A mathematical model for creep, relaxation and strain stiffening in parallel-fibered collagenous tissues

A simple model is presented for the description of relaxation, creep, and strain stiffening phenomena that are observed in parallel-fibered collagenous tissues such as ligaments and tendons. In the model formulation, the tissues are assumed to be composed of collagen fibers aligned along their physiological loading direction. The collagen fibers are gradually recruited under strain and are arranged in parallel with a Maxwell element which accounts for the viscoelasticity of the proteoglycan-rich matrix. Once straight, the collagen fibers are assumed to behave as linear elastic springs. Experimental data published by Hingorani et al. [1] are used to estimate the five model parameters by fitting relaxation and strain stiffening data and the predictions are evaluated by using creep data. The influence of each parameter on describing relaxation, creep, and strain stiffening is presented. The modeling results demonstrate that, by considering the fibers' recruitment and assuming that the matrix is linear viscoelastic, a conceptually simple model can describe relaxation, creep, and strain stiffening phenomena in ligaments and tendons.