Stress transfer in collagen fibrils reinforcing connective tissues: Effects of collagen fibril slenderness and relative stiffness

Unlike engineering fibre composite materials which comprise of fibres that are uniform cylindrical in shape, collagen fibrils reinforcing the proteoglycan-rich (PG) gel in the extra-cellular matrices (ECMs) of connective tissues are taper-ended (paraboloidal in shape). In an earlier paper we have discussed how taper of a fibril leads to an axial stress up-take which differs from that of a uniform cylindrical fibre and implications for fibril fracture. The present paper focuses on the influence of fibre aspect ratio, q (slenderness), and Youngʹs modulus (stiffness), relative to that of the gel phase, ER, on the magnitude of the axial tensile stresses generated within a fibril and wider implications on failure at tissue level. Fibre composite models were evaluated using finite element (FE) and mathematical analyses. When the applied force is low, there is elastic stress transfer between the PG gel and a fibril. FE modelling shows that the stress in a fibril increases with ER and q. At higher applied forces, there is plastic stress transfer. Mathematical modelling predicts that the stress in a fibril increases linearly with q. For small q values, fibrils may be regarded as fillers with little ability to provide tensile reinforcement. Large q values lead to high stress in a fibril. Such high stresses are beneficial provided they do not exceed the fracture stress of collagen. Modulus difference regulates the strain energy release density, u, for interfacial rupture; large ER not only leads to high stress in a fibril but also insures against interfacial rupture by raising the value of u.