Proposing a new nonlinear hyperviscoelastic constitutive model to describe uniaxial compression behavior and dependence of stress-relaxation response on strain levels for isotropic tissue-equivalent material

Document Type : Article

Authors

1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, P.O. Box 8415683111, Iran

2 Small Medical Devices, Bio-MEMS & LoC Lab, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Postal Code 14399-55961, Iran.

3 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, P.O. Box 8415683111, Iran.

Abstract

Predicting the nonlinear response of biological tissues is challenging issue, due to strain rate- (short term) and time-dependent (long-term) nature of its response. While many of the tissue properties have already been extensively examined, some are left unnoticed, such as dependence of the stress-relaxation behavior on the strain levels. In this paper, a hyperviscoelastic constitutive model is derived within the integral form presented by Pipkin and Rogers model to remove this limitation. In the suggested model, the hyperelastic and short-term viscous parts are represented by the suitable strain energy function. The long-term viscous function includes the deformation history, which is expressed through a tensorial-relaxation function and has not been considered elsewhere. The constitutive model involves a number of material parameters. The values of those are identified from experimental data for Adiprene-L100 as a tissue-equivalent material. Parameters appearing in constitutive law are estimated by fitting the model with the experimental data. It is assumed that the tissue phantom is slightly compressible, isotropic and homogenous. The obtained results indicate that the presented model can describe the nonlinearity, strain rate- (short-term) and time-dependent (long-term) effects of materials. The validation of the model is investigated and shows very good agreement with the experimental data.

Keywords

Main Subjects


References:
1. Trawinski, Z., Wojcik, J., Nowicki, A., Olszewski, R., Balcerzak, A., Frankowska, E., Zegadlo, A., and Rydzynski, P. "Strain examinations of the left ventricle phantom by ultrasound and multislices computed tomography imaging", Biocyber. Biomed. Eng., 35, pp. 255-263 (2015).
2. Bukala, J., Kwiatkowski, P., and Malachowski, J. "Numerical analysis of stent expansion process in coronary artery stenosis with the use of non-compliant ballon", Biocyber. Biomed. Eng., 36, pp. 145-156 (2016).
3. Eshghi, S.H., Rajabi, H., Darvizeh, A., Nooraeefar, V., Shafiei, A., Mirzababaie Mostofi, T., and Monsef, M. "A simple method for geometric modeling of biological structures using image processing technique", Sci. Iran., 23(5), pp. 2194-2202 (2016).
4. Przytulska, M., Gierblinski, I., Kuliusz, J., and Skoczylas, K. "Quantitative examination of liver tissue ultrasound elastograms", Biocyber. Biomed. Eng., 31(4), pp. 75-85 (2011).
5. Zanetti, M.E., Terzini, M., Mossa, L., Bignardi, C., Costa, P., Audenino, A.L., and Vezzoni, A. "A structural numerical model for the optimization of double pelvic osteotomy in the early treatment of canine hip dysplasia", Vet. Comp. Orthop. Traumatol., 4, pp. 1-9 (2017).
6. Kemper, A.R., Santago, A.C., Stitzel, J.D., Sparks, J.L., and Duma, S.M. "Effect of strain on the material properties of human liver parenchyma in unconfined compression", ASME J. Biomech. Eng., 135, pp. 1-8 (2013).
7. Rashid, B., Destrade, M., and Gilchrist, M.D. "Mechanical characterization of brain tissue in simple shear at dynamic strain rates", J. Mech. Behav. Biomed. Mater., 28, pp. 71-85 (2013).
8. Abbasi, A.A., Ahmadian, M.T., Alizadeh, A., and Tarighi, S. "Application of hyperelastic models in mechanical properties prediction of mouse oocyte and embryo cells at large deformations", Sci. Iran., 25(2), pp. 700-710 (2018).
9. Quapp, K.M. and Weiss, J.A. "Material characterization of human medial collateral ligament", ASME J. Biomech. Eng., 120, pp. 757-763 (1998).
10. Wang, X., Schoen, J.A., and Rentschler, M.E. "Aquantitative comparison of soft tissue compressive viscoelastic model accuracy", J. Mech. Behav. Biomed. Mater., 20, pp. 126-136 (2013).
11. Sharifi Sedeh, R., Ahmadian, M.T., and Janabi-Sharifi, F. "Modeling, simulation, and optimal initiation planning for needle insertion into the liver", ASME J. Biomech. Eng., 132, pp. 1-11 (2010).
12. Matin Ghahfarokhi, Z., Moghimi Zand, M., and Salmani Tehrani, M. "Analytical solution and simulation of the liver tissue behavior under uniaxial compression test", Modares Mechanical Engineering, 16(9), pp. 47-56 (1395) (in Persion).
13. Matin Ghahfarokhi, Z., Salmani Tehrani, M., Moghimi Zand, M., and Mahzoon, M. "A computational study on the effect of different design parameters on the accuracy of biopsy procedure", J. A. MECH., 46(2), pp. 221-231 (2015).
14. Troyer, K.L., Shetye, S.S., and Puttlitz, C.M. "Experimental characterization and finite element implementation of soft tissue nonlinear viscoelasticity", ASME J. Biomech. Eng., 134, pp. 1-8 (2012).
15. Zanetti, E.M., Perrini, M., Bignardi, C., and Audenino, A.L. "Bladder tissue passive response to monotonic and cyclic loading", Biorheol., 49, pp. 49-63 (2012).
16. Natali, A.N., Audenino, A.L., Artibani, W., Fontanella, C.G., Carniel, E.L., and Zanetti, E.M. "Bladder tissue biomechanical behavior: Experimental tests and constitutive formulation", J. Biomech., 48, pp. 3088-3096 (2015).
17. Oaz, H. "A biomechanical comparison between tissue stiffness meter and shore type 00 durometer using fresh human fetal membrane cadavers", Biocyber. Biomed. Eng., 36, pp. 138-144 (2016).
18. Khajehsaeid, H., Baghani, M., and Naghdabadi, R. "Finite strain numerical analysis of elastomeric bushings under multi-axial loadings: a compressible viscohyperelastic approach", Int. J. Mech. Mat. Des., 9, pp. 385-399 (2013).
19. Naghdabadi, R., Baghani, M., and Arghavani, J. "A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation", Finite Elem. Anal. Des., 62, pp. 18-27 (2012).
20. Karimi, A., Navidbakhsh, M., and Beigzadeh, B. "A visco-hyperelastic constitutive approach for modeling polyvinylalcohol sponge", Tissue Cell, 46, pp. 97-102 (2014).
21. Tirella, A., Mattei, G., and Ahluwalia, A. "Strain rate viscoelastic analysis of soft and highly hydrated biomaterials", J. Biomed. Mat. Res., 102A(10), pp. 3352-3360 (2014).
22. Miller, K. "Constitutive model of brain tissue suitable for finite element analysis of surgical procedures", J. Biomech., 32, pp. 531-537 (1999).
23. Pipkin, A.C. and Rogers, T.G. "A nonlinear integral representation for viscoelastic behavior", J. Mech. Phys. Solids., 16, pp. 59-72 (1968).
24. Rajagopal, K.R. and Wineman, A.S. "Response of anisotropic nonlinearly viscoelastic solids", Math. Mech. Solids., 14, pp. 490-501 (2009).
25. Holzapfel, G.A., Nonlinear Solid Mechanics. A Continuum Approach for Engineering, pp. 205-256, Wiley, UK (2000).
26. Holzapfel, G.A. and Gasser, T.C. "A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications", Comput. Meth. Appl. Mech. Eng., 190, pp. 4379-4403 (2001).
27. Lu, Y.T., Zhu, H.X., Richmond, S., and Middleton, J. "A visco-hyperelastic model for skeletal muscle tissue under high strain rates", J. Biomech., 43, pp. 2629- 2632 (2010).
28. Limbert, G. and Middleton, J. "A constitutive model of the posterior cruciate ligament", Med. Eng. Phys., 28, pp. 99-113 (2006).
29. Laksari, k., Sadeghipour, K., and Darvish, K. "Mechanical response of brain tissue under blast loading", J Mech Behav Biomed Mater, 32, pp. 132-144 (2014).
30. Mansouri, M. and Darijani, H. "Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self- contained approach", Int. J. Solids Struct., 51(25), pp. 4316-4326 (2014).
31. Khan, A.S., Lopez-Pamies, O., and Kazmi, R. "Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures", Int. J. Plas., 22, pp. 581-601 (2006).
32. Khan, A.S. and Lopez-Pamies, O. "Time and temperature dependent response and relaxation of a soft polymer", Int. J. Plas., 18, pp. 1359-1372 (2002).
33. Limbert, G. and Middleton, J. "A transversely isotropic viscohyperelastic material application to the modeling of biological soft connective tissues", Int. J. Solis Struct., 41(15), pp. 4237-4260 (2004).