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A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. (English) Zbl 1120.74634
Summary: This paper presents a composites-based hyperelastic constitutive model for soft tissue. Well organized soft tissue is treated as a composite in which the matrix material is embedded with a single family of aligned fibers. The fiber is modeled as a generalized neo-Hookean material in which the stiffness depends on fiber stretch. The deformation gradient is decomposed multiplicatively into two parts: a uniaxial deformation along the fiber direction and a subsequent shear deformation. This permits the fiber-matrix interaction caused by inhomogeneous deformation to be estimated by using effective properties from conventional composites theory based on small strain linear elasticity and suitably generalized to the present large deformation case. A transversely isotropic hyperelastic model is proposed to describe the mechanical behavior of fiber-reinforced soft tissue. This model is then applied to the human annulus fibrosus. Because of the layered anatomical structure of the annulus fibrosus, an orthotropic hyperelastic model of the annulus fibrosus is developed. Simulations show that the model reproduces the stress-strain response of the human annulus fibrosus accurately. We also show that the expression for the fiber-matrix shear interaction energy used in a previous phenomenological model is compatible with that derived in the present paper.
Reviewer: Reviewer (Berlin)

74L15 Biomechanical solid mechanics
92C10 Biomechanics
Full Text: DOI
[1] Acaroglu, E.R.; Iatridis, J.C.; Setton, L.A.; Foster, R.J.; Mow, V.C.; Weidenbaum, M., Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus, Spine, 20, 24, 2690-2701, (1995)
[2] Adams, M.A.; Green, T.P., Tensile properties of the annulus fibrosus, Europe spine J., 2, 203-208, (1993)
[3] Bass, E.C.; Ashford, F.A.; Segal, M.R.; Lotz, J.C., Biaxial testing of human annulus fibrosus and its implications for a constitutive formulation, Ann. biomed. eng., 32, 9, 1231-1242, (2004)
[4] Best, B.A.; Guilak, F.; Setton, L.A.; Zhu, W.B.; Saednejad, F.; Ratcliffe, A.; Weidenbaum, M.; Mow, V.C., Compressive mechanical-properties of the human anulus fibrosus and their relationship to biochemical-composition, Spine, 19, 2, 212-221, (1994)
[5] Caner, F.C., and Carol, I., 2006. Microplane constitutive model and computational framework for blood vessel tissue. J. Biomech. Eng.—Trans. ASME, in press.
[6] Criscione, J.C.; Douglas, A.S.; Hunter, W.C., Physically based strain invariant set for materials exhibiting transversely isotropic behavior, J. mech. phys. solids, 49, 4, 871-897, (2001) · Zbl 0980.74012
[7] Ebara, S.; Iatridis, J.C.; Setton, L.A.; Foster, R.J.; Mow, V.C.; Weidenbaum, M., Tensile properties of nondegenerate human lumbar anulus fibrosus, Spine, 21, 4, 452-461, (1996)
[8] Eberlein, R.; Holzapfel, G.A.; Frohlich, M., Multi-segment FEA of the human lumbar spine including the heterogeneity of the annulus fibrosus, Comput. mech., 34, 2, 147-163, (2004) · Zbl 1138.74370
[9] Elliott, D.M.; Setton, L.A., A linear material model for fiber-induced anisotropy of the anulus fibrosus, J. biomech. eng.—trans. ASME, 122, 2, 173-179, (2000)
[10] Elliott, D.M.; Setton, L.A., Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions, J. biomech. eng. —tran. ASME, 123, 3, 256-263, (2001)
[11] Fujita, Y.; Duncan, N.A.; Lotz, J.C., Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent, J. orthop. res., 15, 6, 814-819, (1997)
[12] Fujita, Y.; Wagner, D.R.; Biviji, A.A.; Duncan, N.A.; Lotz, J.C., Anisotropic shear behavior of the annulus fibrosus: effect of harvest site and tissue prestrain, Med. eng. phys., 22, 5, 349-357, (2000)
[13] Fung, Y.C., Biomechanics : mechanical properties of living tissues, (1981), Springer New York
[14] Galante, J.O., Tensile properties of human lumbar annulus fibrosus, Acta orthop. scand., S, 9, (1967)
[15] Gasser, C.T.; Ogden, R.W.; Holzapfel, G., Hyperelastic modelling of arterial layers with distributed collagen fibre orientations, J. R. soc. interface, 3, 6, 15-35, (2006)
[16] Guo, Z.Y., Peng, X.Q., Moran, B., 2006. Mechanical response and stability of neo-Hookean fiber reinforced incompressible nonlinearly elastic solids, Int. J. Solids. Struct., Submitted for publication. · Zbl 1108.74011
[17] Halpin, J.C.; Finlayson, K.M., Primer on composite materials analysis, (1992), Technomic Pub. Co. Lancaster, Pa
[18] Holzapfel, G.A.; 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, 34, 4379-4403, (2001)
[19] Holzapfel, G.A.; Gasser, T.C.; Ogden, R.W., A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. elasticity, 61, 1-3, 1-48, (2000) · Zbl 1023.74033
[20] Holzapfel, G.A.; Gasser, T.C.; Stadler, M., A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis, Eur. J. mech. solids, 21, 3, 441-463, (2002) · Zbl 1100.74597
[21] Holzapfel, G.A.; Schulze-Bauer, C.A.J.; Feigl, G.; Regitnig, P., Single lamellar mechanics of the human lumbar anulus fibrosus, Biomech. modeling mechanobiol., 3, 3, 125-140, (2005)
[22] Humphrey, J.D., Continuum biomechanics of soft biological tissues, Proc. R. soc. London series math. phys. eng. sci., 459, 2029, 3-46, (2003) · Zbl 1116.74385
[23] Humphrey, J.D.; Rajagopal, K.R., A constrained mixture model for growth and remodeling of soft tissues, Math. models meth. appl. sci., 12, 3, 407-430, (2002) · Zbl 1021.74026
[24] Kelsey, J.L.; White, A.A., Epidemiology and impact of low-back-pain, Spine, 5, 2, 133-142, (1980)
[25] Marchand, F.; Ahmed, A.M., Investigation of the laminate structure of lumbar-disk anulus fibrosus, Spine, 15, 5, 402-410, (1990)
[26] Peng, X.Q., Guo, Z.Y., Moran, B., 2005. An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus. J. Appl. Mech., in press. · Zbl 1111.74590
[27] Qiu, G.Y.; Pence, T.J., Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids, J. elasticity, 49, 1, 1-30, (1997) · Zbl 0964.74008
[28] Quapp, K.M.; Weiss, J.A., Material characterization of human medial collateral ligament, J. biomech. eng.—trans. ASME, 120, 6, 757-763, (1998)
[29] Rao, A.A.; Dumas, G.A., Influence of material properties on the mechanical-behavior of the L5-S1 intervertebral-disk in compression—A nonlinear finite-element study, J. biomed. eng., 13, 2, 139-151, (1991)
[30] Shirazi-Adl, A., On the fiber composite-material models of disk annulus—comparison of predicted stresses, J. biomech., 22, 4, 357-365, (1989)
[31] Skaggs, D.L.; Weidenbaum, M.; Iatridis, J.C.; Ratcliffe, A.; Mow, V.C., Regional variation in tensile properties and biochemical-composition of the human lumbar anulus fibrosus, Spine, 19, 12, 1310-1319, (1994)
[32] Spencer, A.J.M., Continuum theory of the mechanics of fibre-reinforced composites, (1984), Springer Wein, New York · Zbl 0559.00015
[33] Spilker, R.L.; Jakobs, D.M.; Schultz, A.B., Material constants for a finite-element model of the intervertebral-disk with a fiber composite annulus, J. biomech. eng.—trans. ASME, 108, 1, 1-11, (1986)
[34] Sun, D.D.N.; Leong, K.W., A nonlinear hyperelastic mixture theory model for anisotropy, transport, and swelling of annulus fibrosus, Ann. biomed. eng., 32, 1, 92-102, (2004)
[35] van Loon, R.; Huyghe, J.M.; Wijlaars, M.W.; Baaijens, F.P.T., 3D FE implementation of an incompressible quadriphasic mixture model, Int. J. numer. meth. eng., 57, 9, 1243-1258, (2003) · Zbl 1062.74634
[36] Wagenseil, J.E.; Elson, E.L.; Okamoto, R.J., Cell orientation influences the biaxial mechanical properties of fibroblast populated collagen vessels, Ann. biomed. eng., 32, 5, 720-731, (2004)
[37] Wagner, D.R.; Lotz, J.C., Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus, J. orthop. res., 22, 4, 901-909, (2004)
[38] Wang, J., Development and validation of a viscoelastic finite element model of an L2/L3 motion segment, Theor. appl. frac. mech., 28, 1, 81-93, (1997)
[39] Wang, J.; Parnianpour, M.; Shirazi-Adl, A.; Engin, A., Rate effect on sharing of passive lumbar motion segment under load-controlled sagittal flexion: viscoelastic finite element analysis, Theor. appl. frac. mech., 32, 2, 119-128, (1999)
[40] Wang, J.L.; Parnianpour, M.; Shirazi-Adl, A.; Engin, A.E., Viscoelastic finite-element analysis of a lumbar motion segment in combined compression and sagittal flexion—effect of loading rate, Spine, 25, 3, 310-318, (2000)
[41] White, A.A.; Panjabi, M.M., Clinical biomechanics of the spine, (1978), Lippincott Philadelphia
[42] Wilber, J.P.; Walton, J.R., The convexity properties of a class of constitutive models for biological soft issues, Math. mech. solids, 7, 3, 217-235, (2002) · Zbl 1072.74052
[43] Wu, H.C.; Yao, R.F., Mechanical-behavior of human annulus fibrosis, J. biomech., 9, 1, 1-7, (1976)
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