A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

References

• Abaqus [2014] Abaqus Theory Manual (Dassault Systemes Simulia Corporation). Google Scholar
• Baaijens, F. P. T. [1998] “ Mixed finite element methods for viscoelastic flow analysis: A review,” J. Non-Newtonian Fluid Mech. 79, 361–385. Crossref, ISI, Google Scholar
• Bathe, K. J. [2014] Finite Element Procedures (Klaus-Jurgen Bathe). Google Scholar
• Batra, R. C. [1980] “ Finite plane strain deformations of rubberlike materials,” Int. J. Numer. Methods Eng. 15, 145–160. Crossref, ISI, Google Scholar
• Bel-Brunon, A., Kehl, S., Martin, C., Uhlig, S. and Wall, W. A. [2014] “ Numerical identification method for the non-linear viscoelastic compressible behavior of soft tissue using uniaxial tensile tests and image registration — Application to rat lung parenchyma,” J. Mech. Behav. Biomech. Mater. 29, 360–374. Crossref, ISI, Google Scholar
• Belytschko, T., Liu, W. K. and Moran, B. [2000] Nonlinear Finite Elements for Continua and Structures (Wiley). Google Scholar
• Bols, J., Degroote, J., Trachet, B., Verhegghe, B., Segers, P. and Vierendeels, J. [2013] “ A comparative study of several material models for prediction of hyperelastic properties: Application to silicone-rubber and soft tissues,” J. Comput. Appl. Math. 246, 10–17. Crossref, Google Scholar
• Bols, J., Degroote, J., Trachet, B., Verhegghe, B., Segers, P. and Vierendeels, J. [2013] “ Finite element modelling of cell wall properties for onion epidermis using a fibre-reinforced hyperelastic model,” J. Comput. Appl. Math. 246, 10–17. Crossref, Google Scholar
• Borst, R. de [1988] “ Modelling and analysis of rubberlike materials,” Heron. 33, 1–56. Google Scholar
• Bower, A. F. [2009] Applied Mechanics of Solids (CRC Press). Crossref, Google Scholar
• COMSOL [2012] COMSOL Multiphysics User’s Guide (COMSOL Inc). Google Scholar
• Cervera, M., Chiumenti, M. and Codina, R. [2010] “ Mixed stabilized finite element methods in nonlinear solid mechanics Part I: Formulation,” Comput. Methods Appl. Mech. Eng. 199, 2559–2570. Crossref, ISI, Google Scholar
• Chuong, C. J. and Fung, Y. C. [1983] “ Three-dimensional stress distribution in arteries,” J. Biomech. Eng. 105, 268–274. Crossref, ISI, Google Scholar
• Chuong, C. J. and Fung, Y. C. [1986] “ On residual stress in arteries,” J. Biomech. Eng. 108, 189–192. Crossref, ISI, Google Scholar
• Demiray, H. [1972] “ A note of elasticity of soft biological tissues,” J. Biomech. 5, 309–311. Crossref, ISI, Google Scholar
• Fu, Y. B., Chui, C. K. and Teo, C. L. [2013] “ Liver tissue characterization from uniaxial stress–strain data using probabilistic and inverse finite element methods,” J. Mech. Behav. Biomech. Mater. 20, 105–112. Crossref, ISI, Google Scholar
• Fung, Y. C. [1967] “ Elasticity of soft tissues in simple elongation,” Am. J. Physiol. 213 1532–1544. Crossref, ISI, Google Scholar
• Fung, Y. C. [1993] Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York). Crossref, Google Scholar
• Gajewski, M., Szczerba, R. and Jemiolo, S. [2015] “ Modelling of elastomeric bearings with application of Yeoh hyperelastic material model,” Proc. Eng. 111, 220–227. Crossref, Google Scholar
• Green, A. E. and Zerna, W. [1968] Theoretical Elasticity (Oxford University Press). Google Scholar
• Guo, X., Liu, Y. and Kassab, G. S. [2012] “ Diameter-dependent axial prestretch of porcine coronary arteries and veins,” J. Appl. Physiol. 112, 982–989. Crossref, ISI, Google Scholar
• Herrmann, L. R. [1965] “ Elasticity equations for incompressible and nearly incompressible materials by a variational theorem,” AIAA J. 3, 1896–1900. Crossref, Google Scholar
• Holzapfel, G. A. [2000] Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley). Google Scholar
• Holzapfel, G. A. and Gasser, T. C. [2000] “ A new constitutive framework for arterial wall mechanics and a comparative study of material models,” J. Elasticity 61, 1–48. Crossref, ISI, Google Scholar
• Holzapfel, G. A. and Ogden, R. W. [2003] Biomechanics of Soft Tissue in Cardiovascular Systems (Springer-Verlag, Wien). Crossref, Google Scholar
• Hu, H. [1954] “ On some variational principles in the theory of elasticity and the theory of plasticity,” Acta Phys. Sin. 10, 259–290. Google Scholar
• Karimi, A., Navidbakhsh, M., Alizadeh, M. and Shojaei, A. [2014] “ A comparative study on the mechanical properties of the umbilical vein and umbilical artery under uniaxial loading,” Artery Res. 8, 51–56. Crossref, Google Scholar
• Karimi, A., Navidbakhsh, M., Beigzadeh, B. and Faghihi, S. [2013] “ Hyperelastic mechanical behavior of rat brain infected by Plasmodium berghei ANKA — experimental testing and constitutive modelling,” Int. J. Damage Mech. 0, 1–15. Google Scholar
• Kaster, T., Sack, I. and Samani, A. [2011] “ Measurement of the hyperelastic properties of ex vivo brain tissue slices,” J. Biomech. 44, 1158–1163. Crossref, ISI, Google Scholar
• Li, Y., Tang, S., Kroger, M. and Liu, W. K. [2016] “ Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers,” J. Mech. Phys. Solids. 88, 204–226. Crossref, ISI, Google Scholar
• Maltzahn, W. W., Von Warriyar, R. G. and Keitzer, W. F. [1984] “ Experimental measurments of elastic properties of media and adventitia of bovine carotid arteries,” J. Biomech. 17, 839–847. Crossref, ISI, Google Scholar
• Mass, S. A., Ellis, B. J., Ateshian, G. A. and Weiss, J. A. [2012] “ FEBio: Finite elements for biomechanics,” J. Biomech. Eng. 134, 1–10. ISI, Google Scholar
• Masson, I., Boutouyrie, P., Laurent, S., Humphrey, J. D. and Zidi, M. [2008] “ Characterization of arterial wall mechanical behavior and stresses from human clinical data,” J. Biomech. 41, 2618–2627. Crossref, ISI, Google Scholar
• Masson, I., Fassot, C. and Zidi, M. [2010] “ Finite dynamic deformations of a hyperelastic, anisotropic, incompressible and prestressed tube. Applications to in vivo arteries,” Eur. J. Mech. A/Solids 29, 523–529. Crossref, ISI, Google Scholar
• Mooney, M. [1940] “ A theory of large elastic deformation,” J. Appl. Phys. 11, 582–592. Crossref, Google Scholar
• Nicholson, D. W. [1995] “ Tangent modulus matrix for finite element analysis of hyperelastic materials,” Acta Mech. 112, 187–201. Crossref, ISI, Google Scholar
• Oberai, A. A., Gokhale, N. H., Goenezen, S., Barbone, P. E., Hall, T. J., Sommer, A. M. and Jiang, J. [2009] “ Linear and nonlinear elasticity imaging of soft tissue in vivo: Demonstration of feasibility,” Phys. Med. Biol. 54, 1191–1207. Crossref, ISI, Google Scholar
• Oden, J. T. [2006] Finite Elements of Nonlinear Continua (Dover Publications). Google Scholar
• Ogden, R. W. [1972] “ Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids,” Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 326, 565–584. Crossref, ISI, Google Scholar
• O’Hagen, J. J. and Samani, A. [2009] “ Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples,” Phys. Med. Biol. 54, 2557–2569. Crossref, ISI, Google Scholar
• Ohayon, J., Dubreuil, O., Tracqui, P., Floc’h, S. Le, Rioufol, G., Chalabreysse, L., Thivolet, F., Pettigrew, R. I. and Finet, G. [2007] “ Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: Potential impact for evaluating the risk of plaque rupture,” Am. J. Physiol. Heart Circulatory Physiol. 293, H1987–H1996. Crossref, ISI, Google Scholar
• Papadopoulos, P. and Taylor, R. L. [1992] “ A mixed formulation for the finite elment solution of contact problems,” Comput. Methods Appl. Mech. Eng. 94, 373–389. Crossref, ISI, Google Scholar
• Qian, M., Wells, D. M., Jones, A. and Becker, A. [2010] “ Finite element modelling of cell wall properties for onion epidermis using a fiber-reinforced hyperelastic model,” J. Struct. Biol. 172, 300–304. Crossref, ISI, Google Scholar
• Rashid, B., Destrade, M. and Gilchrist, M. D. [2013] “ Mechanical characterization of brain tissue in simple shear at dynamic strain rates,” J. Mech. Behav. Biomech. Mater. 28, 71–85. Crossref, ISI, Google Scholar
• Rausch, S. M. K., Martin, C., Bornemann, P. B., Uhlig, S. and Wall, W. A. [2011] “ Material model of lung parenchyma based on living precision — cut lung slice testing,” J. Mech. Behav. Biomech. Mater. 4, 583–592. Crossref, ISI, Google Scholar
• Rhodin, J. A. G. [1980] Handbook of Physiology, The Cardiovascular System (John Wiley and Sons). Google Scholar
• Rivlin, R. S. [1948] “ Large elastic deformations of isotropic materials,” Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 241, 379–397. Crossref, ISI, Google Scholar
• Saraf, H., Ramesh, K. T., Lennon, A. M., Merkle, A. C. and Roberts, J. C. [2007] “ Mechanical properties of soft human tissues under dynamic loading,” J. Biomech. 40, 1960–1967. Crossref, ISI, Google Scholar
• Sharma, S. [2003] “Critical Comparison of Popular Hyper-Elastic Material Models in Design of Anti-Vibration Mounts for Automotive Industry Through FEA” (Swets and Zeitlinger). Google Scholar
• Simo, J. C. and Rifai, M. S. [1990] “ A class of mixed assumed strain methods and the method of incompatible modes,” Int. J. Numer. Methods Eng. 29, 1595–1638. Crossref, ISI, Google Scholar
• Steinmann, P., Hossain, M. and Possart, G. [2012] “ Hyperelastic models for rubber-like materials: Consistent tangent operators and suitability for Treloar’s data,” Arch. Appl. Mech. 82, 1183–1217. Crossref, ISI, Google Scholar
• Suchocki, C. [2011] “ A finite element implementation of Knowles stroed-energy function: Theory, coding and applications,” Arch. Mech. Eng. LVIII, 319–346. Crossref, Google Scholar
• Umale, S., Deck, C., Bourdet, N., Dhumane, P., Soler, L., Marescaux, J. and Winger, R. [2013] “ Experimental mechanical characterization of abdominal organs: Liver, kidney and spleen,” J. Mech. Behav. Biomech. Mater. 17, 22–33. Crossref, ISI, Google Scholar
• Untaroiu, C. D., Lu, Y. C., Siripurapu, S. K. and Kemper, A. R. [2015] “ Modeling the biomechanics and injury response of human liver parenchyma under tensile loading,” J. Mech. Behav. Biomech. Mater. 41, 280–291. Crossref, ISI, Google Scholar
• Veronda, D. R. and Westmann, R. A. [1970] “ Mechanical characterization of skin-finite deformations,” J. Biomech. 3, 111–124. Crossref, ISI, Google Scholar
• Veubeke, B. F. de [1965] Displacement and Equilibrium Models in the Finite Element Method (Wiley). Google Scholar
• Weiss, J. A., Maker, B. N. and Govindjee, S. [1996] “ Finite element implementation of incompressible, transversely isotropic hyperelasticity,” Comput. Methods Appl. Mech. Eng. 135, 107–128. Crossref, ISI, Google Scholar
• Wex, C., Arndt, S., Stoll, A., Bruns, C. and Kupriyanova, Y. [2015] “ Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: A review,” Biomed. Tech. (Berl.) 60, 577–592. Crossref, ISI, Google Scholar
• Xie, J., Zhou, J. and Fung, Y. C. [1995] “ Bending of blood vessel wall: Stress-strain laws of the intima-media and adventitial layers,” J. Biomech. Eng. 117, 136–145. Crossref, ISI, Google Scholar
• Yeoh, O. H. [1993] “ Some forms of the strain energy function for rubber,” Rubber Chem. Technol. 66, 754–771. Crossref, ISI, Google Scholar
• Yeoh, O. H. [1990] “ Characterization of elastic properties of carbon black filled rubber vulcanizates,” Rubber Chem. Technol. 63, 792–805. Crossref, ISI, Google Scholar
• Zaeimdar, S. [2014] Mechanical Characterization of Breast Tissue Constituents for Cancer Assessment (Simon Fraser University). Google Scholar
• Zhao, J., Liao, D., Chen, P., Kunwald, P. and Gregersen, H. [2008] “ Stomach stress and strain depend on location, direction and the layered structure,” J. Biomech. 41, 3441–3447. Crossref, ISI, Google Scholar
• Zienkiewicz, O. C. and Taylor, R. L. [2005] The Finite Element Method for Solid and Structural Mechanics (Elsevier). Google Scholar