave scattering by cracks at macro- and nano-scale in anisotropic plane under conditions of plane strain is studied in this work. Furthermore, time-harmonic loads due to incident plane longitudinal P- or shear SV- wave are assumed to hold. In a subsequent step, the elastodynamic fundamental solution for general anisotropic continua derived in closed-form via the Radon transform is implemented in a numerical scheme based on the traction boundary integral equation method (BIEM). The surface elasticity effect in the case of nano-crack is taken into consideration via non-classical boundary condition along the crack surface proposed by Gurtin and Murdoch [1]. The numerical results obtained herein reveal substantial differences between anisotropic materials containing a macro- and a nano-crack in terms of their dynamic stress response, where the latter case demonstrates clearly the strong influence of the size-effects. Finally, these types of examples serve to illustrate the present approach and to show its potential for evaluating the stress concentration fields (SCF) inside cracked nanocomposites. The obtained results concern the reliability and safety of the advancing nanomaterials.

Elastic analysis for contact problems with surface effects under normal load

2016 ◽  
Vol 22 (1) ◽  
pp. 53-61 ◽  
Author(s):  
LY Wang
Keyword(s):  
Elasticity Theory ◽  
Normal Load ◽  
Deformation Gradient ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Contact Problems ◽  
Fundamental Solutions ◽  
Concentrated Force ◽  
Nano Scale ◽  
Variable Function

Based on surface elasticity theory, contact problems with surface effects at the nano-scale are considered in this paper. The complex variable function method is adopted to derive the fundamental solutions for the contact problem. As examples, the deformations induced by uniformly distributed normal pressures and concentrated force are analyzed in detail. The results reveal some interesting characteristics in contact mechanics, which are distinctly different from those in classical elasticity theory. At the nano-scale, the deformation gradient on the deformed surface varies smoothly across the loading boundary as a result of surface effects. In addition, for nano-indentation, the indent depth depends strongly on the surface stress.

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