Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media

2017 ◽  
Vol 84 (3) ◽  
Author(s):  
Ruize Hu ◽  
Caglar Oskay
Keyword(s):  
Heterogeneous Media ◽  
Spatial Scales ◽  
Gradient Elasticity ◽  
Layered Media ◽  
Wave Dispersion ◽  
Momentum Balance ◽  
Eighth Order ◽  
Homogenization Model ◽  
Dispersion And Attenuation ◽  
Periodic Layered Media

This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.

scholarly journals FORMULATION OF THE HEAT CONDUCTION EQUATION FOR HETEROGENEOUS MEDIA WITH MULTIPLE SPATIAL SCALES USING REITERATED HOMOGENIZATION

2016 ◽  
Vol 15 (1) ◽  
pp. 96
Author(s):  
E. Iglesias-Rodríguez ◽  
M. E. Cruz ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
R. Rodríguez-Ramos ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Small Parameter ◽  
Heat Conduction Equation ◽  
Heterogeneous Media ◽  
Spatial Scales ◽  
Conduction Equation ◽  
Small Scale ◽  
Multiple Spatial Scales ◽  
Effective Coefficients ◽  
Reiterated Homogenization

Heterogeneous media with multiple spatial scales are finding increased importance in engineering. An example might be a large scale, otherwise homogeneous medium filled with dispersed small-scale particles that form aggregate structures at an intermediate scale. The objective in this paper is to formulate the strong-form Fourier heat conduction equation for such media using the method of reiterated homogenization. The phases are assumed to have a perfect thermal contact at the interface. The ratio of two successive length scales of the medium is a constant small parameter ε. The method is an up-scaling procedure that writes the temperature field as an asymptotic multiple-scale expansion in powers of the small parameter ε . The technique leads to two pairs of local and homogenized equations, linked by effective coefficients. In this manner the medium behavior at the smallest scales is seen to affect the macroscale behavior, which is the main interest in engineering. To facilitate the physical understanding of the formulation, an analytical solution is obtained for the heat conduction equation in a functionally graded material (FGM). The approach presented here may serve as a basis for future efforts to numerically compute effective properties of heterogeneous media with multiple spatial scales.

scholarly journals Wave Dispersion and Attenuation on Human Femur Tissue

Sensors ◽  
2014 ◽  
Vol 14 (8) ◽  
pp. 15067-15083 ◽  
Author(s):  
Maria Strantza ◽  
Olivia Louis ◽  
Demosthenes Polyzos ◽  
Frans Boulpaep ◽  
Danny van Hemelrijck ◽  
...  
Keyword(s):  
Wave Dispersion ◽  
Human Femur ◽  
Dispersion And Attenuation

Periodic Layered Media

2019 ◽  
pp. 37-62
Author(s):  
Subhendu K. Datta ◽  
Arvind H. Shah
Keyword(s):  
Layered Media ◽  
Periodic Layered Media
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