Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite

Buttermann, G.R., Beaubien, B.P.: Biomechanical characterization of an annulus-sparing spinal disc prosthesis. Spine J. 9, 744–753 (2009)

Büttner-Janz, K., Schellnack, K., Zippel, H.: Biomechanics of the SB Charit lumbar intervertebral disc endoprosthesis. Int. Orthop. 13, 173–176 (1989)

Carter, D.R., Hayes, W.C.: The compressive behavior of bone as a two-phase porous structure. J. Bone Jt. Surg., Am. Vol. 59, 954–962 (1977)

Ciambella, J., Paolone, A., Vidoli, S.: A comparison of nonlinear integral-based viscoelastic models through compression tests on filled rubber. Mech. Mater. 42, 932–944 (2010)

Coleman, B.D.: Thermodynamics of materials with memory. Arch. Ration. Mech. Anal. 17, 3–46 (1964)

Coleman, B.D., Noll, W.: Foundations of linear viscoelasticity. Rev. Mod. Phys. 3(2), 239–249 (1961)

de Groot, J.H., de Vrijer, R., Pennings, A.J., Klompmaker, J., Veth, R.P.H., Jansen, H.W.B.: Use of porous polyurethanes for meniscal reconstruction and meniscal prostheses. Biomaterials 17, 163–173 (1996)

Fung, Y.C.: Foundations of Solid Mechanics. Prentice Hall, New York (1965)

Fung, Y.C.: Biomechanics: Mechanical Properties of Living Tissues. Springer, New York (1993)

Gamradt, S.C., Wang, J.C.: Lumbar disc arthroplasty. Spine J. 5, 95–103 (2005)

Goh, S.M., Charalambides, M.N., Williams, J.G.: Determination of the constitutive constants of non-linear viscoelastic materials. Mech. Time-Depend. Mater. 8, 255–268 (2004)

Haut, R.C., Little, R.W.: A constitutive equation for collagen fibers. J. Biomech. 5, 423–430 (1972)

Holzapfel, G.A.: Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Wiley, Chichester (2000)

Hoppen, H.J., Leenslag, J.W., Pennings, A.J., van der Lei, B., Robinson, P.H.: Two-ply biodegradable nerve guide: basic aspects of design, construction and biological performance. Biomaterials 11, 286–290 (1990)

Koerner, H., Liu, W., Alexander, M., Mirau, P., Dowty, H., Vaia, R.A.: Deformation–morphology correlations in electrically conductive carbon nanotube—thermoplastic polyurethane nanocomposites. Polymer 46, 4405–4420 (2005)

Krag, M.H., Seroussi, R.E., Wilder, D.G., Pope, M.H.: Internal displacement distribution from in vitro loading of human thoracic and lumbar spinal motion segments: experimental results and theoretical predictions. Spine 12, 1001–1007 (1987)

Lambda, N.M.K., Woodhouse, K.A., Cooper, S.L.: Polyurethanes in Biomedical Applications. CRC Press, Boca Raton (1998)

Lelah, M.D., Cooper, S.L.: Polyurethanes in Medicine Authors. CRC Press, Boca Raton (1986)

Linde, F.: Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Dan. Med. Bull. 41(2), 119–138 (1994)

Macosko, C.W.: Rheology: Principles, Measurement and Applications. VCH, Weinheim (1994). ISBN 1-56081-579-5

Maksimov, R.D., Ivanova, T., Kalnins, M., Zicans, J.: Mechanical properties of high-density polyethylene/chlorinated polyethylene blends. Mech. Compos. Mater. 40, 331–340 (2004)

Ogden, R.W.: Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 326, 565–584 (1972)

Ogden, R., Saccomandi, G., Sgura, I.: Fitting hyperelastic models to experimental data. Comput. Mech. 34, 484–502 (2004)

Pawlikowski, M.: Cortical bone tissue viscoelastic properties and its constitutive equation—preliminary studies. Arch. Mech. Eng. LIX, 31–52 (2012)

Pioletti, D.P., Rakotomanana, L.R.: Non-linear viscoelastic laws for soft biological tissues. Eur. J. Mech. A, Solids 19, 749–759 (2000)

Rivlin, R.S.: Some applications of elasticity theory to rubber engineering. In: Collected Papers of R.S. Rivlin, vol. 1 and 2. Springer, Berlin (1997)

Robinson, P.H., van der Lei, B., Knol, K.E., Pennings, A.J.: Patency and long-term biological fate of a two-ply biodegradable microarterial prosthesis in the rat. Br. J. Plast. Surg. 42, 544–549 (1989)

Ryszkowska, J.L., Jurczyk-Kowalska, M., Szymborski, T., Kurzydłowski, K.J.: Dispersion of carbon nanotubes in polyurethane matrix. Physica E 39, 124–127 (2007)

Ryszkowska, J.L., Auguścik, M., Sheikh, A., Boccaccini, A.R.: Biodegradable polyurethane composite scaffolds containing Bioglass® for bone tissue engineering. Compos. Sci. Technol. 70, 1894–1908 (2010)

Schulz, M.J., Kelkar, A.D., Sundaresan, M.J.: Nanoengineering of Structural Functional, and Smart Materials, pp. 285–326. CRC Press, New York (2006)

Suchocki, C.: A finite element implementation of knowles stored-energy function: theory, coding and applications. Arch. Mech. Eng. LVIII, 319–346 (2011)

Sun, W., Yuan, Y.-X.: Optimization Theory and Methods. Nonlinear Programming. Springer, Berlin (2006)

Sun, W., Chaikof, E.L., Levenston, M.E.: Numerical approximation of tangent moduli for finite element implementations of nonlinear hyperelastic material models. J. Biomech. Eng. 130, 061003 (2008)

Taylor, R.L., Pister, K.S., Goudreau, G.L.: Thermomechanical analysis of viscoelastic solids. Int. J. Numer. Methods Eng. 2, 45–59 (1970)

Truesdell, C., Noll, W.: The Non-linear Field Theories. Springer, Berlin (1992)

Webster, T.J., Ejiofor, J.U.: Increased osteoblast adhesion on nanophase metals: Ti, Ti6Al4V, and CoCrMo. Biomaterials 25, 4731–4739 (2004)

Wei, G., Ma, P.X.: Structure and properties of nano-hydroxyapatite/polymer composite scaffolds for bone tissue engineering. Biomaterials 25, 4749–4757 (2004)

Weiss, J.A., Gardiner, J.C.: Computational modeling of ligament mechanics. Crit. Rev. Biomed. Eng. 29(4), 1–70 (2001)

Weiss, J.A., Maker, B.N., Govindjee, S.: Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Methods Appl. Mech. Eng. 135, 107–128 (1996)

Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66, 754–771 (1993)