Regional stretch method to measure the elastic and hyperelastic properties of soft materials

JunYuan Sheng; HaoYuan Guo; YanPing Cao; XiQiao Feng

doi:10.1007/s11433-017-9118-0

SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 61, Issue 2: 024611(2018) https://doi.org/10.1007/s11433-017-9118-0

Regional stretch method to measure the elastic and hyperelastic properties of soft materials

JunYuan Sheng, HaoYuan Guo, YanPing Cao^*, XiQiao Feng^*

More info

ReceivedAug 31, 2017
AcceptedOct 11, 2017
PublishedDec 18, 2017

PACS numbers

Previous Table of Contents Next

Rating

Abstract

Characterizing the mechanical properties of soft materials and biological tissues is of great significance for understanding their deformation behaviors. In this paper, a regional stretching method is proposed to measure the elastic and hyperelastic properties of a soft material with an adhesive surface or with the aid of glue. Theoretical and dimensional analyses are performed to investigate the regional stretch problem for soft materials that obey the neo-Hookean model, the Mooney-Rivlin model, or the Arruda-Boyce model. Finite element simulations are made to determine the expressions of the dimensionless functions that correlate the stretch response with the constitutive parameters. Thereby, an inverse approach is established to determine the elastic and hyperelastic properties of the tested materials. The regional stretch method is also compared to the indentation technique. Finally, experiments are performed to demonstrate the effectiveness of the proposed method.

Funded by

National Natural Science Foundation of China(11432008)

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11432008, 11572179, and 11172155).

References

[1] Johnson C. L., McGarry M. D. J., Gharibans A. A., Weaver J. B., Paulsen K. D., Wang H., Olivero W. C., Sutton B. P., Georgiadis J. G.. Neuroimage, 2013, 79: 145 CrossRef PubMed Google Scholar

[2] Chang J. M., Moon W. K., Cho N., Yi A., Koo H. R., Han W., Noh D. Y., Moon H. G., Kim S. J.. Breast Cancer Res. Treat., 2011, 129: 89 CrossRef PubMed Google Scholar

[3] Karimi A., Navidbakhsh M., Shojaei A., Faghihi S.. Mater. Sci. Eng.-C, 2013, 33: 2550 CrossRef PubMed Google Scholar

[4] Murphy M. C., Huston Iii J., Jack Jr C. R., Glaser K. J., Manduca A., Felmlee J. P., Ehman R. L.. J. Magn. Reson. Imag., 2011, 34: 494 CrossRef PubMed Google Scholar

[5] Smith S. B., Finzi L., Bustamante C.. Science, 1992, 258: 1122 CrossRef ADS Google Scholar

[6] Ziemann F., Radler J., Sackmann E.. Biophys. J., 1994, 66: 2210 CrossRef ADS Google Scholar

[7] Swaminathan V., Mythreye K., O’Brien E. T., Berchuck A., Blobe G. C., Superfine R.. Cancer Res., 2011, 71: 5075 CrossRef PubMed Google Scholar

[8] Chowdhury F., Na S., Li D., Poh Y. C., Tanaka T. S., Wang F., Wang N.. Nat. Mater., 2010, 9: 82 CrossRef PubMed ADS Google Scholar

[9] Hochmuth R. M.. J. Biomech., 2000, 33: 15 CrossRef Google Scholar

[10] Roan E., Vemaganti K.. J. Biomech. Eng., 2006, 129: 450 CrossRef PubMed Google Scholar

[11] Guilak F., Jones W. R., Ting-Beall H. P., Lee G. M.. Osteoarthr. Cartilage, 1999, 7: 59 CrossRef PubMed Google Scholar

[12] Evans E. A.. Biophys. J., 1983, 43: 27 CrossRef ADS Google Scholar

[13] Zhang M. G., Cao Y. P., Li G. Y., Feng X. Q.. J. Mech. Phys. Solids, 2014, 68: 179 CrossRef ADS Google Scholar

[14] Boudou T., Ohayon J., Arntz Y., Finet G., Picart C., Tracqui P.. J. Biomech., 2006, 39: 1677 CrossRef PubMed Google Scholar

[15] Zhao R., Sider K. L., Simmons C. A.. Acta Biomater., 2011, 7: 1220 CrossRef PubMed Google Scholar

[16] Cheng Y. T., Cheng C. M.. Mater. Sci. Eng. R.-Rep., 2004, 44: 91 CrossRef Google Scholar

[17] Oommen B., Van Vliet K. J.. Thin Solid Films, 2006, 513: 235 CrossRef ADS Google Scholar

[18] Hu Y., Zhao X., Vlassak J. J., Suo Z.. Appl. Phys. Lett., 2010, 96: 121904 CrossRef ADS Google Scholar

[19] Hu Y., Chen X., Whitesides G. M., Vlassak J. J., Suo Z.. J. Mater. Res., 2011, 26: 785 CrossRef ADS Google Scholar

[20] J. Harding, and I. Sneddon, The Elastic Stresses Produced by the Indentation of the Plane Surface of a Semi-Infinite Elastic solid by a Rigid Punch (Cambridge University Press, Cambridge, 1945). Google Scholar

[21] I. N. Sneddon, Boussinesq’s Problem for a Flat-Ended Cylinder (Cambridge University Press, Cambridge, 1946). Google Scholar

[22] G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics (Cambridge University Press, Cambridge, 1996). Google Scholar

[23] J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations (Courier Corporation, North Chelmsford, 2014). Google Scholar

[24] Dieci L., Papini A.. Numer. Algorithms, 2001, 28: 137 CrossRef ADS Google Scholar

[25] Cao Y., Lu J.. Acta Mater., 2004, 52: 1143 CrossRef Google Scholar

[26] X. Q. Feng, Y. P. Cao, and B. Li, Surface Wrinkling Mechanics of Soft Materials (Science Press, Beijing, 2017). Google Scholar

Click to view Download high-quality image

Figure 1
(Color online) Schematic of the regional stretch test of a soft material.
Click to view Download high-quality image

Figure 2
(Color online) (a) The finite element model of the regional stretch test and (b) the magnified view of the local stretch region.
Click to view Download high-quality image

Figure 3
(Color online) Relationships between dimensionless functions Π and the hyperelastic parameters $α$ and $λ_{m}$ under different values of $h / a$ . (a) Mooney-Rivlin model; (b) Arruda-Boyce model.
Click to view Download high-quality image

Figure 4
(Color online) Comparison between the hyperelastic solutions and the Sneddon’s solution. (a) Mooney-Rivlin model; (b) Arruda-Boyce model.
Click to view Download high-quality image

Figure 5
(Color online) The relationship between the reciprocals of condition number $1 / Ψ$ and (a) $α$ for the Mooney-Rivlin model; and (b) $λ_{m}$ for the Arruda-Boyce model.
Click to view Download high-quality image

Figure 6
(Color online) ElectroForce^? 3100 test instrument used in our experiments.
Click to view Download high-quality image

Figure 7
(Color online) Force-displacement curves obtained from the regional stretch tests.
Click to view Download high-quality image

Figure 8
(Color online) Load-depth curves obtained from the indentation tests.
Click to view Download high-quality image

Figure 9
(Color online) Force-displacement curves obtained by using indenters of different cross-sectional shapes.

Table 1 Comparison between the identified parameters and the values taken in FEM simulations

Neo-Hookean
	Actual $μ_{0}$ (MPa)	Identified $μ_{0}$ (MPa)
	2	1.97

Mooney-Rivlin
$\| Ψ_{MR} \|$	Actual $μ_{0}$ (MPa)	Identified $μ_{0}$ (MPa)	Actual α	Identified α
10.95	2	2.011	0.5	0.527
5.76	2	1.998	0.7	0.692
4.86	2	1.985	0.9	0.872

Arruda-Boyce
$\| Ψ_{AB} \|$	Actual $μ_{0}$ (MPa)	Identified $μ_{0}$ (MPa)	Actual $λ_{m}$	Identified $λ_{m}$
5.15	2	2.052	1.1	1.263
7.34	2	2.044	1.5	1.810
11.87	2	2.041	2	2.741

Table 2 Initial shear modulus determined from the regional stretch tests. Here, the Sneddon’s solution in eq. (4) and the neo-Hookean solution in eq. (5) are used to analyze the data

Shear modulus	Test-1	Test-2	Test-3	Test-4	Test-5	Test-6	Test-7	Test-8	Test-9
$μ_{0}$ in eq. (4) (kPa)	2.95	2.68	2.87	2.63	2.71	2.54	2.29	2.88	2.73
$μ_{0}$ in eq. (5) (kPa)	2.94	2.63	2.82	2.59	2.66	2.53	2.26	2.82	2.68

Table 3 Initial shear modulus determined from the indentation test. The Hertzian solution in eq. (15) and the neo-Hookean solution in eq. (16) are used to fit the data

Shear modulus	Test-1	Test-2	Test-3	Test-4	Test-5
$μ_{0}$ in eq. (15) (kPa)	2.29	2.92	2.91	3.18	2.90
$μ_{0}$ in eq. (16) (kPa)	2.50	3.19	3.18	3.49	3.16

Table 4 Comparison of the F-h curves obtained by using indenters of different shapes

Cross-sectional shape	Slope of F-h curves (N/m)
Circle	9009.91
Square	9188.61
Regular triangle	9446.47
Rectangle-I	9430.63
Rectangle-II	10022.95

1

Citations
0

Altmetric
Article metrics

Email
Export


46.25.-y	Static elasticity
46.80.+j	Measurement methods and techniques in continuum mechanics of solids (for mechanical instruments, equipment, and techniques, see 07.10.-h in instruments)
68.35.Np	Adhesion (for polymer adhesion, see 82.35.Gh: for cell adhesion, see 87.17.Rt in biological physics

Regional stretch method to measure the elastic and hyperelastic properties of soft materials

Abstract

Funded by

Acknowledgment

References

1

0

Interesting search

Top 5Related Articles