Fractional viscoelastic models applied to biomechanical constitutive equations
J.E. Palomares-Ruizª, M. Rodriguez-Madrigalb, J.G. Castro Lugoª, and A.A. Rodriguez-Sotob
a Maestría en Ingeniería Mecatrónica, Instituto Tecnológico Superior de Cajeme, Carretera Internacional a Nogales km 2, Ciudad Obregón, Sonora, México, e-mail: jepalomares@itesca.edu.mx, jcastro@itesca.edu.mx, Phone: 01 644 4108650 ext. 1311.
b Facultad de Ingeniería Mecánica, Instituto Superior Politécnico José Antonio Echeverría, Calle 114, No. 11901, Entre Ciclovía y 129, Cujae, Marianao, Ciudad de La Habana, Cuba, e-mail: melchor@mecanica.cujae.edu.cu, arodriguezs@mecanica.cujae.edu.cu
]]> Received 17 March 2015.
Abstract
The aim of this work consist to compare the traditional viscoelastic material models vs the fractional ones, determinate the fractional order of the differential operator that characterize the mechanical stress-strain relation, the stress relaxation and the creep compliance of this models for a biological soft tissue, in particular a femoral artery. Apply the Laplace transform for Mittag-Leffler function type and the convolution on fractional standard lineal solid differential equation, known as Zener model, to obtain analytical solution. Simulated the force-pressure related by singular blood flow pulse and the displacement response.
Keywords: Fractional; viscoelastic; biomechanics; soft tissues.
PACS: 45.10.Hj; 46.35.+Z; 87.10.Ed
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1. W. Lin, Journal of Mathematical Analysis and Applications 332 (2007) 709-726. [ Links ]
2. H. Ertik, A. Calik, and H. Sirin, Rev. Mex. Fis. 61 58-63 (2015). [ Links ]
3. H. Nour, W. Raslan, and E. El-Shazly. Journal of Fractional Calculus and Applications 9 (2013) 1-9. [ Links ]
4. F. Gómez-Aguilar, M. Guía-Calderón, J. Rosales- García, and J. Bernal-Alvarado. Ing. Investig. Tecnolog. 13 (2012) 375-384. [ Links ]
5. J. Gómez, R. Razo, and D. Granados, Rev. Mex. Fis. 60 (2014) 32-38. [ Links ]
6. J. Gómez, J. Rosales, J. Bernal, T. Córdova, and R. Guzmán. Rev. Mex. Fis. 58 (2012) 348-352. [ Links ]
7. J. Awrejcewicz, V. Krysko, I. Papkova, and A. Krysko Chaos, Solitons & Fractals 45 (2012) 687-708. [ Links ]
8. F. Gómez, J. Bernal, J. Rosales, and T. Cordova, Journal of Electrical Bioimpedance 3 (2012) 2-11. [ Links ]
9. R. Magin, Computers and mathematics with applications 59 (2010) 1586-1593. [ Links ]
10. D. Nagehan and T. Ergin, Acta of Bioengineering and Biomechanics 16 (2014) 13-21. [ Links ]
11. G. Davis, M. Kohandel, S. Sivaloganathan, and G. Tenti, Medical engineering & physics 28 (2006) 455-459. [ Links ]
12. C. Wex, C. Bruns, and A. Stoll, Scottish Journal of Arts, Social Sciences and Scientific Studies 32 (2014) 69-74. [ Links ]
13. Y. Kobayashi, A. Kato, H. Watanabe, T. Hoshi, K. Kawamura, and M. Fujie, Journal of Biomechanical Science and Engineering 7 (2012) 177-187. [ Links ]
14. D. Craiem, F. Rojo, J. Atienza, R. Armentano, and G. Guinea, Physics in Medicine and Biology 53 (2008) 4543-4554. [ Links ]
15. D. Craiem and R. Armentano, Biorheology 44 (2007) 251-263. [ Links ]
16. J. Shen, C. Li, H. Wu, and M. Kalantari, Korea- Australia Rheology Journal 2 (2013) 87-93. [ Links ]
17. P. Smyth and I. Green, Mechanics of Time-Dependent Materials (2015). [ Links ]
18. A. Freed and K. Diethelm, Biomechanics and modeling in mechanobiology 5 (2006) 203-215. [ Links ]
19. A. Tsamis, J. Krawiec, and D. Vorp, Journal of The Royal Society Interface 83 (2013) 14-21. [ Links ]
20. Y. Fung, Biomechanics: mechanical properties of livingtissues (Springer, 1981). [ Links ]
21. Y.C. Fung, Biomechanics: Motion, Flow, Stress, and Growth. (Springer, 1990). [ Links ]
22. F. Meral, T. Royston, and R. Magin, Commun Nonlinear Sci Numer Simulat 15 (2010) 939-945. [ Links ]
23. S. Müller, M. Kästner, J. Brummund, and V. Ulbricht, Computational Mechanics 51 (2013) 999-1012. [ Links ]
24. O. Agrawal, Journal of Mathematical Analysis and Applications 337 (2008) 1-12. [ Links ]
25. M. Caputo, Annals of Geophysics, 46 (2003). [ Links ]
26. Y. Luchko and R. Gorenflo, Acta Mathematica Vietnamica 24 (1999) 207-233. [ Links ]
27. Igor Podlubny, Fractional diferential equations (Academic Press, 1999). [ Links ]
28. B. Xu and H. Li, Journal of Biomechanical Engineering 135 2013 1-4. [ Links ]
29. A. Freed, Modeling and Simulation in Science, Engineering and Technology X (2014) 209-275. [ Links ]
30. J. Palacio, S. Hammer, D. Good, S. McNeill, S. Grant, R. Reuben, and Y. Chen, Journal of the mechanical behavior of biomedical materials 41 (2015) 149-160. [ Links ]
31. M. Bulíček, P. Kaplický, and M. Steinhauer, Pacific Journal of Mathematics 262 (2013) 11-33. [ Links ]
32. C. Ingo, R. Magin, and T. Parrish, Entropy 16 (2014) 5838-5852. [ Links ]
33. D. Craiem, F. Rojo, J. Atienza, G. Guinea, and R. Armentano, Latin American Applied Research 38 (2008) 141-145. [ Links ]
34. T. Kaneko, H. Hasegawa, and H. Kanai, Japanese Journal of Applied Physics 46 (2007) 4881-4888. [ Links ]
35. B. Arindam and H. Chattopadhyay, Acta of Bioengineering and Biomechanics 16 (2014) 33-44. [ Links ]
36. D. Jodko, D. Obidowski, P. Reorowicz, and K. Jóźcuwik. Acta of Bioengineering and Biomechanics 16 (2014) 69-74. [ Links ]
37. S. Momani and Z. Odibat, Chaos Solitons & Fractals 31 (2007) 1248-1255. [ Links ]
38. I. Petráš. Advances in Difference Equations 652789 (2011) 1-14. [ Links ]
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