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Research Papers

Determination of the Reduced Creep Function of Viscoelastic Compliant Materials Using Pipette Aspiration Method

[+] Author and Article Information
Yan-Ping Cao

AML, Institute of Biomechanics and Medical
Engineering,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: caoyanping@tsinghua.edu.cn

Guo-Yang Li, Man-Gong Zhang, Xi-Qiao Feng

AML, Institute of Biomechanics and Medical
Engineering,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Manuscript received February 14, 2014; final manuscript received March 7, 2014; accepted manuscript posted March 13, 2014; published online April 1, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(7), 071006 (Apr 01, 2014) (7 pages) Paper No: JAM-14-1068; doi: 10.1115/1.4027159 History: Received February 14, 2014; Revised March 07, 2014; Accepted March 13, 2014

Determining the mechanical properties of soft matter across different length scales is of great importance in understanding the deformation behavior of compliant materials under various stimuli. A pipette aspiration test is a promising tool for such a purpose. A key challenge in the use of this method is to develop explicit expressions of the relationship between experimental responses and material properties particularly when the tested sample has irregular geometry. A simple scaling relation between the reduced creep function and the aspiration length is revealed in this paper by performing a theoretical analysis on the aspiration creep tests of viscoelastic soft solids with arbitrary surface profile. Numerical experiments have been performed on the tested materials with different geometries to validate the theoretical solution. In order to incorporate the effects of the rise time of the creep pressure, an analytical solution is further derived based on the generalized Maxwell model, which relates the parameters in reduced creep function to the aspiration length. Its usefulness is demonstrated through a numerical example and the analysis of the experimental data from literature. The analytical solutions reported here proved to be independent of the geometric parameters of the system under described conditions. Therefore, they may not only provide insight into the deformation behavior of soft materials in aspiration creep tests but also facilitate the use of this testing method to deduce the intrinsic creep/relaxation properties of viscoelastic compliant materials.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematic plot of the creep function; (b) illustration of the aspiration test, negative pressure is imposed to the surface of a tested material through a cylindrical tube with the inner radius R0 and outer radius Re

Grahic Jump Location
Fig. 2

Finite element models used to examine the effects of the variation in the contact area on the identified reduced creep function using Eq. (10). (a) and (b) represent the computational model and the deformation of the tested material for case I; (c) and (d) represent the computational model and the deformation of the tested material for case II; (e) and (f) are the computational model and the deformed configuration of the tested material for case III.

Grahic Jump Location
Fig. 3

A comparison of the identified reduced creep functions using Eq. (10) with the actual solution input in the finite element simulations:  J˜ (t) = 1 + (1 − exp (− t /10)) for different cases

Grahic Jump Location
Fig. 4

Numerical experiments used to illustrate the usefulness of the analytical solution given by Eq. (10). (a), (c), and (e) represent the finite element models for examples A, B, and C, respectively. A1 and A2 in (a) and (c) are fixed to eliminate the rigid-body motion of the tested materials, other points can be selected which has on effects on the identified results. (b), (d), and (f) are the deformed configurations. The displacements at Bi(i=1,2,3) are recorded as the aspiration lengths.

Grahic Jump Location
Fig. 5

Pipette aspiration test of soft layer bonded to rigid substrate. (a) Finite element model; (b) deformed configuration of the tested material, the displacement at the center point of the upper surface is recorded as the aspiration length.

Grahic Jump Location
Fig. 6

A comparison of the identified reduced creep functions using Eq. (10) and the aspiration lengths given by finite element simulations with the actual solution. The actual solution is taken here as J˜(t) = 1 + 0.1(1 − exp (−t)) + 0.9(1 − exp (−t/18)). Here, the actual solution represents the reduced creep function input in the finite element simulations.

Grahic Jump Location
Fig. 7

(a) Illustration of the loading procedure in an aspiration creep test, where tr is the time at which the negative pressure reach the maximum value and then is kept as constant; (b) schematic plot of the generalized Maxwell model, where Ke,K1,K2,…,Kj are spring constants and η1,η2,…,ηj are viscosity coefficients; (c) normalized aspiration lengths given by finite element simulations and those predicted using Eqs. (10) and (13)

Grahic Jump Location
Fig. 8

Experimental data used to illustrate the difference between the result identified using Eq. (10) and that given by Eq. (13). (a) Variation of the aspiration length with time given by the experiments of Ref. [20]; (b) normalized aspiration length l˜(t) at the creep stage.

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