A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus

Z. Y. Guo*, X. Q. Peng, B. Moran

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

137 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1952-1971
Number of pages20
JournalJournal of the Mechanics and Physics of Solids
Issue number9
StatePublished - Sep 2006
Externally publishedYes


  • Fiber reinforced composite
  • Hyperelasticity
  • Intervertebral disc
  • Multiplicative decomposition
  • Soft tissue

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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