Tractions, Balances, and Boundary Conditions for Nonsimple Materials with Application to Liquid Flow at Small-Length Scales

2006 ◽  
Vol 182 (3) ◽  
pp. 513-554 ◽  
Author(s):  
Eliot Fried ◽  
Morton E. Gurtin
Author(s):  
G. Rossini ◽  
A. Caimi ◽  
A. Redaelli ◽  
E. Votta

AbstractA Finite Element workflow for the multiscale analysis of the aortic valve biomechanics was developed and applied to three physiological anatomies with the aim of describing the aortic valve interstitial cells biomechanical milieu in physiological conditions, capturing the effect of subject-specific and leaflet-specific anatomical features from the organ down to the cell scale. A mixed approach was used to transfer organ-scale information down to the cell-scale. Displacement data from the organ model were used to impose kinematic boundary conditions to the tissue model, while stress data from the latter were used to impose loading boundary conditions to the cell level. Peak of radial leaflet strains was correlated with leaflet extent variability at the organ scale, while circumferential leaflet strains varied over a narrow range of values regardless of leaflet extent. The dependency of leaflet biomechanics on the leaflet-specific anatomy observed at the organ length-scale is reflected, and to some extent emphasized, into the results obtained at the lower length-scales. At the tissue length-scale, the peak diastolic circumferential and radial stresses computed in the fibrosa correlated with the leaflet surface area. At the cell length-scale, the difference between the strains in two main directions, and between the respective relationships with the specific leaflet anatomy, was even more evident; cell strains in the radial direction varied over a relatively wide range ($$0.36-0.87$$ 0.36 - 0.87 ) with a strong correlation with the organ length-scale radial strain ($$R^{2}= 0.95$$ R 2 = 0.95 ); conversely, circumferential cell strains spanned a very narrow range ($$0.75-0.88$$ 0.75 - 0.88 ) showing no correlation with the circumferential strain at the organ level ($$R^{2}= 0.02$$ R 2 = 0.02 ). Within the proposed simulation framework, being able to account for the actual anatomical features of the aortic valve leaflets allowed to gain insight into their effect on the structural mechanics of the leaflets at all length-scales, down to the cell scale.


1995 ◽  
Vol 99 (3-4) ◽  
pp. 509-511
Author(s):  
Roser Valent� ◽  
Claudius Gros

2018 ◽  
Vol 97 (13) ◽  
Author(s):  
J. Simmendinger ◽  
S. Ruoss ◽  
C. Stahl ◽  
M. Weigand ◽  
J. Gräfe ◽  
...  

2007 ◽  
Vol 74 (6) ◽  
pp. 1087-1094 ◽  
Author(s):  
Renfu Li ◽  
George A. Kardomateas

In this paper, the vibrational behavior of the multiwalled carbon nanotubes (MWCNTs) embedded in elastic media is investigated by a nonlocal shell model. The nonlocal shell model is formulated by considering the small length scales effects, the interaction of van der Waals forces between two adjacent tubes and the reaction from the surrounding media, and a set of governing equations of motion for the MWCNTs are accordingly derived. In contrast to the beam models in the literature, which would only predict the resonant frequencies of bending vibrational modes by taking the MWCNT as a whole beam, the current shell model can find the resonant frequencies of three modes being classified as radial, axial, and circumferential for each nanotube of a MWCNT. Big influences from the small length scales and the van der Waals’ forces are observed. Among these, noteworthy is the reduction in the radial frequencies due to the van der Waals’ force interaction between two adjacent nanotubes. The numerical results also show that when the spring constant k0 of the surrounding elastic medium reaches a certain value, the lowest resonant frequency of the double walled carbon nanotube drops dramatically.


Author(s):  
Alvaro J. Ramirez ◽  
Amador M. Guzman ◽  
Rodrigo A. Escobar

The Lattice-Boltzmann Method (LBM) has been used for investigating flow behavior and characteristics in mini, micro and nano channels with the objective of describing the transition among different length scales. In particular, we have used the LBM to describe the air bearing lubrication problem at very small scales. For doing this, first we simulate and characterize the Poiseuille flow through different length scale and compare the LBM numerical results to existing experimental and numerical results. We put special attention on the application of the slip boundary condition on the channel wall for very small length scales. Our numerical results for the Poiseuille flow show an acceptable agreement with the Fukui & Kaneko numerical solution for continuous and slip-velocity regimes. For both, the rarified flow regime and the free molecular flow regime our solutions do not show an acceptable agreement with the Fukui & Kaneko Model. Then, we focus on the Couette flow characterization at very small length scales. The pressure distribution on both walls for different Knudsen numbers is obtained and compared to existing numerical results. Last, we concentrate in the air bearing problem. We have looked at the best simulation parameters for successfully describing this device flow dynamics, and particularly, for determining the pressure distribution and the net force with a good accuracy.


2005 ◽  
Vol 15 (15) ◽  
pp. 645-646
Author(s):  
Martha A. Gallivan ◽  
Mustafa Khammash
Keyword(s):  

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