Constitutive equations for fibrous connective tissues

Abstract

A general multiaxial theory for the constitutive relations in fibrous connective tissues is developed on the basis of microstructural and thermodynamic considerations. It is compatible with existing general material theories. In elastic tissues, the theory considers the strain-energy function to be the sum of strain-energies of the tissue's components. The stresses are derived from this strain-energy function. Viscoelastic constitutive relations are obtained in an analogous manner. Few examples are developed in detail. The results of the present strain-energy based theory are identical with those of the author's previous structural models (Lanir, 1979a, b) which are based on detailed equilibrium analysis. It turns out, however, that the analytical work involved in solving boundary value problems is considerably shorter if the present theory is used. The advantages of structural theories in avoiding ambiguity in material characterization and in offering an insight into the function, structure and mechanics of tissue components are discussed.