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http://dx.doi.org/10.12989/anr.2020.8.3.255

Post-buckling analysis of aorta artery under axial compression loads  

Akbas, Seref Doguscan (Bursa Technical University, Department of Civil Engineering, Yildirim Campus)
Mercan, Kadir (Mehmet Akif Ersoy University, Faculty of Engineering-Architecture, Civil Engineering Department, Division of Mechanics)
Civalek, Omer (China Medical University)
Publication Information
Advances in nano research / v.8, no.3, 2020 , pp. 255-264 More about this Journal
Abstract
Buckling and post-buckling cases are often occurred in aorta artery because it affected by higher pressure. Also, its stability has a vital importance to humans and animals. The loss of stability in arteries may lead to arterial tortuosity and kinking. In this paper, post-buckling analysis of aorta artery is investigated under axial compression loads on the basis of Euler-Bernoulli beam theory by using finite element method. It is known that post-buckling problems are geometrically nonlinear problems. In the geometrically nonlinear model, the Von Karman nonlinear kinematic relationship is employed. Two types of support conditions for the aorta artery are considered. The considered non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The aorta artery is modeled as a cylindrical tube with different average diameters. In the numerical results, the effects of the geometry parameters of aorta artery on the post-buckling case are investigated in detail. Nonlinear deflections and critical buckling loads are obtained and discussed on the post-buckling case.
Keywords
aorta artery; post-buckling analysis; finite element method; Von Karman nonlinear;
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1 Zhang, J., Liu, Q. and Han, H.C. (2014), "An in vivo rat model of artery buckling for studying wall remodeling", Ann. Biomed. Eng., 42(8), 1658-1667. https://doi.org/10.1007/s10439-014-1017-5   DOI
2 Gammie, J.S., Shah, A.S., Hattler, B.G., Kormos, R.L., Peitzman, A.B., Griffith, B.P. and Pham, S.M. (1998), "Traumatic aortic rupture: diagnosis and management", Ann. Thorac. Surg., 66(4), 1295-1300. https://doi.org/10.1016/S0003-4975(98)00778-4   DOI
3 Garcia, J.R., Lamm, S.D. and Han, H.C. (2013), "Twist buckling behavior of arteries", Biomech. Model. Mechanobiol., 12(5), 915-927. https://doi.org/10.1007/s10237-012-0453-0   DOI
4 Kim, J. and Baek, S. (2011), "Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test", J. Biomech., 44(10), 1941-1947. https://doi.org/10.1016/j.jbiomech.2011.04.022   DOI
5 Lee, W.A., Matsumura, J.S., Mitchell, R.S., Farber, M.A., Greenberg, R.K., Azizzadeh, A., Murad, M.H. and Fairman, R.M. (2011), "Endovascular repair of traumatic thoracic aortic injury: clinical practice guidelines of the Society for Vascular Surgery", J. Vasc. Surg., 53(1), 187-192. https://doi.org/10.1016/j.jvs.2010.08.027   DOI
6 Levesque, M. and Nerem, R. (1985), "The elongation and orientation of cultured endothelial cells in response to shear stress", J. Biomech. Eng., 107, 341-347. https://doi.org/10.1115/1.3138567   DOI
7 Gore, R.W. (1974), "Pressures in cat mesenteric arterioles and capillaries during changes in systemic arterial blood pressure", Circ. Res., 34, 581-591. https://doi.org/10.1161/01.RES.34.4.581   DOI
8 Akgoz, B. and Civalek, O. (2017c), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024   DOI
9 ANSYS(R) Academic Research Mechanical.
10 Garcia, J.R., Sanyal, A., Fatemifar, F., Mottahedi, M. and Han, H.C. (2017), "Twist buckling of veins under torsional loading", J. Biomech., 58, 123-130. https://doi.org/10.1016/j.jbiomech.2017.04.018   DOI
11 Gore, R.W. and Bohlen, H. (1975), "Pressure regulation in the microcirculation", Fed. Proceed., 34(11), 2031-2037.
12 Han, H.C. (2007), "A biomechanical model of artery buckling", J. Biomech., 40(16), 3672-3678. https://doi.org/10.1016/j.jbiomech.2007.06.018   DOI
13 Han, H.C. (2009a), "The mechanical buckling of curved arteries", Mol. Cell. Biomech., 6(2), 93-99. http://test.techscience.com/mcb/v6n2/28480
14 Han, H.C. (2009b), "The theoretical foundation for artery buckling under internal pressure", J. Biomech. Eng., 131(12), 124501. https://doi.org/10.1115/1.4000080   DOI
15 Han, H.C., Chesnutt, J.K., Garcia, J.R., Liu, Q. and Wen, Q. (2013), "Artery buckling: new phenotypes, models, and applications", Ann. Biomed. Eng., 41(7), 1399-1410. https://doi.org/10.1007/s10439-012-0707-0   DOI
16 Liu, Q. and Han, H.C. (2012), "Mechanical buckling of artery under pulsatile pressure", J. Biomech., 45(7), 1192-1198. https://doi.org/10.1016/j.jbiomech.2012.01.035   DOI
17 Levy, B.I. and Tedgui, A. (2007), Biology of the Arterial Wall Vol. 1, Springer Science & Business Media, MA, Boston, USA.
18 Lillie, M., Shadwick, R. and Gosline, J. (2010), "Mechanical anisotropy of inflated elastic tissue from the pig aorta", J. Biomech., 43(11), 2070-2078. https://doi.org/10.1016/j.jbiomech.2010.04.014   DOI
19 Lillie, M., Armstrong, T., Gerard, S., Shadwick, R. and Gosline, J. (2012), "Contribution of elastin and collagen to the inflation response of the pig thoracic aorta: assessing elastin's role in mechanical homeostasis", J. Biomech., 45(12), 2133-2141. https://doi.org/10.1016/j.jbiomech.2012.05.034   DOI
20 Liu, Q., Wen, Q., Mottahedi, M. and Han, H.C. (2014), "Artery buckling analysis using a four-fiber wall model", J. Biomech., 47(11), 2790-2796. https://doi.org/10.1016/j.jbiomech.2014.06.005   DOI
21 Martinez, R., Fierro, C.A., Shireman, P.K. and Han, H.C. (2010), "Mechanical Buckling of Veins Under Internal Pressure", Ann. Biomed. Eng., 38(4), 1345-1353. https://doi.org/10.1007/s10439-010-9929-1   DOI
22 Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. DOI: https://doi.org/10.12989/anr.2018.6.2.147
23 Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2D and quasi-3D nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., Int. J., 7(4), 277-292. https://doi.org/10.12989/anr.2019.7.4.277
24 Hayman, D.M., Zhang, J., Liu, Q., Xiao, Y. and Han, H.C. (2013), "Smooth muscle cell contraction increases the critical buckling pressure of arteries", J. Biomech., 46(4), 841-844. https://doi.org/10.1016/j.jbiomech.2012.11.040   DOI
25 Humphrey, J., Kang, T., Sakarda, P. and Anjanappa, M. (1993), "Computer-aided vascular experimentation: a new electromechanical test system", Ann. Biomed. Eng., 21(1), 33-43. https://doi.org/10.1007/BF02368162   DOI
26 Jainandunsing, J.S., Linnemann, R., Bouma, W., Natour, N., Bidar, E., Lorusso, R., Gelsomino, S., Johnson, D.M. and Natour, E. (2019), "Aorto-atrial fistula formation and closure: a systematic review", J. Thorac. Dis., 11, 1031-1046. https://dx.doi.org/10.21037%2Fjtd.2019.01.7   DOI
27 Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ", Compos. Part B: Eng., 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067   DOI
28 Mulvany, M. and Aalkjaer, C. (1990), "Structure and function of small arteries", Physiol. Rev., 70, 921-961. https://doi.org/10.1152/physrev.1990.70.4.921   DOI
29 Berghouti, H., Bedia, E.A.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
30 Bertrand, S., Cuny, S., Petit, P., Trosseille, X., Page, Y., Guillemot, H. and Drazetic, P. (2008), "Traumatic rupture of thoracic aorta in real-world motor vehicle crashes", Traffic Inj. Prev., 9(2), 153-161. https://doi.org/10.1080/15389580701775777   DOI
31 Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191
32 Jalaei, M.H., Arani, A.G. and Nguyen-Xuan, H. (2019), "Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory", Int. J. Mech. Sci., 161, 105043. https://doi.org/10.1016/j.ijmecsci.2019.105043   DOI
33 Jalaei, M.H. and Arani, A.G. (2018), "Size-dependent static and dynamic responses of embedded double-layered graphene sheets under longitudinal magnetic field with arbitrary boundary conditions", Compos. Part B: Eng., 142, 117-130. https://doi.org/10.1016/j.compositesb.2017.12.053   DOI
34 Jalaei, M.H. and Thai, H.T. (2019), "Dynamic stability of viscoelastic porous FG nanoplate under longitudinal magnetic field via a nonlocal strain gradient quasi-3D theory", Compos. Part B: Eng., 175, 107164. https://doi.org/10.1016/j.compositesb.2019.107164   DOI
35 Jalaei, M.H., Arani, A.G. and Tourang, H. (2018), "On the dynamic stability of viscoelastic graphene sheets", Int. J Eng. Sci., 132, 16-29. https://doi.org/10.1016/j.ijengsci.2018.07.002   DOI
36 Richens, D., Kotidis, K., Neale, M., Oakley, C. and Fails, A. (2003), "Rupture of the aorta following road traffic accidents in the United Kingdom 1992-1999. The results of the co-operative crash injury study", Eur. J. Cardiothorac. Surg., 23(2), 143-148. https://doi.org/10.1016/S1010-7940(02)00720-0   DOI
37 Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001   DOI
38 Presley, R. (1979), "The primitive course of the internal carotid artery in mammals", Cell. Tissue. Organ., 103(2), 238-244. https://doi.org/10.1159/000145015   DOI
39 Rachev, A.A. (2009), "Theoretical study of mechanical stability of arteries", J. Biomech. Eng., 131(5), 051006. https://doi.org/10.1115/1.3078188   DOI
40 Sahmani, S. and Fattahi, A.M.B. (2018), "Development of efficient size-dependent plate models for axial buckling of single-layered graphene nanosheets using molecular dynamics simulation", Microsyst. Technol., 24, 1265-1277. https://doi.org/10.1007/s00542-017-3497-3   DOI
41 Sahmani, S. and Safaei, B. (2019), "Nonlinear free vibrations of bi-directional functionally graded micro/nano-beams including nonlocal stress and microstructural strain gradient size effects", Thin-Wall. Struct., 140, 342-356. https://doi.org/10.1016/j.tws.2019.03.045   DOI
42 Schembri, P., Crane, D.L. and Reddy, J.N. (2004), "A threedimensional computational procedure for reproducing meshless methods and the finite element method", Int. J. Numer. Method. Eng., 61(6), 896-927. https://doi.org/10.1002/nme.1095   DOI
43 Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mech., 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5   DOI
44 Civalek, O. and Demir, C. (2011a), "Buckling and bending analyses of cantilever carbon nanotubes using the euler-bernoulli beam theory based on non-local continuum model", Asian J. Civil Eng., 12(5), 651-661.
45 Civalek, O. and Demir, C. (2011b), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 35(5), 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004   DOI
46 Agah, M.R. (2015), "Material characterization of aortic tissue for traumatic injury and buckling", Ph.D. Dissertation; Temple University, PA, USA.
47 Akgoz, B. and Civalek, O. (2014), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Vib. Control, 20(4), 606-616. https://doi.org/10.1177%2F1077546312463752   DOI
48 Kheroubi, B., Benzair, A., Tounsi, A. and Semmah, A. (2016), "A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams", Adv. Nano Res., Int. J., 4(4), 251-264. https://doi.org/10.12989/anr.2016.4.4.251
49 Jezkova, K., Rathouska, J., Nemeckova, I., Fikrova, P., Dolezelova, E., Varejckova, M., Vitverova, B., Bernabeu, C., Novoa, J.M., Chlopicki, S. and Nachtigal, P. (2016), "Vascular Biology: Endothelium and Smooth Muscle Cells. High Levels of Soluble Endoglin Induce Inflammation and Oxidative Stress in Aorta Compensated with Preserved No-Dependent Vasodilatation Mice Fed High Fat Diet", Atheroscler., 252, E160-E160. https://doi.org/10.1016/j.atherosclerosis.2016.07.771
50 Kaniowsk, T., Bross, T., Koltowsk, R., Kustrzyc, A. and Olejak, B. (1970), "Kinking or Buckling of Aorta", Pol. Rev. Radiol. Nucl. Med., 34, 187-+.
51 De Garis, C.F., Black, I.H. and Riemenschneider, E.A. (1933), "Patterns of the Aortic Arch in American White and Negro Stocks, with Comparative Notes on Certain Other Mammals", J. Anat., 67, 599-619.
52 Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronaut., 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021   DOI
53 Akgoz, B. and Civalek, O. (2017a), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024   DOI
54 Akgoz, B. and Civalek, O. (2017b), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.039   DOI
55 Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352. https://doi.org/10.1016/j.amc.2016.05.034   DOI
56 Civalek, O. and Kiracioglu, O. (2010), "Free vibration analysis of Timoshenko beams by DSC method", Int. J. Num. Method. Biomed. Eng., 26(12), 1890-1898. https://doi.org/10.1002/cnm.1279   DOI
57 Demir, C. and Civalek, O. (2013), "Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models", Appl. Math. Model., 37(22), 9355-9367. https://doi.org/10.1016/j.apm.2013.04.050   DOI
58 Demir, C. and Civalek, O. (2017a), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016   DOI
59 Demir, C. and Civalek, O. (2017b), "A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix", Compos. Struct., 168, 872-884. https://doi.org/10.1016/j.compstruct.2017.02.091   DOI
60 Schulze-Bauer, C.A., Morth, C. and Holzapfel, G.A. (2003), "Passive biaxial mechanical response of aged human iliac arteries", J. Biomech. Eng., 125(3), 395-406. https://doi.org/10.1115/1.1574331   DOI
61 Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by nonlocal FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
62 Smyth, P.T. and Edwards, J.E. (1972), "Pseudocoarctation, kinking or buckling of the aorta", Circ., 46(5), 1027-1032. https://doi.org/10.1161/01.CIR.46.5.1027   DOI
63 Sobhy, M. and Zenkour, A.M. (2019), "Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory", Compos. Struct., 220, 289-303. https://doi.org/10.1016/j.compstruct.2019.03.096   DOI
64 Ebrahimi, F. and Barati, M.R. (2018), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magnetoelectrical field in thermal environment", J. Vib. Control, 24(3), 549-564. https://doi.org/10.1177%2F1077546316646239   DOI
65 Demir, C., Akgoz, B., Erdinc, M.C., Mercan, K. and Civalek, O. (2017), "Free vibration analysis of graphene sheets on elastic matrix", J. Fac. Eng. Archit. Gazi Univ., 32(2), 551-562. https://dx.doi.org/10.17341/gummfd.61874
66 Ebrahimi, F. and Barati, M.R. (2016), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 451. https://doi.org/10.1007/s00339-016-0001-3   DOI
67 Ebrahimi, F. and Barati, M.R. (2017), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936. https://doi.org/10.1080/15376494.2016.1196795   DOI
68 Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24(10), 820-829. https://doi.org/10.1080/15376494.2016.1196786   DOI
69 Ebrahimi, F. and Hosseini, S.H.S. (2016), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684   DOI
70 Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 9561504. https://doi.org/10.1155/2016/9561504
71 Youcef, D.O., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., Int. J., 3(4), 177-191. https://doi.org/10.12989/anr.2015.3.4.177   DOI
72 Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Dimitri, R. (2015a), "Dynamic analysis of thick and thin elliptic shell structures made of laminated composite materials", Compos. Struct., 133, 278-299. https://doi.org/10.1016/j.compstruct.2015.06.052   DOI
73 Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015b), "Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method", Compos. Part B: Eng., 81, 196-230. https://doi.org/10.1016/j.compositesb.2015.07.012   DOI
74 Williams, J.S., Graff, J.A., Uku, J.M. and Steinig, J.P. (1994), "Aortic injury in vehicular trauma", Ann. Thorac. Surg., 57(3), 726-730. https://doi.org/10.1016/0003-4975(94)90576-2   DOI
75 Fantuzzi, N., Tornabene, F., Bacciocchi, M. and Dimitri, R. (2017), "Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates", Compos. Part B: Eng., 115, 384-408. https://doi.org/10.1016/j.compositesb.2016.09.021   DOI
76 Ebrahimi, F. and Salari, E. (2015), "Size-dependent thermoelectrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007   DOI
77 Ebrahimi, F. and Salari, E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397. https://doi.org/10.1080/15376494.2015.1091524   DOI
78 Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980   DOI
79 Ebrahimi, F., Babaei, R. and Shaghaghi, G.R. (2018), "Vibration analysis thermally affected viscoelastic nanosensors subjected to linear varying loads", Adv. Nano Res., Int. J., 6(4), 399-422. https://doi.org/10.12989/anr.2018.6.4.399
80 Ebrahimi, F., Karimiasl, M. and Mahesh, V. (2019), "Vibration analysis of magneto-flexo-electrically actuated porous rotary nanobeams considering thermal effects via nonlocal strain gradient elasticity theory", Adv. Nano Res., Int. J., 7(4), 221-231. https://doi.org/10.12989/anr.2019.7.4.221   DOI
81 Fung, Y.C., Fronek, K. and Patitucci, P. (1979), "Pseudoelasticity of arteries and the choice of its mathematical expression", Am. J. Physiol. Heart and Circ. Physiol., 237(5), H620-H631. https://doi.org/10.1152/ajpheart.1979.237.5.H620   DOI