An Axisymmetric Boundary Integral Model for Assessing Elastic Cell Properties in the Micropipette Aspiration Contact Problem

2002 ◽  
Vol 124 (5) ◽  
pp. 586-595 ◽  
Author(s):  
Mansoor A. Haider ◽  
Farshid Guilak

The micropipette aspiration technique has been used extensively in recent years to measure the mechanical properties of living cells. In the present study, a boundary integral formulation with quadratic elements is used to predict the elastic equilibrium response in the micropipette aspiration contact problem for a three-dimensional incompressible spherical continuum cell model (Young’s modulus E). In contrast to the halfspace model [19], the spherical cell model accounts for nonlinearities in the cell response which result from a consideration of geometric factors including the finite cell dimension (radius R), curvature of the cell boundary, evolution of the cell-micropipette contact region and curvature of the edges of the micropipette (inner radius a, edge curvature radius ε). The efficiency of the boundary element method facilitates the quantification of cell response as a function of the scaled pressure p/E, for the range of parameters a/R=0.4-0.7,ε/a=0.02-0.08, in terms of two measures that can be quantified using video microscopy. These are the aspiration length, which measures projection of the cell into the micropipette, and a characteristic strain, which measures stretching along the symmetry axis. For both measures of cell response, the resistance to aspiration is found to decrease with increasing values of the aspect ratio a/R and curvature parameter ε/a, and the nonlinearities in the cell response are most pronounced in the earlier portion of the aspiration test. The aspiration length is found to exhibit less sensitivity to the aspect ratio a/R than to the curvature parameter ε/a, whereas the characteristic strain, which provides a more realistic measure of overall cell stiffness, exhibits sensitivity to the aspect ratio a/R. The resistance to aspiration in the spherical cell model is initially less than that of the half space model but eventually exceeds the halfspace prediction and the deviation between the two models increases as the parameter ε/a decreases. Adjustment factors for the Young’s modulus E, as predicted by the halfspace model, are presented and the deviation from the spherical cell model is found to be as large as 35%, when measured locally on the response curve. In practice, the deviation will be less than the maximum figure but its precise value will depend on the number of data points available in the experiment and the specific curve-fitting procedure. The spherical cell model allows for efficient and more realistic simulations of the micropipette aspiration contact problem and quantifies two observable measures of cell response that, using video microscopy, can facilitate the determination of Young’s modulus for various cell populations while, simultaneously, providing a means of evaluating the validity of continuum cell models. Furthermore, this numerical model may be readily extended to account for more complex geometries, inhomogeneities in cellular properties, or more complex constitutive descriptions of the cell.

2021 ◽  
Author(s):  
Hui Cao ◽  
Wenke Chen ◽  
Zhiyuan Rui ◽  
Changfeng Yan

Abstract Metal nanomaterials exhibit excellent mechanical properties compared with corresponding bulk materials and have potential applications in various areas. Despite a number of studies of the size effect on Cu nanowires mechanical properties with square cross-sectional, investigations of them in rectangular cross-sectional with various sizes at constant volume are rare, and lack of multifactor coupling effect on mechanical properties and quantitative investigation. In this work, the dependence of mechanical properties and deformation mechanisms of Cu nanowires/nanoplates under tension on cross-sessional area, aspect ratio of cross-sectional coupled with orientation were investigated using molecular dynamics simulations and the semi-empirical expressions related to mechanical properties were proposed. The simulation results show that the Young’s modulus and the yield stress sharply increase with the aspect ratio except for the <110>{110}{001} Cu nanowires/nanoplates at the same cross-sectional area. And the Young’s modulus increases while the yield stress decreases with the cross-sectional area of Cu nanowires. However, both of them increase with the cross-sectional area of Cu nanoplates. Besides, the Young’s modulus increases with the cross-sectional area at all the orientations. The yield stress shows a mildly downward trend except for the <111> Cu nanowires with increased cross-sectional area. For the Cu nanowires with a small cross-sectional area, the surface force increases with the aspect ratio. In contrast, it decreases with the aspect ratio increase at a large cross-sectional area. At the cross-sectional area of 13.068 nm2, the surface force decreases with the aspect ratio of the <110> Cu nanowires while it increases at other orientations. The surface force is a linearly decreasing function of the cross-sectional area at different orientations. Quantitative studies show that Young’s modulus and yield stress to the aspect ratio of the Cu nanowires satisfy exponent relationship. In addition, the main deformation mechanism of Cu nanowires is the nucleation and propagation of partial dislocations while it is the twinning-dominated reorientation for Cu nanoplates.


e-Polymers ◽  
2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Vadoud Molajavadi ◽  
Hamid Garmabi

AbstractThe Halpin-Tsai equations were used for the composites with low level content of reinforcements, which contain lamellar shape, high modulus and high aspect ratio. These characteristics of reinforcements were taken into consideration to simplify the Halpin-Tsai equations. The effect of different parameters on the longitudinal Young’s modulus of well aligned polymer/clay nanocomposites was investigated for both exfoliated and intercalated microstructures. It was shown that the applied simplification had negligible effect on the prediction of the Halpin-Tsai model. For the intercalated structures with a high number of platelets per stack (n), increase in the gallery spacing did not influence the predicted modulus values. In an intercalated structure, the surface area of a stack, as the interface of fillermatrix, is n times lower than that of the exfoliated state. By considering the effect of the degree of exfoliation in the proposed model, a new equation was developed to predict the modulus enhancement in the nanocomposites filled with Montmorillonite (MMT). The theoretical predictions were supported by the experimental results.


2013 ◽  
Vol 290 ◽  
pp. 15-20
Author(s):  
Dong Mei Luo ◽  
Hong Yang ◽  
Qiu Yan Chen ◽  
Ying Long Zhou

In this paper, two kinds of micro-mechanical models are utilized to predict the effective Young's modulus for hybrid composites including fiber-like, spherical and needle inclusions in an isotropic matrix. The two models of Multi-Phase Mori-Tanaka Model (MP model) and Multi-Step Mori-Tanaka Model (MS model) are proposed by the authors in a series of interrelated research. The results show that the shape and the Young’s modulus of inclusion, aspect ratio of fiber-like inclusion are the controlling factors to influence the Young's modulus, and MP model is more rational to predict the effective Young’s modulus of hybrid composites reinforced with multi-shape inclusions.


2018 ◽  
Vol 226 ◽  
pp. 03027 ◽  
Author(s):  
Vladimir B. Zelentsov ◽  
Evgeniy V. Sadyrin ◽  
Aleksandr G. Sukiyazov ◽  
Nataliya Yu. Shubchinskaya

On the base of modernized NanoTest 600 Platform 3 indentation method is proposed to determine elastic parameters – Poisson’s ratio and Young’s modulus – of a material while loading in an elastic region. The experiment is based on procedure: lateral surface of indenter tip with the shape of parabolic cylinder penetrates into the specimen. NanoTest 600 was equipped by additional optics, backlight and device for spatial orientation of the specimen. This modernization allows to control the process of the indenter penetration both along its length and from the edges, so that one can observe and measure the width of the contact area and control the depth of the indentation area in a sample material. Mathematical modeling of the indentation process was conducted within the framework of plane theory of elasticity. This required solution of the contact problem on indentation of a rigid indenter with a parabolic shape into an elastic strip coupled with a non-deformable substrate. The fulfilment of condition of zeroing the contact stresses at the edges of the indenter with a known width of the contact area allows to determine the Poisson’s ratio, and condition of static equilibrium of the contact problem helps to find Young’s modulus of a strip material.


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