Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average.

We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress–strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.