Fibre-Matrix Interaction in Soft Tissue

Abstract

Although the mechanical behaviour of soft tissue has been extensively studied, the interaction between the collagen fibres and the ground matrix has not been well understood and is therefore ignored by most constitutive models of soft tissue. In this paper, the human annulus fibrosus is used as an example and the potential fibre-matrix interaction is identified by careful investigation of the experimental results of biaxial and uniaxial testing of the human annulus fibrosus. First, the uniaxial testing result of the HAF along the axial direction is analysed and it is shown that the mechanical behaviour of the ground matrix can be well simulated by the incompressible neo-Hookean model when the collagen fibres are all under contraction. If the collagen fibres are stretched, the response of the ground matrix can still be described by the incompressible neo-Hookean model, but the effective stiffness of the matrix depends on the fibre stretch ratio. This stiffness can be more than 10 times larger than the one obtained with collagen fibres under contraction. This phenomenon can only be explained by the fibre-matrix interaction. Furthermore, we find that the physical interpretation of this interaction includes the inhomogeneity of the soft tissue and the fibre orientation dispersion. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by the fibre orientation dispersion. The significant effect of the fibre-matrix interaction strain energy on mechanical behaviour of the soft tissue is also illustrated by comparing some simulation results.